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RIP PS Vita: Is this the beginning of the end for dedicated handhelds?

If you’ve been following the gaming world, you’ve probably already heard the bad news: the PlayStation Vita has officially been discontinued. We first caught wind of Sony’s plans a couple of weeks ago, when it updated the listings for the two remaining PS Vita models to say that production would be ending soon. Then, over the weekend – only a short time after those updated listings were discovered – Sony finally pulled the plug.

This is almost certainly the end of Sony’s handheld ambitions. Though we can expect it to have some kind of gaming presence on smartphones and tablets in the future, it’s hard to imagine the company making another dedicated gaming handheld. After all, the PS Vita wasn’t quite the hit Sony was looking for, though it did manage to build a cult following for itself over the years.

With Sony probably out of contention, that leaves Nintendo as the only manufacturer of dedicated gaming handhelds with the 3DS. Handhelds have been a core part of Nintendo’s business ever since the days of the Game & Watch and the Game Boy in the 1980s, but even it may not be immune to a shifting industry. Is the discontinuation of the PS Vita the beginning of the end for dedicated gaming handhelds?

If it is, then Nintendo is at least partly to blame. It’s true that smartphones and tablets have been eating away at the userbase for dedicated handhelds for years now, but Nintendo has been doing that as well after the introduction of the Switch. The Switch, of course, attempts to blur the lines between home console gaming and handheld gaming by being both a console that can be played on a TV and a portable system that can be played on the go.

With the Switch on shelves and selling like hotcakes, it seems unlikely that Nintendo will want to make a follow up to the 3DS when the time comes to put it to bed. For its part, Nintendo hasn’t given any indication of when it may discontinue the 3DS, but recent financials for the company show a sharp decline in sales, perhaps prompted by the success of the Switch and certainly due to the simple fact that there aren’t many new games launching for the handheld, which is turning 8 years old later this month.

In fairness, Nintendo hasn’t said anything official about a 3DS successor, so it isn’t certain that the 3DS will be the end of its dedicated handheld line. In the end, Nintendo will have to ask itself if sales of a new handheld will be cannibalized by the Switch and Nintendo’s own mobile gaming efforts. Over the past few years, Nintendo has been bringing a number of its franchises to Android and iOS, including Mario, Fire Emblem, and Animal Crossing.

The saving grace of dedicated handhelds might be the fact that mobile gaming isn’t really a true replacement for these handheld systems. Games on mobile devices are usually vastly different from games on other platforms in terms of both design and monetization. Nintendo’s own mobile releases, namely Animal Crossing: Pocket Camp and Fire Emblem Heroes, prove that, so there could indeed be a market for dedicated handhelds even with mobile devices becoming popular platforms for gaming. It might be a niche one, but it could still support one dedicated system.

For now, we’ll have to wait and see what Nintendo decides to do with its handheld arm. At this point next year, though, we might be looking at a gaming industry that doesn’t have a single dedicated handheld in production, and the death of the PS Vita might be the harbinger of that.

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Sony Answers All Your Ps Vita Questions

Answer: There will be a phased roll out from the end of the year 2011 throughout all the SCE regions.

Q: How much will PS Vita cost?

A: It will cost $249 USD for the Wi-Fi version and $299 USD for the 3G version available through AT&T stores.

Q: What is the official name?

A: The official name will be PlayStation Vita (PS Vita). “Vita,” which means “Life” in Latin, was chosen as the name for our next-generation portable entertainment system because it enables a revolutionary combination of rich gaming and social connectivity within a real world context.

Q: PS Vita supports 3G network connectivity, does this mean PS Vita will be sold through cell-phone providers?

A: Partnering with AT&T, which powers the nation’s fastest mobile broadband network, who will serve as the exclusive service provider for PS Vita in the United States. By having both Wi-Fi and 3G/Wi-Fi models available, PS Vita will enable infinite possibilities for you to “encounter,” “connect,” “discover,” “share” and “play” with your friends wherever they are.

Q: Do all PS Vita users have to sign up with a cell phone provider?

A: No. Users can enjoy PS Vita using only Wi-Fi.

Q: How do you buy PS Vita games?

A: You can download PS Vita games and other content from PlayStation Store to a storage media via the Internet or buy the new game medium at retailers.

Q: What game format will the PS Vita use?

A: PS Vita will utilize the new game medium.

Q: Will users be able to access PlayStation Store from both 3G and Wi-Fi?

A: PlayStation Store will be able to be accessed from both 3G and Wi-Fi.

Q: Which carrier will users need to subscribe to use the 3G networks?

A: Partnering with AT&T, which powers the nation’s fastest mobile broadband network, who will serve as the exclusive service provider for PS Vita in the United States.

Q: Can you use PS Vita as a phone?

A: No.

Q: What are the specs of the OLED screen?

A: 5 inches (16:9), 960×544 pixels, Approx. 16,770,000 colors displayed

Q: What colors will be available at launch?

A: This will be announced at a later time.

