Homework7key[1]

5 10 ea1x1 a2x2 a1ex1 a2ex2 52 104

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Unformatted text preview: = 1.0 E(a1X1 + a2X2) = a1E(X1) + a2E(X2) = (5)(2) + (10)(4) = 50 Since they are independent, Var(a1X1 + a2X2) = = 52(0.5)2 + 102(1.0)2 = 106.25 b) If X1 and X2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? e) If the situation is as described in part (a) except that Corr(X1,X2) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? 2 (3.5 pts.) 6.4 (p. 240). The article from which the data of exercise 1 was extracted also gave the accompanying strength observations for the cylinders. Suppose that the Xi’s constitute a random sample from the beams from a distribution with mean μ1. and standard deviation σ1 and that the Yi’s form a random sample from the cylinders (independent of the Xi’s) from another distribution with mean μ2 and standard deviation σ2. beam strength (X, 1) 5.9 7.0 9.7 7.2 6.3 7.8 7.3 7.9 7.7 6.3 9.0 11.6 8.1 8.2 11.3 6.8 8.7 11.8 7.0 7.8 10.7 7.6 9.7 6.8 7.4 6.5 7.7 7.1 8...
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