Problem #2: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the loads is a₁X₁ + a2X₂. Problem #2(a): 0 X1 a X₂ c Suppose that X₁ and X₂ are independent random variables with means 4 and 6 kips, respectively, and standard deviations 0.8 and 1.3 kips, respectively. Suppose that a₁ = 7 ft and a2 = 10 ft. (a) Find the expected value of the bending moment. (b) Find the standard deviation of the bending moment. (c) If X₁ and X2 are normally distributed, what is the probability that the bending moment will exceed 104 kip-ft?

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