please explain in detail

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 alX1 + aZXZ. XI X: l l \"1 \"2 0 la USE LT (a) Suppose that X1 and X2 are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.2 and 2.4 kip, respectively. If .31 = 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 E kip-ft standard deviation E kip-ft (b) Ile and X2 are normally distributed, what is the probability that the bending moment will exceed 75 kipeft? (Round your answer to four decimal places.) E (c) Suppose the positions of the two loads are random variables. Denoting them byA1 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 Al's and Xf's are independent of one another. What is the expected moment now? E mm (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) S kw (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? Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal distribution, and the three times are independent of one another. The mean values are 15, 30, and 20 min, respectively, and the standard deviations are 2, 1, and 1.9 min, respectively. What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component? (Round your answer to four decimal places.) IE USE SALT E A shipping company handles containers in three different sizes: (1) 27 fts (3 x 3 x 3), (2) 125 fts, and (3) 512 fts. Let X; (i = 1, 2, 3) denote the number of type / containers shipped during a given week. With u; = E(X;) and o;