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Expected Value of a Random Variable or a Function of a Random Variable

Let Y be a discrete random variable with the probability mass function p(y). Then, the expected

value of Y is given by:

Note: the expected value exists if:

o

If p(y) is an accurate characterization of the population frequency, then E(Y) is the

population mean.

o

Expected Value

Example.

o Toss a coin three times and let Y = number of heads:

0, 1/8. 1, 3/8. 2, 3/8. 3, 1/8

o A supervisor in a manufacturing plant has three men and three women working

for him. He wants to choose two workers for a special job. Not wishing to show

any biases in his selection, he decides to select the two workers at random. Let Y

denote the number of women in his selection. Find the probability distribution for

Y.

o A group of four components is known to contain two defectives. An inspector

tests the components one at a time until the two defectives are located. Once she

locates the two defectives, she stops testing, but the second defective is tested to

ensure accuracy. Let Y denote the number of the test on which the second

defective component is found. Find the probability distribution for Y.

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