Assignment 5.docx

Assignment 5.docx - 3.97 a b Mean and Variance X f(x xf(x 0...

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3.97 a) b) Mean and Variance X f(x) xf(x) x- μ (x- μ ) 2 f(x) 0 0.10 0.00 -2.5 0.6250
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1 0.15 0.15 -1.5 0.3375 2 0.25 0.50 -0.5 0.0625 3 0.25 0.75 0.5 0.0625 4 0.15 0.60 1.5 0.3375 5 0.10 0.50 2.5 0.6250 Total 1.00 μ = 2.5 σ 2 = 2.05 Mean μ = E (X) = i = 1 n x i f ( x i ) = 2.5 Variance σ 2 = V ( X ) = ¿ x i μ ¿ 2 f ( x i )= 2.05 ¿ i = 1 n ¿ c) P (X < 2) = P (X = 0) + P (X = 1) 0.1 + 0.15 = 0.25 d) P (X 3.5 ¿ = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) 0.1 + 0.15 + 0.25 + 0.25 = 0.75 3.100 a) P (X < 0.25) = P (X = 0.1) + P (X = 0.2) 0.1 + 0.1 = 0.2 b) P (0.15 < X 4.5 ¿ = P (X = 0.2) + P (X = 0.3) + P (X = 0.4) + P (X = 0.5) + P (X = 0.6) 0.1 + 0.3 + 0.2+ 0.2 + 0.1 = 0.9
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d) μ = E (X) = i = 1 n x i f ( x i ) (0.1)(0.1) + (0.2)(0.1) + (0.3)(0.3) + (0.4)(0.2) + (0.5)(0.2) + (0.6)(0.1) = 0.36 seconds 3.102 a) Binomial random variable X with n=10 and p=0.5 0 2 4 6 8 10 12 0 0.05 0.1 0.15 0.2 0.25 0.3 PMF X P
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b) Cumulative Distribution function X 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 CDF X F(x) c) What value of X is mostly likely? The most likely to occur is X = 5 d) What value(s) of X is (are) least likely? The least likely to occur is X = 0 and X = 10 3.104 a) Binomial variable X with n = 10 and p = 0.01 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PMF P
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b) Cumulative Distribution 0 2 4 6 8 10 12 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 CDF X F(X) c) What value of X is most likely?
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