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 a X mum X a Suppose that X and X are independent rv s with means 2 and 4 kips respectively and standard devia tions 5 and 1 0 kip respectively If a 5 ft and o 10 ft what is the expected bending moment and what is the standard deviation of the bending b If X and X are normally distributed what is the probability that the bending moment will exceed c Suppose the positions of the two loads are random variables De oting them by A and A assume that these variables have means of 5 and 10 ft respec uvely that each has a standard deviation of 5 and that all A s and X s are independent of one another What is the expected moment now d For the situation of part c what is the variance of the bending moment e If the situation is as described in part a except that Com X X 5 so that the two loads are not inde pendent what is the variance of the bending