Question

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If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a1X1 + a2X2. X x2 a1 02 0 (a) Suppose that X1 and X2 are independent rv's with means 2 and 4 kips, respectively, and standard deviations 1.1 and 2.2 kip, respectively. If a1 = 7 ft and a2 = 14 ft, what is the expected bending moment? 70 What is the standard deviation of the bending moment? (Give answer accurate to 2 decimal places.) 31.75 (b) If X1 and X2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Give answer accurate to 3 decimal places.) 0.440 x

Answer 1

Ang weri a) Expected value: zu X 2D + ILUX IDE 11871+ 2x + € 2 for Varienice : a, 2 x 5, 2 + a2²xSq² +2x1.12 + 14² X 2.22 16.94 +94e8.64 965.58 slaridard deviatione: 965.58 31.073r b) pl Expected value > 75) → P(Z > 75-70 31.075 > p (7 > 0.1609) >> I-P(Z <0.1609) 0.43609 r