Determining the Mean of a Discrete Random Variable
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: 3.4
In 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, onequarter are age 19, and onequarter are age 20, what is the average age of the students in the class?
Answer: 18.75
In 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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