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Unformatted text preview: Chapter 8.2: Expected Value Suppose we were to repeat an experiment many times. We might be interested in the average value of our random variable. For example, consider a game where we might either earn or lose money each time we play. Suppose our random variable X represented the amount of money won or lost. The average value of our random variable X would tell us whether we should expect to win or lose money in the long run. This measurement is called the expected value of the random vari able. We write the expected value of X as E ( X ). To find the expected value of X , we take each value that X can take and multiply it by its probability. We then take all these products and add them together. Example: Suppose that X has the following distribution. x 5 15 100 P ( X = x ) 1 3 1 4 5 12 Find E ( X ). E ( X ) = 5 P ( X = 5) + 15 P ( X = 15) + 100 P ( X = 100) E ( X ) = 5 parenleftbigg 1 3 parenrightbigg + 15 parenleftbigg 1 4 parenrightbigg + 100 parenleftbigg 5 12 parenrightbigg E ( X ) = 5 3 + 15 4 + 500 12 47 . 1666 E ( X ) is approximately 47.1666. Note that E ( X ) does not need to be one of the values that X can take, as E ( X ) is measuring an average ....
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 Spring '11
 stephenlang
 Calculus

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