ST 558 Homework 5

ST 558 Homework 5 - x C(x) = 1200 - 50x 2 P(C(x))...

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Kelly Harrison 2/21/10 ST 558 D Homework 5 PROBLEM 1 This is a Binomial Distribution with n = 3 and p = ¼. μ = np = 3(1/4) = ¾ = .75 PROBLEM 2 x P(x) xP(x) 0 0.41 0 1 0.37 0.37 2 0.16 0.32 3 0.05 0.15 4 0.01 0.04 0.88 μ = xP(x) = .88 PROBLEM 3 In a gambling game a woman is paid $3 if she draws a jack or a que n and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. xP(x) = 0 3(8/52) + 5(8/52) + x(36/52) = 0 x = $1.78. PROBLEM 4 x g(x) = (2x+1) 2 p(g(x)) g(x)P(g(x)) -3 25 0.16666 7 4.16666666 7 6 169 0.5 84.5 9 361 0.33333 3 120.333333 3 209 μ g(x) = g(x)P(g(x)) = 209 PROBLEM 5 A large industrial firm purchases several new word proces ors at the end of each year, the exact number depending on the frequency of repairs in the previous year.
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Unformatted text preview: x C(x) = 1200 - 50x 2 P(C(x)) C(x)P(C(x)) 1200 0.1 120 1 1150 0.3 345 2 1000 0.4 400 3 750 0.2 150 1015 E(C(x)) = C(x)P(C(x)) = 1015. PROBLEM 6 x P(x) xP(x) x 2 P(x) 0.4 1 0.3 0.3 0.3 2 0.2 0.4 0.8 3 0.1 0.3 0.9 1 2 = xP(x) = 1 2 = x 2 P(x) 2 = 2 1 2 = 2 1 = 1 PROBLEM 7 E(y) = E(3x-2) = 3E(x) 2 First: x / 4 1 E(x) e dx 4 4 x-= = E(y) = 3E(x) 2 = 3(4) 2 = 10 V(ax+b) = a 2 V(x) V(3x-2) = 3 2 V(x) = 9V(x) First: 2 2 2 x / 4 2 2 1 V(x) x f(x)dx x e dx 4 4 32 4 16-=- =-=-= V(3x-2) = 9(16) = 144...
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ST 558 Homework 5 - x C(x) = 1200 - 50x 2 P(C(x))...

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