Q: Can you use a commercially available Bluetooth keyboard / mouse? Can you connect the PS3 wireless controller to the PS Vita like the PSPgo?

A: No. Users cannot use commercially available Bluetooth keyboard / mouse or a PS3 wireless controller on the PS Vita.

Q: Can you access the Internet by connecting PS Vita to a Bluetooth supported cell phone?

A: No.

Q: Why didn’t you introduce stereoscopic 3D (without glasses) to PS Vita?

A: In the development process, we studied the possibility of introducing stereoscopic 3D feature to PS Vita, but decided not to install it. After careful consideration of our goal of offering users the ultimate portable entertainment experience with revolutionary user interface, we have decided to focus on the features and spec announced first.

Q: Does PS Vita have internal memory?

A: PS Vita is equipped with the storage media slot so that users can choose what memory capacity they want to utilize depending on their use.

Q: What is “Near”?

A: Near is a core PS Vita feature composed of location-based services, that utilize PlayStation Network. Near, developed specifically for this service and the network , will be pre-installed in the system to let users find out what their friends in the vicinity are playing now or what they were playing recently. Users can meet their friends and new players virtually, regardless of what games they are playing, simply by sharing their game information across different dimensions of time and distance.

Q: Do you need 3G network connection to enjoy Near?

A: Users can enjoy Near using Wi-Fi, but to enjoy further what Near offers, 3G connection is preferred. Users will be able to obtain more information and encounter new players in real time by using 3G connection.

Q: What is “LiveArea”?

A: Every game title for PS Vita will be provided with a space called “LiveArea™” where users can share the fun and excitement with other players. Users will have access to the latest information of games provided from SCE and 3rd party developers and publishers through PlayStation Network. Additionally, PS Vita users will be able to view “Activity” log that is constantly updated with accomplishments from users who are playing the same game, which in turn can trigger active real-time communication among users.

Q: Will existing services like Remote Play, Skype, SenseMe, and Comic content for PSP be available for PS Vita as well?

A: We are evaluating the opportunity to offer non-gaming applications/content and will announce details at a later time.

Q: Will Youtube, Flash content and files like PDF be viewable on PS Vita?

A: We are evaluating the opportunity to offer non-gaming applications/content and will announce details at a later time.

Q: What is the difference between the PSP system and the PS Vita in terms of hardware specs?

A:

Advanced portable entertainment system

A high performance CPU / GPU combined with OLED enables rich, visually striking graphics never seen before on a portable entertainment system. PS Vita also adopts the Super Oval Design form factor, which fits comfortably in users’ hands.

Revolutionary User Interface

A unique multi-touch pad on the rear, with the front touch display. Two cameras on it’s front and rear, as well as three motion sensors, gyroscope, accelerometer, and electronic compass.

LiveArea™

Every game title for PS Vita will be provided with a space called “LiveArea™” where users can share the fun and excitement with other players.

Location-based services

SCE will provide location-based services on PS Vita as part of the basic features utilizing PlayStation Network. The new application called “Near,” developed specifically for this service and the network, will be pre-installed in the system.

Wi-Fi and 3G network connectivity

PS Vita is equipped with 3G in addition to Wi-Fi.

Closely coordinated with PlayStation Suite

The newly developed and released game content for Android based portable devices can also be enjoyed on PS Vita.

Q: There are two slots on the PS Vita, what are they for?

A: One is for the new game medium, the other is for storage media to be utilized for personal content and download content.

Q: What kind of game medium will PS Vita support? What is the official name? Why did you decide to introduce it?

Q: What type of storage media will PS Vita support?

A: This will be announced at a later date.

Q: What are the features of the new game medium / storage media?

A:

New game medium

It can not only store the full software titles but also save data as well as additional game content data. Therefore, the game title can be concluded with one piece of card.

Users can play games by just inserting the game medium into PS Vita. (a separate storage media is not required.)

As for storage media, we will announce details at a later date.

Q: How many software titles will be available at launch (in the new game medium/download for each region)?

A: We will announce details at a later date.

Q: What will software pricing look like?

A: We will announce details at a later date.

Q: If you buy download content for PS Vita, up to how many systems can you copy it to?

A: We will announce details at a later date.

Q: Is PS Vita compatible with other PlayStation platform games like PS3, PS2, or PSP? Do you have any plan to support other PlayStation platforms in the future?

A: Users can play PSP titles, minis and PSone classics titles which are offered on PS Store. We do no have any plans to make PS Vita compatible with PS3 or PS2 titles at this point.

Q: Is PS Vita compatible with PSP content other than games such as video and comics available on PlayStation Store?

A: SCE plans to make those content available on PS Vita.

Q: Can PS Vita users continue using their save data for PSP games that they have also downloaded from PlayStation Store to PS Vita?

A: We are looking into the opportunity to do so.

Q: PS Vita doesn’t support UMD but do you have any plan to introduce peripherals like “UMD readers” for PS Vita?

A: We do not have plans to introduce such peripherals at this point in time.

