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:
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?
In this case, X represents the number of classes. The possible values of X are 4 and 3, denoted x1 and x2, respectively; their proportions (probabilities) are equal to 0.40 and 0.60 (denoted p1 and p2, respectively).
To find the average number of classes, or the mean of X, multiply each value, xi, by its probability, pi, 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?
In this case, X represents the age of a student. The possible values of X are 18, 19, and 20, denoted x1, x2, and x3, respectively; their proportions (probabilities) are equal to 0.50, 0.25, and 0.25 (denoted p1, p2, and p3, respectively).
To find the mean of X, or the average age of the students in the class, multiply each value, xi, by its probability, pi, and then add the products:
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