ex 0865 b what are the variance and standard

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Unformatted text preview: isk & Uncertainty Spring 2011 (Bond) Homework 5 Expected Values, More Distributions a) What is the mean of X? Table below shows this calculation. X and P(X) are taken from the previous table. µ = E(X) = Σ x P(x) The product x P(x) is given in column 7 and the sum is shown at the bottom. µ = E(X) = 0.865 b) What are the variance and standard deviation of X? σ = E[(X ­µ)2] = Σ (x ­µ)2 P(x) The value (x ­µ) is shown in column 8. The product (x ­µ)2 P(x) is shown in column 9. Sum is at the bottom σ2 = 0.659 σ = 0.812 1 X, No. paying cards 0 1 2 3 4 5 6 7 8 9 P(X) x P(X) x ­µ 0.3704 0.4274 0.1709 0.0292 0.0021 0.0000 SUM 0 0.427359405 0.341887524 0.087556561 0.00833872 0.000242405 0.865384615  ­0.865 0.135 1.135 2.135 3.135 4.135 10 (x ­µ)2 P(x) (x ­µ)3 P(x) 0.277372691 0.007744309 0.220064806 0.132986241 0.020483677 0.000828784 0.659480508  ­ 0.240034059 0.001042503 0.249688915 0.283874477 0.06420845 0.003426702 0.362206987 c) If the game pays $5 per numeric spade, what is the expected value (mean) of the payout? Do not subtract the entry fee from this calculation. Let Y be the payout. Y = 5 X E(Y) = 5 E(X) = 5 (0.865) = 4.33 d) What is the standard deviation of the payout? σY = 5 σX = 5 (0.812) = 4.06 2/7 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 5 Expected Values,...
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This document was uploaded on 03/06/2014 for the course CEE 202 at University of Illinois, Urbana Champaign.

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