# Ch 42: Probability Distributions and Statistical Inference

### About This Chapter

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards