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4-2_expvalue

# 4-2_expvalue - 4.2(cont Expected Value of a Discrete Random...

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4.2 (cont.) Expected Value of a Discrete Random Variable A measure of the “middle” of the values of a random variable

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-4 -2 0 2 4 6 8 10 12 Profit Probability Lousy OK Good Great .05 .10 .15 .40 .20 .25 .30 .35 Center The mean of the probability distribution is  the expected value  of X, denoted E(X) E(X) is also denoted by the Greek letter  µ   (mu)
k = the number of possible values (k=4) E(x)=  µ  = x 1 ∙p(x 1 ) + x 2 ∙p(x 2 ) + x 3 ∙p(x 3 ) + ... +  x k ∙p(x k ) Weighted mean Mean or Expected Value k i i i=1 ( ) = x P(X=x ) E x μ = Probability Great 0.20 Good 0.40 OK 0.25 Economic Scenario Profit (\$ Millions) 5 1 -4 Lousy 0.15 10 P(X=x 4 ) X x 1 x 2 x 3 x 4 P P(X=x 1 ) P(X=x 2 ) P(X=x 3 )

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k = the number of outcomes (k=4) µ  = x 1 ∙p(x 1 ) + x 2 ∙p(x 2 ) + x 3 ∙p(x 3 ) + ... + x k ∙p(x k ) Weighted mean Each outcome is weighted by its probability Mean or Expected Value Sample Mean n n 1 = i i X = X n x n 1 + ... + 3 x n 1 + 2 x n 1 + 1 x n 1 = n n x + ... + 3 x + 2 x + 1 x = X k i i i=1 ( ) = x P(X=x ) E x μ =
Other Weighted Means Stock Market: The  Dow Jones Industrial  Average The “ Dow ” consists of 30 companies (the 30  companies in the “ Dow ” change periodically)

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4-2_expvalue - 4.2(cont Expected Value of a Discrete Random...

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