# Chapter 4: Discrete Probability Distribution

**Advanced**Created by: CK-12

## Introduction

Often times, we settle things with a coin toss, such as who gets to pick the first team member for a game of capture the flag, or who has to take out the trash. Suppose you have a fair coin, and you are going to toss it one or more times. If you only toss the coin once, since it is fair, the probability of either outcome, heads or tails, is the same or equal. But suppose you toss the coin twice, how many heads can you expect to get? You will learn how to answer questions like these in this chapter.

When you have a fair coin, most people think that if you toss it several times, say a 100 times, that you should roughly get heads or tails every other time. People don't usually expect to get several heads in a row before getting the first head. Theoretically, you could get 100 heads out of 100 tosses, although the chances of this occurring are very low.

In this chapter, we will learn how to model different situations such a coin toss and find probabilities of interesting events by using discrete probability distributions. You will also learn how to calculate expected values, for example, the expected number of heads out of some number of coin tosses, as well as the variance and standard deviations of these expected values.

- 4.1.
## Discrete and Continuous Random Variables

- 4.2.
## Probability Distribution

- 4.3.
## Mean and Standard Deviation of Discrete Random Variables

- 4.4.
## Sums and Differences of Independent Random Variables

- 4.5.
## Binomial Distributions and Probability

- 4.6.
## Poisson Probability Distributions

- 4.7.
## Geometric Probability Distributions

### Chapter Summary

## Summary

This chapter focuses on introducing students to probability distributions by covering random variables, discrete and continuous variables, and binomial, Poisson, and geometric distributions. It demonstrates how to calculate the expected value, or mean, as well as the variance and standard deviations for the different distributions as well as for any given discrete probability distribution. Additionally, this chapter covers linear transformations of random variables.

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