When working with random variables, you need to be able to calculate and interpret the mean. For these problems, let *X* be the number of classes taken by a college student in a semester. Use the formula for the mean of a discrete random variable *X* to answer the following problems:

## Sample questions

If 40% of all the students are taking four classes, and 60% of all the students are taking three classes, what is the mean (average) number of classes taken for this group of students?

**Answer:**3.4In this case,

*X*represents the number of classes. The possible values of*X*are 4 and 3, denoted*x*_{1}and*x*_{2}, respectively; their proportions (probabilities) are equal to 0.40 and 0.60 (denoted*p*_{1}and*p*_{2}, respectively).To find the average number of classes, or the mean of

*X*, multiply each value,*x*_{i}*,*by its probability,*p*_{i}*,*and then add the products:The mean of X is denoted by

If half of the students in a class are age 18, one-quarter are age 19, and one-quarter are age 20, what is the average age of the students in the class?

**Answer:**18.75In this case,

*X*represents the age of a student. The possible values of*X*are 18, 19, and 20, denoted*x*_{1},*x*_{2}, and*x*_{3}, respectively; their proportions (probabilities) are equal to 0.50, 0.25, and 0.25 (denoted*p*_{1},*p*_{2}, and*p*_{3}, respectively).To find the mean of

*X,*or the average age of the students in the class, multiply each value,*x*_{i}*,*by its probability,*p*_{i}*,*and then add the products:

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