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Unformatted text preview: Section 8.2 Expected Value 1 Section 8.2 Expected Value The average (mean) of n numbers, x 1 , x 2 , x 3 ,, x n is x . n x x x x n + + + = ... 2 1 Expected Value of a Random Variable X Let X denote a random variable that assumes the values x 1 , x 2 , x 3 ,, x n with associated probabilities p 1 p 2 , , p n , respectively. The expected value of X , E ( X ), is given by n n p x p x p x X E + + + = ... ) ( 2 2 1 1 The expected value of a random variable X is a measure of the central tendency of the probability distribution associated with X . In repeated trials of an experiment with random variable X , the average of the observed values of X gets closer and closer to the expected value of X as the number of trials gets larger and larger. Geometrically, the expected value of a random variable X has the following simple interpretation: If a laminate is made of the histogram of a probability distribution associated with a random variable X , then the expected value of X corresponds to the point on the base of the laminate at which the latter will balance perfectly when the point is directly over a Fulcrum. Section 8.2 Expected Value Section 8....
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- Spring '08