Discrete Random Variables
Day 53 - Lesson 6.1
Use the probability distribution of a discrete random variable to calculate the probability of an event.
Make a histogram to display the probability distribution of a discrete random variable and describe its shape.
Calculate and interpret the mean (expected value) of a discrete random variable.
Activity: How Many Children Are in Your Family?
We included step siblings and half siblings in our total to increase the amount of variability in the class results. Students were able to work through this activity with very little guidance. The big AHA! moment is when students realize that finding the average number of children per family cannot be done by simply adding and dividing by the number of families (like we did in Chapter 1). They realized that some of the X values needed to be weighted more than others because they occurred more often.
Discrete vs Continuous
Discrete random variables take a fixed set of possible values with gaps between them. A continuous random variable can take any value on an interval. Some students will naturally think that all discrete random variables need to take only integer values. Challenge their thinking by bringing up shoe size. Shoe sizes can be decimals (7.5 or 8.5) but there are still a fixed set of possible values with gaps between them (there is no 7.9 shoes size). Therefore shoe size is a discrete random variable.
Calculating the Mean of a Discrete Random Variable
If your school or your class uses weighted grades, then students are likely already familiar with the calculation of a mean for a discrete random variable. Suppose in your class that homework is worth 10%, quizzes are worth 30%, and tests are worth 60%.
Student grade = (0.10) * HW average + (0.30) * quiz average + (0.60) * test average
This is exactly the formula for calculating the mean of a discrete random variable.