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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
- Calculus, insurance company, Dice