Copyright

Ch 42: Probability Distributions and Statistical Inference

About This Chapter

Use the following video lessons and quizzes to help you understand the differences between discrete and continuous random variables. Learn to generate probability distributions, find expected values and apply them to games of chance.

Probability Distributions and Statistical Inference - Chapter Summary

If you've ever flipped a coin, you already know something of the possible outcomes statisticians take into consideration when they develop probability distributions. Instructors teaching this chapter explain why a countable number of values - like heads or tails - is a type of discrete random variable that can be used to calculate the likelihood of an event's outcome.

They'll also introduce you to the uses of continuous random variables that represent values of infinite number before demonstrating the steps required to generate both discrete and continuous probability distributions, either empirically or theoretically. There are also lessons showing you how to graph probability distributions and find the expected values for each type.

The rest of the chapter helps drive these concepts home. Instructors show you how to apply probability distributions in order to find expected values in games of chance. You can also use this knowledge to compare game strategies and solve other real-life problems. The final lesson explores the uses of probabilities to determine a geometric region's area. By the time you finish this chapter, you should be familiar with the following:

  • Discrete random variables
  • Continuous random variables
  • Probability distributions
  • Expected values

Let our informed and experienced instructors help you wrap your head around these topics and more with video lessons that make the material entertaining and approachable. The same content can be found in the transcripts, which also include links to supplementary vocabulary lessons. Self-assessment quizzes are included as well to help affirm your understanding of each lesson's main ideas.

7 Lessons in Chapter 42: Probability Distributions and Statistical Inference
Test your knowledge with a 30-question chapter practice test
Random Variables: Definition, Types & Examples

1. Random Variables: Definition, Types & Examples

This lesson defines the term random variables in the context of probability. You'll learn about certain properties of random variables and the different types of random variables.

Graphing Probability Distributions Associated with Random Variables

2. 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.

Finding & Interpreting the Expected Value of a Continuous Random Variable

3. 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.

Finding & Interpreting the Expected Value of a Discrete Random Variable

4. Finding & Interpreting the Expected Value of a Discrete Random Variable

Discrete random variables appear in your life a lot more than you think. You can use expected values to find the probability of a discrete random variable, as shown in this lesson.

How to Apply Continuous Probability Concepts to Problem Solving

5. How to Apply Continuous Probability Concepts to Problem Solving

Continuous probability distributions can be a good approximation of many real world processes and phenomena. In this lesson, you will gain a conceptual understanding of continuous probability distributions and how to apply their properties to solve problems.

How to Apply Discrete Probability Concepts to Problem Solving

6. 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.

Probabilities as Areas of Geometric Regions: Definition & Examples

7. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support