# Statistics Foundations: Understanding Probability and Distributions

###### Course info

###### Course info

###### Description

We live in a world of big data: huge amounts of data generated by social networks, governments, consumers and markets. Someone needs to make sense of all this data. In this course, Statistics Foundations: Understanding Probability and Distributions, you will learn the fundamental topics essential for understanding probability and statistics. First, you will have an introduction to set theory, a non-rigorous introduction to probability, an overview of key terms and concepts of statistical research. Then, you will discover different statistical distributions, discrete and continuous random variables, probability density functions, and moment generating functions. Finally, you will use key distribution measures such as mean and variance, and explore topics of covariance and correlation. By the end of this course, you’ll be able to look at data and reason about it in terms of its descriptive statistics and possible distributions.

###### Section Introduction Transcripts

Course Overview

(Music) Hi everyone. My name is Dmitri Nesteruk, and welcome to my course on Statistics Foundations: Understanding Probability and Distributions. I am a quantitative analyst and software developer and have spent over a decade applying some of the skills presented in this course to analyze the financial markets, so I'm very happy to take you on this journey into the world of statistics. Now, we live in a world of big data, huge amounts of data generated by social networks and governments and consumers and markets, and all of this data needs someone to analyze it, which is why the profession of a data scientist becomes more and more popular nowadays. Someone needs to make sense of all of this data. In this course, we're going to cover all of the fundamentals that you need to understand in order to be able to efficiently analyze data, formulate hypotheses, and generally reason about what the ocean of data that's out there is actually telling you. Some of the major topics that we're going to cover in this course include the following. We going to talk about the notion of probability of course, we're going to take a look at random variables, we'll discuss statistical distributions, the idea of expectation, as well as things like covariance and correlation. By the end of this course, you'll be able to look at data and reason about it in terms of its descriptive statistics and possible distributions. Before beginning this course, you should be familiar with mathematics at a school level, you should also be familiar with the R statistical environment. I hope you'll join me on this journey to learn statistics, with the Statistics Foundations course, here at Pluralsight.

Calculating the Conditional Probability of Events

Hi there, and welcome to this module on calculating the conditional probability of events. So the goal of this module, there's only one goal, is for you to understand the concept of conditional probability and learn how to apply it to particular problems. So here's what we're going to see in this particular module. First of all, we'll obviously have to discuss what conditional probability actually is, then we'll discuss the idea of dependence or independence of individual events, we'll talk about the different laws of conditional probability, we'll also discuss the idea of partitions, and we'll use the idea of partitions in our discussion of the Law of Total Probability. Then we'll take a look at the Bayes' Theorem, and finally, we'll take a look at one particular problem, which is very relevant to conditional probability, the Gambler's Ruin Problem.

Understanding Random Variables and Distributions

Hi there. In this section of the course, we're going to take a look at random variables and their distributions. So the goal of this section of the course is fairly simple. I want you to understand this notion of a random variable, and we're going to take a look at some of the common distributions of random variables, how they behave, and what they're actually used for, or why would you want to even discuss them in the first place. So here is what we're going to see in this section of the course. First of all, we'll discuss the obvious part, which is what is a random variable and why do we care about them? We'll also discuss the difference between discrete and continuous random variables. Then we'll discuss some of the concepts associated with random variables, such as the idea of distributions and probability functions. And then we'll discuss the two classes of random variables. So first of all, we'll discuss the discrete distributions. So uniform, binomial, geometric, and hypergeometric, and then we'll discuss the continuous distributions, the uniform distribution, the very popular normal distribution, as well as the gamma and beta distributions.

Introducing the Concept of Expectation

Hello, and welcome to this module of the statistics course. In this module, we're going to discuss the concept of expectation. So the goal of this course might appear to be simple. I want you to understand what expectation is in the mathematical sense, but we're also going to take a look at quite a few other statistical measures which rely on your understanding of the concept of expectation. So here's what we're going to see as part of this module. First of all, we'll discuss what expectation is and what it's used for. We'll discuss the associated idea of the mean or the average of a data set, and then we're going to talk about a few other things. We'll discuss of Law of the Unconscious Statistician, we're going to discuss the idea of variance, we'll take a look at moments and the idea of a moment generating function, we'll take a look at joint distributions, and we'll finish off the discussion with a look at covariance and correlation.

Looking at Some Special Statistical Distributions

In this module of the course, we're going to take a look at some special statistical distributions. So, the goal of this course is, once again, fairly simple. We're going to explore some of the more exotic aspects of certain statistical distributions, and here's what we're going to take a look at. So first of all, we'll take a look at the Bernoulli Distribution. We'll discuss the Poisson Distribution. We'll take a look once again at the Normal Distribution to look specifically at one of its aspects. We're also going to discuss the Lognormal Distribution, and we'll finish off the module with a discussion of the Multinomial Distribution.