**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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