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solutions hw 2

# solutions hw 2 - f(0 = 0.3487 f(1 = 0.3874 f(2 = 0.1937...

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Solutions to HW2 1 b x f(x) xf(x) 20 0.20 4.00 17.1125 25 0.15 3.75 2.7094 30 0.25 7.50 0.1406 35 0.40 14.00 13.2250 29.25 33.1875 f(x ≤ 25) = f(x = 20) + f(x = 25) = 0.35 2 a f(x > 30) = f(x = 35) = 0.4 3 c E(x) = ∑xf(x) = 29.25 4 b 33.1875 5 b x f(x) f(x) -100 0.10 0.10 0 0.20 0.20 50 0.30 0.30 100 0.25 0.25 150 0.10 0.10 200 - 0.05 0.95 1.00 f(x = 200) = 1 - 0.95 = 0.05 6 a f(x > 0) = 1 - f(x ≤ 0) = 0.70 7 c f(x ≥ 100) = f(100) + f(150) + f(200) = 0.4 8 d x f(x) xf(x) -100 0.10 -10 2402.50 0 0.20 0 605.00 50 0.30 15 7.50 100 0.25 25 506.25 150 0.10 15 902.50 200 0.05 10 1051.25 E(x) = ∑xf(x) = 55 5475.00 9 a 5475 10 b E(x + 100) = E(x) + 100 = 155 var(x + 100) = var(x) = 5475 11 a E(2x) = 2E(x) = 110 21900 12 b x f(x) xf(x) 3 0.25 0.75 2.25 6 0.5 3.00 0.00 9 0.25 2.25 2.25 E(x) = ∑xf(x) = 6.00 4.50 13 a 4.50 sd(x) = 2.12 14 c Define the weekly income as y = 100 + 20x E(y) = 100 + 20E(x) E(y) = 100 + 20(60) E(y) = 1300 Now define the annaul income as Y = 48y E(Y) = E(48y) = 48E(y) E(Y) = 62400 15 d sd(x) = 15 sd(y) = sd(20x) sd(y) = 20sd(x) = 20(15) = 300 Y = 48y sd(Y) = 48sd(y) = 48(300) = 14400 16 c 0.1937 17 a f(x ≤ 2) = f(0) + f(1) + f(2)
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Unformatted text preview: f(0) = 0.3487 f(1) = 0.3874 f(2) = 0.1937 0.9298 18 d f(x ≥ 1) = 1 − f(0) = 0.6513 19 d E(x) = nπ = 10(0.1) = 1 20 a var(x) = nπ(1 - π) = 0.9 sd(x) = √0.9 = 0.9487 21 a n = 25 π = 0.01 f(x ≤ 2) = f(0) + f(1) + f(2) f(0) = 0.7778 f(1) = 0.1964 f(2) = 0.0238 f(x ≤ 2) = 0.9980 22 a The number of correct guesses, x, has a binomial distribution with n = 30 and π = 0.20 E(x) = nπ = 30(0.20) = 6 23 d n = 5 π = 0.15 0.3915 24 a f(x ≥ 1) = 1 - f(x = 0) = 0.5563 25 c E(x) = nπ = 5(0.15) = 0.75 Expected number of tickets Expected or average cost of tickets is: E(20x) = 20E(x) = 15 (x - μ) 2 f(x) var(x) = ∑(x - μ) 2 f(x) = (x - μ) 2 f(x) var(x) = ∑(x - μ) 2 f(x) = var(2x) = 2 2 var(x) = (x - μ) 2 f(x) var(x) = ∑(x - μ) 2 f(x) = f(X = x) = C(n, x)(π x )(1 − π) (n − x) = f(x = 2) = C(10,2)(0.10) 2 (0.9) 8 = f(x = 1) = 5(0.15)(0.85) 4 =...
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