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. X₁ X₂ 42 (a) Suppose that X1 and X2 are independent rv's with means 4 and 8 kips, respectively, and standard deviations 0.9 and 1.8 kip, respectively. If a₁ = 6 ft and a2 = 12 ft, what is the expected bending moment and what is the standard deviation of the bending moment? (Round your standard deviation to three decimal places.) expected bending moment standard deviation kip-ft kip-ft (b) If X1 and X2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.) (c) Suppose the positions of the two loads are random variables. Denoting them by A₁ and A2, assume that these variables have means of 6 and 12 ft, respectively, that each has a standard deviation of 0.5, and that all A,'s and X's are independent of one another. What is the expected moment now? kip-ft (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) kip-ft² (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? kip-ft²