Q: I have UMD games but do I need to buy them again from PlayStation Store to play the same game on PS Vita?

Q: Will you bring all UMD games to the new game medium or on the PlayStation Store for PS Vita?

A: SCE with the support of third party developers and publishers have been offering select UMD titles on PlayStation Store and will continue our effort to deliver these content in the form of game medium for PS Vita going forward. However, we will need to clear all copyright / legal related issues and due to this not all software titles will become available on PS Vita. We will announce details for each title when ready.

Q: Will PS Vita support all content that will become available on PlayStation Suite?

A: PS Suite content developed in the new game development environment provided for PS Suite can be enjoyed on PS Vita.

Q: Are PSP/PS3 user’s PSN accounts also available on PS Vita?

A: The same PSN accounts will be available on PS Vita.

Q: Do you have any plans to introduce a video output cable? Will PS Vita have HDMI output?

A: No, PS Vita does not have a video output feature.

Q: Can you take out the battery from the system?

A: No. We have adopted embedded battery since PS Vita is equipped with a rear touch pad.

“Not The End Of The Struggle, But An Opening”

“Not The End of The Struggle, But An Opening” Paul Farmer draws record crowd to MLK Day remarks

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With a record-breaking crowd before him and President-elect Barack Obama’s inauguration ahead, Paul Farmer celebrated Martin Luther King, Jr. (GRS’55, Hon.’59) yesterday by describing King as “a work in progress.”

“If Martin Luther King were here with us today in the flesh, as he is in spirit, he would surely be pleased,” said Farmer, the founder of the international aid organization Partners in Health, at Boston University’s annual Martin Luther King, Jr., Day celebration. “But he would not regard this momentous event as the end of the struggle, but as an opening, a space, a chance in which the larger social justice agenda might be pursued.

“He was moving forward in his own moral, intellectual, and political path,” Farmer added. “He was changing, and growing, and learning all the time.”

Farmer was the keynote speaker at this year’s BU event, and he drew a crowd that filled the George Sherman Union’s Metcalf Hall to capacity. The theme of the 2009 celebration was The Drum Major Instinct, based on King’s sermon of the same name. In it, King called on his congregation to find the instinct that makes us “all want to be important, to surpass others, to achieve distinction, to lead the parade” and use it to be a leader in love, in moral excellence, and in generosity.

Farmer, a medical anthropologist and physician, discussed the conflicting ideals that King examined in his sermon and encouraged his audience to learn from King’s example by using leadership opportunities for growth and discovery instead of for personal gain.

“We can’t forget that he was a controversial figure in his time — even among his supporters, who couldn’t always see where he was going or how the parts of his program fit together,” Farmer said. “The drum major instinct, if not held in check, might have motivated King to accept positions more palatable to the mainstream media. Today we celebrate his courage and his paradoxical relationship to the drum major instinct. Let us all take inspiration from a man who years after winning the Nobel Prize would seek to learn and grow.”

Peter Fu (CAS’09), one of BU’s Martin Luther King, Jr., Scholars, a group of academically gifted students with leadership abilities, acommitment to social justice, and a record of community involvement whoare given full scholarships by the University, read an excerpt from King’s sermon during the program. The program also included a poem by the student slam-poetry group Speak for Yourself and performances by the Inner Strength Gospel Choir, led by choir director Herbert Jones, and the student group Xception Step Team, which performed both traditional and modern versions of African step dances.

At the end of the program, Dean of Students Kenneth Elmore encouraged audience members to leave flowers and notes at the base of the Free at Last sculpture honoring King on Marsh Plaza, as many students, faculty, and staff did on the day after Obama’s election.

“This statue keeps me strong to my values,” said Khadijah Britton (LAW’10, SPH’10), who said that Farmer’s work inspires her own plans for a career in international health. “It’s a lonely road, and each of us individually is not strong enough to do it without sharing in this type of community.”

Others wrote tributes to Obama, expressed their hopes for the future of the country, or left personal notes for King.

“Happy B-Day,” one note read. “Peace.”

Jessica Ullian can be reached at [email protected]. Photo by Kalman Zabarsky

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End To End Statistics For Data Science

Statistics is a type of mathematical analysis that employs quantified models and representations to analyse a set of experimental data or real-world studies. The main benefit of statistics is that information is presented in an easy-to-understand format.

Data processing is the most important aspect of any Data Science plan. When we speak about gaining insights from data, we’re basically talking about exploring the chances. In Data Science, these possibilities are referred to as Statistical Analysis.

Most of us are baffled as to how Machine Learning models can analyse data in the form of text, photos, videos, and other extremely unstructured formats. But the truth is that we translate that data into a numerical form that isn’t exactly our data, but it’s close enough. As a result, we’ve arrived at a crucial part of Data Science.

Data in numerical format gives us an infinite number of ways to understand the information it contains. Statistics serves as a tool for deciphering and processing data in order to achieve successful outcomes. Statistics’ strength is not limited to comprehending data; it also includes methods for evaluating the success of our insights, generating multiple approaches to the same problem, and determining the best mathematical solution for your data.

