# Ch 6: Common Core HS Statistics & Probability: Random Variables

Let us help you teach your high school students about random variables to fulfill the requirements for Common Core. Lessons in this chapter offer advice about how you can utilize these lessons in your classroom in addition to learning how to recognize when students have fully mastered the standard.

Standard: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. (CCSS.Math.Content.HSS.MD.A.1)

Standard: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. (CCSS.Math.Content.HSS.MD.A.2)

Standard: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. (CCSS.Math.Content.HSS.MD.A.3)

Standard: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. (CCSS.Math.Content.HSS.MD.A.4)

Standard: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. (CCSS.Math.Content.HSS.MD.B.5)

Standard: Find the expected payoff for a game of chance. (CCSS.Math.Content.HSS.MD.B.5.B)

Standard: Evaluate and compare strategies on the basis of expected values. (CCSS.Math.Content.HSS.MD.A.4)

Standard: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). (CCSS.Math.Content.HSS.MD.B.6)

Standard: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). (CCSS.Math.Content.HSS.MD.B.7)

With a thorough knowledge of random variables, students will be able to graph probability distributions and find and interpret expected values of continuous and discrete random variables. Students will also have the ability to use expected values to compare game strategies and generate random numbers.

The lesson topics for this standard include:

• Identifying types of random variables
• Graphing probability distributions of random variables
• Developing discrete probability distributions
• Finding expected values of games of chance
• Applying probability concepts to problem solving

Students will show you they've mastered these standards when they can explain how to interpret the expected values of different types of random variables and know how to develop discrete probability distributions theoretically and empirically. These standards and lessons can prepare students for college and for careers in finance, engineering, construction and science.

### How to Use These Lessons in Your Classroom

Below are suggestions from Study.com that you could include in your regular curriculum to help you meet Common Core standards.

#### Random Variable Identification Lessons

Have students watch the video lessons that cover the definition of random variables and identify the different types of variables in class or as a homework assignment. List several examples of random variables, like tossing a coin or rolling the dice) and have students identify which is discrete and which is continuous.

#### Expected Values in Games of Chance Lessons

Watch the lessons on finding expected values of random variables and games of chance in class. Create practice problems to find expected values for games like raffles and lotteries. Divide students into teams and have them compete to see who can correctly solve the problem first.

#### Pre-Quiz and Post-Quiz Lessons

Have students take the quizzes for Generating random numbers and Applying probability concepts to problem solving lessons. Watch the video lessons, then have students re-take the quizzes to test their comprehension of these subjects.

10 Lessons in Chapter 6: Common Core HS Statistics & Probability: Random Variables
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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