About This Chapter
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)
About This Chapter
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.
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. 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.
6. 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.
7. Dice: Finding Expected Values of Games of Chance
This lesson examines the various combinations and probabilities behind rolling dice. We will look at a game of dice and what to expect to win or lose in a game. In addition we will extend these concepts to playing with different sided dice.
8. Blackjack: Finding Expected Values of Games of Chance with Cards
In this video we learn about games of cards, and how to calculate probabilities. We look at the game of Blackjack and calculate the probability of getting certain hands. In addition we demonstrate how to calculate the expected value of a game that involves betting.
9. Lotteries: Finding Expected Values of Games of Chance
Most of us won't have a problem with winning the lottery. But is it a realistic goal? Do you really have a chance? In this lesson, learn how luck and probability collide when finding expected values in games of chance.
10. Comparing Game Strategies Using Expected Values: Process & Examples
While statistics and probability leave a lot to chance, we can use expected values to help inform our decisions. This lesson shows us how to use expected values to make the best determinations possible.
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Other chapters within the Common Core Math - Statistics & Probability: High School Standards course