Table of Contents

· Importance of Statistics

· Type of Analytics

· Probability

· Properties of Statistics

· Central Tendency

· Variability

· Relationship Between Variables

· Probability Distribution

· Hypothesis Testing and Statistical Significance

· Regression

Importance of Statistics

1) Using various statistical tests, determine the relevance of features.

2) To avoid the risk of duplicate features, find the relationship between features.

3) Putting the features into the proper format.

4) Data normalization and scaling This step also entails determining the distribution of data as well as the nature of data.

5) Taking the data for further processing and making the necessary modifications.

6) Determine the best mathematical approach/model after processing the data.

7) After the data are acquired, they are checked against the various accuracy measuring scales.

Acknowledge the Different Types of Analytics in Statistics

 

1. Descriptive Analytics – What happened?

It tells us what happened in the past and helps businesses understand how they are performing by providing context to help stakeholders interpret data.

Descriptive analytics should serve as a starting point for all organizations. This type of analytics is used to answer the fundamental question “what happened?” by analyzing data, which is often historical.

It examines past events and attempts to identify specific patterns within the data. When people talk about traditional business intelligence, they’re usually referring to Descriptive Analytics.

Pie charts, bar charts, tables, and line graphs are common visualizations for Description Analytics.

This is the level at which you should begin your analytics journey because it serves as the foundation for the other three tiers. To move forward with your analytics, you must first determine what happened.

Consider some sales use cases to gain a better understanding of this. For instance, how many sales occurred in the previous quarter? Was it an increase or a decrease?

2. Diagnostic Analytics – Why did it happen?

It goes beyond descriptive data to assist you in comprehending why something occurred in the past.

This is the second step because you want to first understand what occurred to work out why it occurred. Typically, once an organisation has achieved descriptive insights, diagnostics will be applied with a bit more effort.

3. Predictive Analytics – What is likely to happen?

It forecasts what is likely to happen in the future and provides businesses with data-driven actionable insights.

The transition from Predictive Analytics to Diagnostics Analytics is critical. multivariate analysis, forecasting, multivariate statistics, pattern matching, predictive modelling, and forecasting are all a part of predictive analytics.

These techniques are more difficult for organisations to implement because they necessitate large amounts of high-quality data. Furthermore, these techniques necessitate a thorough understanding of statistics as well as programming languages such as R and Python.

Many organisations may lack the internal expertise required to effectively implement a predictive model.

So, why should any organisation bother with it? Although it can be difficult to achieve, the value that Predictive Analytics can provide is enormous.

A Predictive Model, for example, will use historical data to predict the impact of the next marketing campaign on customer engagement.

If a company can accurately identify which action resulted in a specific outcome, it can predict which actions will result in the desired outcome. These types of insights are useful in the next stage of analytics.

4. Prescriptive Analytics – What should be done?

It makes recommendations for actions that will capitalise on the predictions and guide the potential actions toward a solution.

Prescriptive Analytics is an analytics method that analyses data to answer the question “What should be done?”

Techniques used in this type of analytics include graph analysis, simulation, complex event processing, neural networks, recommendation engines, heuristics, and machine learning.

This is the toughest level to reach. The accuracy of the three levels of the analytics below has a significant impact on the dependability of Prescriptive Analytics. The techniques required to obtain an effective response from a prescriptive analysis are determined by how well an organisation has completed each level of analytics.

Considering the quality of data required, the appropriate data architecture to facilitate it, and the expertise required to implement this architecture, this is not an easy task.

Its value is that it allows an organisation to make decisions based on highly analysed facts rather than instinct. That is, they are more likely to achieve the desired outcome, such as increased revenue.

Once again, a use case for this type of analytics in marketing would be to assist marketers in determining the best mix of channel engagement. For instance, which segment is best reached via email?

Probability

In a Random Experiment, the probability is a measure of the likelihood that an event will occur. The number of favorable outcomes in an experiment with n outcomes is denoted by x. The following is the formula for calculating the probability of an event.

Probability (Event) = Favourable Outcomes/Total Outcomes = x/n

Let’s look at a simple application to better understand probability. If we need to know if it’s raining or not. There are two possible answers to this question: “Yes” or “No.” It is possible that it will rain or not rain. In this case, we can make use of probability. The concept of probability is used to forecast the outcomes of coin tosses, dice rolls, and card draws from a deck of playing cards.

Properties of Statistics 

· Complement: Ac, the complement of an event A in a sample space S, is the collection of all outcomes in S that are not members of set A. It is equivalent to rejecting any verbal description of event A.

P(A) + P(A’) = 1

· Intersection: The intersection of events is a collection of all outcomes that are components of both sets A and B. It is equivalent to combining descriptions of the two events with the word “and.”

P(A∩B) = P(A)P(B)

· Union: The union of events is the collection of all outcomes that are members of one or both sets A and B. It is equivalent to combining descriptions of the two events with the word “or.”

