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Unformatted text preview: 500 may have a minor injury a) Create a model for X=profit on one policy b) What is the company expected profit on a policy? c) What is its standard deviation? a) b) c) x 1009,9002,900 P(X=x) 0.9975 0.0005 0.0020 x P(X=x) xP(X=x) (x ) (x  ) 2 P(X=x) 100 0.9975 99.75 11 120.709,900 0.00054.959989 49890.062,900 0.00205.82989 17868.24 Total 1 89 67879.00 E(X) = 89 Var(X) = 67879 SD(X) = 67879 = 260.54 Properties o E(X c) = E(X) c Var(X c) = Var(X) o E(aX) = a E(X) Var(aX) = a 2 Var(X) o E(X Y) = E(X) E(Y) o If X and Y are independent, then Var(X Y) = Var(X) + Var(Y) (always +) Example. Suppose that X and Y are independent and that E(X)=80, SD(X)=12 E(Y)=10, SD(Y)=3. Let W = X  5Y + 20. Then: E(W) = 80 (5)(10) + 20 = 50 Var(W) = Var(X  5Y + 20) = Var(X  5Y) = = Var(X) + Var(  5Y) = Var(X) + (5) 2 Var(Y) = = 12 2 + 25* 3 2 = 369, SD(W) = 19.21...
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 Summer '08
 dikong

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