Suppose that you are expecting a message at some time past 5 P.M. From experience you know

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Suppose that you are expecting a message at some time past 5 P.M. From experience you know that X , the number of hours after 5 P.M. until the message arrives, is a random variable with the following probability density function:

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The expected amount of time past 5 P.M. until the message arrives is given by

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Hence, on average, you would have to wait three-fourths of an hour

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