P(A∪B) = P(A) + P(B) − P(A∩B)

· Mutually Exclusive Events: If events A and B share no elements, they are mutually exclusive. Because A and B have no outcomes in common, it is impossible for both A and B to occur on a single trial of the random experiment. This results in the following rule

P(A∩B) = 0

Any event A and its complement Ac are mutually exclusive if and only if A and B are mutually exclusive, but A and B can be mutually exclusive without being complements.

· Bayes’ Theorem: it is a method for calculating conditional probability. The probability of an event occurring if it is related to one or more other events is known as conditional probability. For example, your chances of finding a parking space are affected by the time of day you park, where you park, and what conventions are taking place at any given time.

Central Tendency in Statistics

1) Mean: The mean (or average) is that the most generally used and well-known measure of central tendency. It will be used with both discrete and continuous data, though it’s most typically used with continuous data (see our styles of Variable guide for data types). The mean is adequate the sum of all the values within the data set divided by the number of values within the data set. So, if we have n values in a data set and they have values x1,x2, …,xn, the sample mean, usually denoted by “x bar”, is:

2) Median: The median value of a dataset is the value in the middle of the dataset when it is arranged in ascending or descending order. When the dataset has an even number of values, the median value can be calculated by taking the mean of the middle two values.

The following image gives an example for finding the median for odd and even numbers of samples in the dataset.

3) Mode: The mode is the value that appears the most frequently in your data set. The mode is the highest bar in a bar chart. A multimodal distribution exists when the data contains multiple values that are tied for the most frequently occurring. If no value repeats, the data does not have a mode.

4) Skewness: Skewness is a metric for symmetry, or more specifically, the lack of it. If a distribution, or data collection, looks the same to the left and right of the centre point, it is said to be symmetric.

5) Kurtosis: Kurtosis is a measure of how heavy-tailed or light-tailed the data are in comparison to a normal distribution. Data sets having a high kurtosis are more likely to contain heavy tails or outliers. Light tails or a lack of outliers are common in data sets with low kurtosis.

Variability in Statistics

Range: In statistics, the range is the smallest of all dispersion measures. It is the difference between the distribution’s two extreme conclusions. In other words, the range is the difference between the distribution’s maximum and minimum observations.

Range = Xmax – Xmin

Where Xmax represents the largest observation and Xmin represents the smallest observation of the variable values.

Percentiles, Quartiles and Interquartile Range (IQR)

· Percentiles — It is a statistician’s unit of measurement that indicates the value below which a given percentage of observations in a group of observations fall.

For instance, the value QX represents the 40th percentile of XX (0.40)

· Quantiles— Values that divide the number of data points into four more or less equal parts, or quarters. Quantiles are the 0th, 25th, 50th, 75th, and 100th percentile values or the 0th, 25th, 50th, 75th, and 100th percentile values.

· Interquartile Range (IQR)— The difference between the third and first quartiles is defined by the interquartile range. The partitioned values that divide the entire series into four equal parts are known as quartiles. So, there are three quartiles. The first quartile, known as the lower quartile, is denoted by Q1, the second quartile by Q2, and the third quartile by Q3, known as the upper quartile. As a result, the interquartile range equals the upper quartile minus the lower quartile.

IQR = Upper Quartile – Lower Quartile

= Q3 − Q1

· Variance: The dispersion of a data collection is measured by variance. It is defined technically as the average of squared deviations from the mean.

· Standard Deviation: The standard deviation is a measure of data dispersion WITHIN a single sample selected from the study population. The square root of the variance is used to compute it. It simply indicates how distant the individual values in a sample are from the mean. To put it another way, how dispersed is the data from the sample? As a result, it is a sample statistic.

· Standard Error (SE): The standard error indicates how close the mean of any given sample from that population is to the true population mean. When the standard error rises, implying that the means are more dispersed, it becomes more likely that any given mean is an inaccurate representation of the true population mean. When the sample size is increased, the standard error decreases – as the sample size approaches the true population size, the sample means cluster more and more around the true population mean.

Relationship Between Variables

· Causality: The term “causation” refers to a relationship between two events in which one is influenced by the other. There is causality in statistics when the value of one event, or variable, grows or decreases as a result of other events.

Each of the events we just observed may be thought of as a variable, and as the number of hours worked grows, so does the amount of money earned. On the other hand, if you work fewer hours, you will earn less money.

· Covariance: Covariance is a measure of the relationship between two random variables in mathematics and statistics. The statistic assesses how much – and how far – the variables change in tandem. To put it another way, it’s a measure of the variance between two variables. The metric, on the other hand, does not consider the interdependence of factors. Any positive or negative value can be used for the variance.

The following is how the values are interpreted:

· Positive covariance: When two variables move in the same direction, this is called positive covariance.

· Negative covariance indicates that two variables are moving in opposite directions.

· Correlation: Correlation is a statistical method for determining whether or not two quantitative or categorical variables are related. To put it another way, it’s a measure of how things are connected. Correlation analysis is the study of how variables are connected.

Ø Here are a few examples of data with a high correlation:

1) Your calorie consumption and weight.

