4-2_expvalue

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

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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) 
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k = the number of possible values (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 Mean = x P(X = x i i i=1 k 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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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 = x P(X = x i i i=1 k μ ⋅ ) 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
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Other Weighted Means Stock Market: The  Dow Jones Industrial  Average
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4-2_expvalue - 4.2 (cont.) Expected Value of a Discrete...

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