# Chapter 7: Random Variables and Discrete Probability Distributions_

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## 1a | Relative Frequencies + Discrete Variables (Preview)

Length: 11 minutesAuthor: JasonComplexity: Easy Most of the chapter exercises in the text give you a complete probability distribution to work from, but what if you are only presented with frequencies and need to construct your own distribution? I’ll show you how in this video. I also check to see that the two requirements of a probability distribution have been satisfied.

## 1cd | Population Variance V(X) and Standard Deviation (Preview)

Length: 13 minutesAuthor: JasonComplexity: Standard The variance of a probability distribution also differs (in its calculation) from what you learned in Chapter 4. I extend the tabular approach that I used to find the expected value (previous video) so be able to find the variance of x. The standard deviation of x is simply the square root of the variance (just like in Chapter 4)

## 2a | Probability Trees and Discrete Variables

Length: 27 minutesAuthor: JasonComplexity: Standard Here I solve a full Chapter 7 exam question. First , I look at the language used in the question to identify which chapter's techniques are appropriate. Once this is determined to be a discrete probability distribution problem, I use a probability tree (learned in Chapt.6) to find all possible outcomes as well as their probabilities... to construct the Discrete Probability Distribution.

## 2d | Expected Value

Length: 2 minutesAuthor: Jason Time for the tabular approach to finding the expected value of x ( I use a table to keep track of my calculations). The order of operations comes into play here - Remember P.E.D.M.A.S. from high school math?

## 2e | Variance of X

Length: 5 minutesAuthor: Jason Once again, I extend the tabular approach that I used to find the expected value (previous video) so be able to find the variance of x. The standard deviation of x is simply the square root of the variance (just like in Chapter 4)

## 2f | Laws of Expected Value

Length: 13 minutesAuthor: Jason Your textbook can be confusing when it tries to explain the Laws of Expected Value. It can be easier to understand what's happening if you think about them as the Laws of THE NEW Expected Value. I explain in more detail in this video.

## 3-8 | Multiple Choice

Length: 18 minutesAuthor: Jason Test your understanding of Discrete Probability Distributions - each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.

## 9 | Probability Tree

Length: 11 minutesAuthor: Jason One more exam-style question before we get to the Binomial section of Chapter 7. This solution requires the use of the probability tree to find the probability distribution of x.

## The Binomial Probability Distribution (The Formula)

Length: 7 minutesAuthor: JasonComplexity: Standard The binomial formula looks nasty, but it's easy to use once you learn how the different parts work. Your calculator will do most of the heavy work for you, and all you'll need are three numbers that will be given in the question: n, p, and x.

## Using Binomial Tables

Length: 14 minutesAuthor: JasonComplexity: Hard Knowing how to use the binomial tables is a MUST for the test! They can save you critical time compared with using the binomial formula. The tables however are not intuitive and so you'll first need to understand what kind of question the tables are designed to answer. Once that's clear, you can rework most binomial problems so that the table can solve them quickly.

## 10 | Binomial Probability

Length: 22 minutesAuthor: Jason When a discrete variable has only TWO possible outcomes (per observation), then it is a Binomial variable. The calculations of probabilities, expected value and variance are all different from the ones we just covered (for discrete probability distributions). I walk you through a question here that covers all of the new methods introduced with binomial variables.

## 11 | More Binomial

Length: 29 minutesAuthor: Jason This is a typical binomial distribution exam question. It's a trick question - the binomial 'setting' changes with each new question (a, b, c..) - so I show you what needs to be done to handle that. Binomial tables are introduced here and I show how they can be used as a much needed shortcut through the typically long calculations that binomial questions require.

## 13-17 | Multiple Choice

Length: 7 minutesAuthor: Jason Test your understanding of Binomial Distributions - each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.