2) Your eye colour and the eye colours of your relatives.

3) The amount of time you spend studying and your grade point average

Ø Here are some examples of data with poor (or no) correlation:

1) Your sexual preference and the cereal you eat are two factors to consider.

2) The name of a dog and the type of dog biscuit that they prefer.

3) The expense of vehicle washes and the time it takes to get a Coke at the station.

Correlations are useful because they allow you to forecast future behaviour by determining what relationship variables exist. In the social sciences, such as government and healthcare, knowing what the future holds is critical. Budgets and company plans are also based on these facts.

Probability Distributions   Probability Distribution Functions

1) Probability Mass Function (PMF): The probability distribution of a discrete random variable is described by the PMF, which is a statistical term.

The terms PDF and PMF are frequently misunderstood. The PDF is for continuous random variables, whereas the PMF is for discrete random variables. Throwing a dice, for example (you can only choose from 1 to 6 numbers (countable))

2) Probability Density Function (PDF): The probability distribution of a continuous random variable is described by the word PDF, which is a statistical term.

The Gaussian Distribution is the most common distribution used in PDF. If the features / random variables are Gaussian distributed, then the PDF will be as well. Because the single point represents a line that does not span the area under the curve, the probability of a single outcome is always 0 on a PDF graph.

3) Cumulative Density Function (CDF): The cumulative distribution function can be used to describe the continuous or discrete distribution of random variables.

If X is the height of a person chosen at random, then F(x) is the probability of the individual being shorter than x. If F(180 cm)=0.8, then an individual chosen at random has an 80% chance of being shorter than 180 cm (equivalently, a 20 per cent chance that they will be taller than 180cm).

  Continuous Probability Distribution

A coin flip that returns a head or tail has a probability of p = 0.50 and would be represented by a line from the y-axis at 0.50.

2) Normal/Gaussian Distribution: The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centred on the mean, indicating that data around the mean occur more frequently than data far from it. The normal distribution will show as a bell curve on a graph.

Points to remember: –

· A probability bell curve is referred to as a normal distribution.

· The mean of a normal distribution is 0 and the standard deviation is 1. It has a kurtosis of 3 and zero skew.

· Although all symmetrical distributions are normal, not all normal distributions are symmetrical.

· Most pricing distributions aren’t totally typical.

3) Exponential Distribution: The exponential distribution is a continuous distribution used to estimate the time it will take for an event to occur. For example, in physics, it is frequently used to calculate radioactive decay, in engineering, it is frequently used to calculate the time required to receive a defective part on an assembly line, and in finance, it is frequently used to calculate the likelihood of a portfolio of financial assets defaulting. It can also be used to estimate the likelihood of a certain number of defaults occurring within a certain time frame.

4) Chi-Square Distribution: A continuous distribution with degrees of freedom is called a chi-square distribution. It’s used to describe a sum of squared random variable’s distribution. It’s also used to determine whether a data distribution’s goodness of fit is good, whether data series are independent, and to estimate confidence intervals around variance and standard deviation for a random variable from a normal distribution. Furthermore, the chi-square distribution is a subset of the gamma distribution.

Discrete Probability Distribution

1) Bernoulli Distribution: A Bernoulli distribution is a discrete probability distribution for a Bernoulli trial, which is a random experiment with just two outcomes (named “Success” or “Failure” in most cases). When flipping a coin, the likelihood of getting ahead (a “success”) is 0.5. “Failure” has a chance of 1 – P. (where p is the probability of success, which also equals 0.5 for a coin toss). For n = 1, it is a particular case of the binomial distribution. In other words, it’s a single-trial binomial distribution (e.g. a single coin toss).

2) Binomial Distribution: A discrete distribution is a binomial distribution. It’s a well-known probability distribution. The model is then used to depict a variety of discrete phenomena seen in business, social science, natural science, and medical research.

Because of its relationship with a binomial distribution, the binomial distribution is commonly employed. For binomial distribution to be used, the following conditions must be met:

1. There are n identical trials in the experiment, with n being a limited number.

2. Each trial has only two possible outcomes, i.e., each trial is a Bernoulli’s trial.

3. One outcome is denoted by the letter S (for success) and the other by the letter F (for failure) (for failure).

4. From trial to trial, the chance of S remains the same. The chance of success is represented by p, and the likelihood of failure is represented by q (where p+q=1).

5. Each trial is conducted independently.

6. The number of successful trials in n trials is the binomial random variable x.

If X reflects the number of successful trials in n trials under the preceding conditions, then x is said to follow a binomial distribution with parameters n and p.

3) Poisson Distribution: A Poisson distribution is a probability distribution used in statistics to show how many times an event is expected to happen over a certain amount of time. To put it another way, it’s a count distribution. Poisson distributions are frequently accustomed comprehend independent events that occur at a gradual rate during a selected timeframe.

