# Ch 7: Probability: Discrete & Continuous Distributions

### About This Chapter

## Probability: Discrete and Continuous Distributions - Chapter Summary and Learning Objectives

The expert instructors who lead these lessons show you how to use discrete probability and binomial experiments to solve problems. You'll practice finding binomial probabilities after watching lessons that show you the formulas you need to complete this process. These lessons take probability concepts and break them down into small chunks to make your study of this topic simpler and faster. Videos are all followed by self-assessment quizzes that you can use to determine what areas you need to review and which concepts you've mastered. The lessons in this chapter teach you:

- How to use tables to find binomial probabilities
- What formulas to use for determining the mean of a binomial random variable
- How to graph probability distributions
- How to interpret the expected value of a continuous random variable

Video | Objective |
---|---|

How to Apply Discrete Probability Concepts to Problem Solving | Learn methods for solving problems by applying discrete probability concepts. |

Binomial Experiments: Definition, Characteristics & Examples | Identify the conditions that are important in binomial experiments. |

Finding Binomial Probabilities Using Formulas: Process & Examples | Explore the process and formulas that are used to find binomial probabilities. |

Practice Problems for Finding Binomial Probabilities using Formulas | Apply the skills you learned in the previous lesson to sample problems. |

Finding Binomial Probabilities Using Tables | Examine how tables can be used to find binomial probabilities. |

Mean & Standard Deviation of a Binomial Random Variable: Formula & Example | See step-by-step instructions for determining a binomial random variable's mean and standard deviation. |

Solving Problems with Binomial Experiments: Steps & Example | Discover the process that is used to solve problems with binomial experiments. |

Graphing Probability Distributions Associated with Random Variables | Learn how to graph probability distributions. |

Finding & Interpreting the Expected Value of a Continuous Random Variable | Trace the steps that are used to find expected value and interpret it. |

Developing Continuous Probability Distributions Theoretically & Finding Expected Values | Understand how to theoretically discuss the development of continuous probability distributions then learn to find expected values. |

Probabilities as Areas of Geometric Regions: Definition & Examples | Study the ways that probabilities can be considered areas of geometric regions. |

### 1. How to Apply Discrete Probability Concepts to Problem Solving

Discrete probability concepts, such as expected value, success, and failure, can be used to help you solve real-world problems and inform you when making decisions.

### 2. Binomial Experiments: Definition, Characteristics & Examples

Binomial experiments happen in your everyday life far more often than you might think. In this lesson, you will learn the characteristics of binomial experiments that will help you identify them.

### 3. Finding Binomial Probabilities Using Formulas: Process & Examples

You can find the probability of getting a certain number of successes when conducting a binomial experiment. In this lesson, you will learn how to find this information using the binomial probabilities formula.

### 4. Practice Problems for Finding Binomial Probabilities Using Formulas

In this lesson, you will review the binomial probability formula and the combination formula. Then follow along with the practice problems and see if you've mastered these concepts!

### 5. Finding Binomial Probabilities Using Tables

A binomial probability table can look intimidating to use. However, it can make your life a lot easier when trying to figure out binomial probabilities. This lesson will teach you how to read those tables.

### 6. Mean & Standard Deviation of a Binomial Random Variable: Formula & Example

When working with binomial random variables and experiments, it is important to understand the mean and standard deviation. In this lesson, you will learn how to analyze binomial experiments using the mean and standard deviation of a binomial random variable.

### 7. Solving Problems with Binomial Experiments: Steps & Example

Sometimes when conducting research you will need to use binomial experiments to solve problems. In this lesson, you will learn about binomial experiments and how to use probability to solve problems.

### 8. Graphing Probability Distributions Associated with Random Variables

What's a random variable? Does it have anything to do with gambling? What's the difference between a continuous and a discrete variable? This lesson explains the difference and how to graph each one.

### 9. Poisson Distribution: Definition, Formula & Examples

In this lesson, we'll use a hypothetical road trip and some other real-life examples to show you how to use the Poisson distribution, a formula for calculating the probability of events. Then, test what you learned with the quiz questions.

### 10. Finding & Interpreting the Expected Value of a Continuous Random Variable

How can you find the expected value of something like height distributions? This lesson explains how to find and interpret the expected value of a continuous random variable.

### 11. Developing Continuous Probability Distributions Theoretically & Finding Expected Values

What is an expected value? How can you tell how many time you should expect a coin to land on heads out of several flips? This lesson will show you the answers to both questions!

### 12. Probabilities as Areas of Geometric Regions: Definition & Examples

In this lesson, you're going to learn what a random variable is and examine core concepts related to probabilities as areas of geometric regions and expected values of probability distributions.

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### Other Chapters

Other chapters within the DSST Principles of Statistics: Study Guide & Test Prep course

- Data Types & Measurements in Statistics
- Sampling Methods in Statistics
- Descriptive Statistics of Data Sets
- Visual Representations in Statistics
- Probability: Rules for Events
- Probability Combinations, Permutations & Expected Values
- Correlation & Regression in Statistics
- Sampling Distributions in Statistics
- Hypothesis Testing in Inferential Statistics
- DSST Informational Resources
- DSST Principles of Statistics Flashcards