# Ch 47: MTLE Mathematics: Probability Distributions

### About This Chapter

## MTLE Mathematics: Probability Distributions - Chapter Summary

Fun video lessons can help you get reacquainted with important math concepts you will see on the MTLE Mathematics assessment. Explore this chapter to make sure you're prepared to answer probability distributions questions that ask you to:

- Define random variables, and find the expected value of discrete and continuous random variables
- Develop discrete probability distributions theoretically and empirically
- Explain uniform distribution in statistics, and define binomial experiments and normal distribution
- Calculate binomial probabilities using formulas and tables, and understand problems with binomial experiments
- Discuss how to theoretically develop continuous probability distributions
- Share the meaning of probabilities as areas of geometric regions, and demonstrate how to approximate binomial probabilities

Ensure you're ready to tackle probability distributions on the exam by reviewing the lessons in this chapter in any sequence that suits your studies. You can test your comprehension of the subject area by taking short quizzes and a chapter exam. Further boost your knowledge of lesson topics by submitting your questions to our experts.

### 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. 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.

### 3. Developing Discrete Probability Distributions Theoretically & Finding Expected Values

In this lesson, we will look at generating a theoretical probability distribution for a discrete random variable and introduce the concept of expected value.

### 4. Developing Discrete Probability Distributions Empirically & Finding Expected Values

In this lesson, we will look at creating a discrete probability distribution given a set of discrete data. We will also look at determining the expected value of the distribution.

### 5. Uniform Distribution in Statistics: Definition & Examples

In this lesson we will explore uniform distributions and learn how to identify two basic types: discrete and uniform. You'll also learn how to recognize both by the shape and characteristics of their graphs.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 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.

### 13. Normal Distribution: Definition, Properties, Characteristics & Example

In this lesson, we will look at the Normal Distribution, more commonly known as the Bell Curve. We'll look at some of its fascinating properties and learn why it is one of the most important distributions in the study of data.

### 14. Using the Normal Distribution: Practice Problems

In this lesson, we will put the normal distribution to work by solving a few practice problems that help us to really master all that the distribution, as well as Z-Scores, have to offer. Review the concepts with a short quiz at the end.

### 15. Using Normal Distribution to Approximate Binomial Probabilities

Binomial probabilities describe processes in our world. Learn how to create and interpret a binomial probability distribution graph, and discover how the normal distribution can form a good approximation of the binomial distribution.

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### Other Chapters

Other chapters within the MTLE Mathematics: Practice & Study Guide course

- MTLE Mathematics: Basic Arithmetic Operations
- MTLE Mathematics: Properties of Real Numbers
- MTLE Mathematics: Operations with Real Numbers
- MTLE Mathematics: Fractions
- MTLE Mathematics: Decimals
- MTLE Mathematics: Percents
- MTLE Mathematics: Ratios, Rates & Proportions
- MTLE Mathematics: Exponents & Exponential Expressions
- MTLE Mathematics: Mathematical Reasoning & Problem Solving
- MTLE Mathematics: Complex Numbers
- MTLE Mathematics: Sequences & Series
- MTLE Mathematics: Functions
- MTLE Mathematics: Algebraic Expressions & Equations
- MTLE Mathematics: Exponential & Logarithmic Functions
- MTLE Mathematics: Vector Operations
- MTLE Mathematics: Matrices in Linear Algebra
- MTLE Mathematics: Linear Functions
- MTLE Mathematics: Linear Inequalities
- MTLE Mathematics: Quadratic Functions
- MTLE Mathematics: Polynomial Functions
- MTLE Mathematics: Rational Expressions
- MTLE Mathematics: Radical Expressions
- MTLE Mathematics: Absolute Value Functions
- MTLE Mathematics: Continuity & Limits
- MTLE Mathematics: Rate of Change & Derivatives
- MTLE Mathematics: Area Under the Curve & Integrals
- MTLE Mathematics: Trigonometric Functions
- MTLE Mathematics: Solving Trigonometric Equations
- MTLE Mathematics: Trigonometric Identities
- MTLE Mathematics: Principles of Measurement
- MTLE Mathematics: Area & Perimeter
- MTLE Mathematics: Surface Area & Volume
- MTLE Mathematics: Foundations of Geometry
- MTLE Mathematics: Lines & Angles
- MTLE Mathematics: Properties of Triangles
- MTLE Mathematics: Similar & Congruent Triangle Proofs
- MTLE Mathematics: Right Triangle Proofs
- MTLE Mathematics: Quadrilaterals & Polygons
- MTLE Mathematics: Circles & Arc of a Circle
- MTLE Mathematics: Coordinate Geometry
- MTLE Mathematics: Geometric Transformations
- MTLE Mathematics: Parametric, Polar & Vector Functions
- MTLE Mathematics: Organizing Data
- MTLE Mathematics: Summarizing & Analyzing Data
- MTLE Mathematics: Random Sampling
- MTLE Mathematics: Probability
- MTLE Mathematics: Discrete Mathematics
- MTLE Mathematics: Mathematical Connections & Communication
- MTLE Mathematics: From Words to Equations, Expressions & Graphs
- MTLE Mathematics: Content Area Reading Skills
- MTLE Mathematics: Instructional Design & Delivery
- MTLE Mathematics: Teaching & Assessing Diverse Learners
- MTLE Mathematics Flashcards