The Poisson distribution is a discrete function, which means the variable can only take values from a (possibly endless) list of possibilities. To put it another way, the variable can’t take all of the possible values in any continuous range. The variable can only take the values 0, 1, 2, 3, etc., with no fractions or decimals, in the Poisson distribution (a discrete distribution).

Hypothesis testing may be a method within which an analyst verifies a hypothesis a couple of population parameters. The analyst’s approach is set by the kind of the info and also the purpose of the study. the utilization of sample data to assess the plausibility of a hypothesis is thought of as hypothesis testing.

Null and Alternative Hypothesis Null Hypothesis (H0)

A population parameter (such as the mean, standard deviation, and so on) is equal to a hypothesised value, according to the null hypothesis. The null hypothesis is a claim that is frequently made based on previous research or specialised expertise.

Alternative hypothesis (H1)

The alternative hypothesis says that a population parameter is less, more, or different than the null hypothesis’s hypothesised value. The alternative hypothesis is what you believe or want to prove to be correct.

Type 1 and Type 2 error Type 1 error:

A type 1 error, often referred to as a false positive, happens when a researcher rejects a real null hypothesis incorrectly. this suggests you’re claiming your findings are noteworthy after they actually happened by coincidence.

Your alpha level (), which is that the p-value below which you reject the null hypothesis, represents the likelihood of constructing a sort I error. When rejecting the null hypothesis, a p-value of 0.05 suggests that you simply are willing to tolerate a 5% probability of being mistaken.

By setting p to a lesser value, you’ll lessen your chances of constructing a kind I error.

Type 2 error:

A type II error commonly said as a false negative happens when a researcher fails to reject a null hypothesis that’s actually true. during this case, a researcher finds that there’s no significant influence when, in fact, there is.

Beta () is that the probability of creating a sort II error, and it’s proportional to the statistical test’s power (power = 1- ). By ensuring that your test has enough power, you’ll reduce your chances of constructing a sort II error.

This can be accomplished by ensuring that your sample size is sufficient to spot a practical difference when one exists.

 

Interpretation

P-value: The p-value in statistics is that the likelihood of getting outcomes a minimum of as extreme because the observed results of a statistical hypothesis test, given the null hypothesis is valid. The p-value, instead of rejection points, is employed to work out the smallest amount level of significance at which the null hypothesis is rejected. A lower p-value indicates that the choice hypothesis has more evidence supporting it.

Critical Value: it is a point on the test distribution that is compared to the test statistic to see if the null hypothesis should be rejected. You can declare statistical significance and reject the null hypothesis if the absolute value of your test statistic is larger than the crucial value.

Significance Level and Rejection Region: The probability that an event (such as a statistical test) occurred by chance is the significance level of the occurrence. We call an occurrence significant if the level is very low, i.e., the possibility of it happening by chance is very minimal. The rejection region depends on the importance level. the importance level is denoted by α and is that the probability of rejecting the null hypothesis if it’s true.

Z-Test: The z-test may be a hypothesis test within which the z-statistic is distributed normally. The z-test is best utilized for samples with quite 30 because, in line with the central limit theorem, samples with over 30 samples are assumed to be approximately regularly distributed.

The null and alternative hypotheses, also because the alpha and z-score, should all be reported when doing a z-test. The test statistic should next be calculated, followed by the results and conclusion. A z-statistic, also called a z-score, could be a number that indicates what number of standard deviations a score produced from a z-test is above or below the mean population.

T-Test: A t-test is an inferential statistic that’s won’t see if there’s a major difference within the means of two groups that are related in how. It’s most ordinarily employed when data sets, like those obtained by flipping a coin 100 times, are expected to follow a traditional distribution and have unknown variances. A t-test could be a hypothesis-testing technique that will be accustomed to assess an assumption that’s applicable to a population.

ANOVA (Analysis of Variance): ANOVA is the way to find out if experimental results are significant. One-way ANOVA compares two means from two independent groups using only one independent variable. Two-way ANOVA is the extension of one-way ANOVA using two independent variables to calculate the main effect and interaction effect.

Chi-Square Test: it is a test that assesses how well a model matches actual data. A chi-square statistic requires data that is random, raw, mutually exclusive, collected from independent variables, and drawn from a large enough sample. The outcomes of a fair coin flip, for example, meet these conditions.

In hypothesis testing, chi-square tests are frequently utilised. Given the size of the sample and the number of variables in the relationship, the chi-square statistic examines the size of any disparities between the expected and actual results.

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End Notes

Thank you for following with me all the way to the end. By the end of this article, we should have a good understanding of Complete Statistics for Data Science.

I hope you found this article useful. Please feel free to distribute it to your peers.

Hello, I’m Gunjan Agarwal from Gurugram, and I earned a Master’s Degree in Data Science from Amity University in Gurgaon. I enthusiastically participate in Data Science hackathons, blogathons, and workshops.

I’d like to connect with you on Linkedin. Mail me here for any queries.

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Related

Remove A Substring From The End Of A String In Python

In this article, we are going to find out how to remove a substring from the end of a string in Python.

The first approach is by using slicing approach. In this method, we will check if the string is ending with the given substring or not, if it is ending with the given substring then we will slice the string, removing the substring.

The ability to access portions of sequences like strings, tuples, and lists in Python is known as slicing. Additionally, you can use them to add, remove, or edit the elements of mutable sequences like lists. Slices can also be used with external objects like Pandas series, data frames, and NumPy arrays.

Example

In the example given below, we are taking a string and a substring as input and we are removing that substring from the end of the string using slicing −

def remove_substr(str,sub): if str.endswith(sub): return str[:-len(sub)] return str str1 = "Welcome to Tutorialspoint" print("The given string is ") print(str1) substr = "point" print("The given substring is") print(substr) print("Removing the substring from the string") print(remove_substr(str1,substr)) Output

The output of the above example is as follows −

The given string is Welcome to Tutorialspoint The given substring is point Removing the substring from the string Welcome to Tutorials Using sub() method of Regular Expressions

The second approach is by using the sub() method of Regular expressions. This method takes 3 parameters, the substring that you want to substitute, the substring with which you are going to substitute, and the main string. So, we are going to send the end as first parameter, empty string as second parameter ,and main string as third parameter.

Example

In the example given below, we are taking a string and substring as input and we are removing the substring at the end using sub() method −

import re def remove_substr(str,sub): if str.endswith(sub): res = re.sub(sub, '', str) return res return str str1 = "Welcome to Tutorialspoint" print("The given string is ") print(str1) substr = "point" print("The given substring is") print(substr) print("Removing the substring from the string") print(remove_substr(str1,substr)) Output

The output of the above example is as shown below −

The given string is Welcome to Tutorialspoint The given substring is point Removing the substring from the string Welcome to Tutorials Using replace() method

The third approach is by using the replace() method. This method takes 2 parameters, the substring that is to be replaced and the substring with which we are going to replace. So here, the first parameter to be sent is the ending and the next parameter will be empty space.

Example

In the example given below, we are taking a string and a substring as input and we are removing the substring from the ending of the string using replace method −

def remove_substr(str,sub): if str.endswith(sub): res = str1.replace(sub, '') return res return str str1 = "Welcome to Tutorialspoint" print("The given string is ") print(str1) substr = "point" print("The given substring is") print(substr) print("Removing the substring from the string") print(remove_substr(str1,substr)) Output

The output of the above example is given below −

The given string is Welcome to Tutorialspoint The given substring is point Removing the substring from the string Welcome to Tutorials

Comment: Iphone Xr Reviews Confirm This Is The Iphone For Most People

When Apple unveiled its new iPhones last month, I said that the iPhone XS and XS Max were totally overshadowed by the new Watch and the iPhone XR. The iPhone XR reviews, out today, confirm what I thought then.

Finally we come to what should have been the least-interesting iPhone, but is actually the most interesting: the iPhone XR […]

To offer something very close to the iPhone X/XS/Max form factor at a $749 price point is huge. And the near-bezel-free design also meant including the headline feature of last year’s flagship iPhone: Face ID. Throwing in Portrait Mode means you can now buy an iPhone that gets most non-technical customers the flagship design and features they want at 75% of the price of the iPhone XS …

iPhone XR reviews do identify the compromises. The single rear camera means a more limited Portrait mode, limited to human faces, and lacking Stage Light and Stage Light Mono. There’s no proper 3D Touch. And, of course, the LCD screen is lower resolution, older tech and has larger bezels.

If you’re an iPhone aficionado, these things may justify the price difference between the XR and the XS/Max. But for most normals, the iPhone XR gets them the design they want, and the features that matter, for a much more affordable price. And that’s what the iPhone XR reviews say.

The iPhone most people should buy – Engadget

The iPhone XR is everything Apple says it is, and it’s the new iPhone most people should buy – Daring Fireball

Most people—those who don’t spend their lives comparing specs and staring at bezels on multiple models of new smartphones each fall—are going to be very happy with this phone – Wired

Better than good enough – The Verge

The money you’re ‘saving’ by going for this model far outweighs what you’re losing – TechRadar

The iPhone XR has everything you need for hundreds less than the iPhone XS – CNBC

The XR is good enough that I don’t miss the XS. Apple undercut itself, and we’re all better off for it – Gizmodo

I could go on, but just take my word for it (or Google for yourself): there are many more iPhone XR reviews out there, and almost all of them reach the same conclusion. If you’re a techy, maybe look at the XS; if you’re not, buy the XR.

John Gruber made another point about that price difference – it’s actually even bigger than it seems.

Let’s start with the price. For the equivalent amount of storage, the iPhone XR costs $250 less than an iPhone XS, and $350 less than an XS Max.

But in practical terms, the difference is even more striking than that. 64 GB of storage is a credible baseline — a far cry from just a few years ago when storage started at a criminally meager 16 GB for the iPhones 6S in 2024, and 32 GB for the iPhones 7 in 2024. But the sweet spot for most people in 2023, in my opinion, is one tier above 64 GB […]

Photo: CNET

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