10. [-/6 Points] DETAILS DEVORESTAT9 5.5.066.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 a, X, + a2*2- X1 X2 a2 USE SALT (a) Suppose that X, and X2 are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.5 and 3.0 kip, respectively. If a, = 8 ft and a2 = 16 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 standard deviation kip-ft (b) If X, and X, 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 A, and A2, assume that these variables have means of 8 and 16 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(X], X2) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? kip-ft2