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 X2 ↓ a₁ a2 0 (a) Suppose that X₁ and X2 are independent rv's with means 4 and 8 kips, respectively, and standard deviations 1.1 and 2.2 kip, respectively. If a₁ = 10 ft and a2 = 20 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 kip-ft kip-ft standard deviation 200 45.354 (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.) 0.9971 (c) Suppose the positions of the two loads are random variables. Denoting them by A₁ and A2, assume that these variables have means of 10 and 20 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 200 (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) xkip-ft² 1.51 (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