STAT 3201 Lecture 9: Stats 2.6.17

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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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