Problem #4: An assembly consists of two mechanical components. Suppose that the

Question

Problem #4: An assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet specifications are 0.93 and 0.81, respectively. Let X be the number of components in the assembly that meet specifications (a) Find the mean of X. (b) Find the variance of X. Problem #4(a): 0.87 Problem #4(b): 0.0036 Just Save Submit Problem #4 for Grading Problem #41 Attempt #1 | Attempt #2 | Attempt #3 | Your Answer: 4(a) 0.87 14(a) 4(b) 0.0036 4(b) Your Mark:4(a) 0/1x 4(a) 4(b) 0/1X 4(b) 4(a) 4(b) 4(a)

Explanation / Answer

P(X = 0) = (1-0.93)*(1-0.81) = 0.0133

P(X = 1) = 0.93*(1-0.81) + 0.81*(1-0.93) = 0.2334

P(X = 2) = 0.93*0.81 = 0.7533

A) mean, E(X) = 0*0.0133 + 1*0.2334 + 2*0.7533 = 1.74

B) E(X2) = 02*0.0133 + 12*0.2334 + 22*0.7533 = 3.2466

Var(X) = E(X2) - (E(X))2 = 3.2466 - 1.742 =0.219

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