If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the Toads is aįX1 + azX3. Suppose that X1 and X2 are independent random variables with means 4 and 6 kips, respectively, and standard deviations 0.7 and 1.3 kips, respectively. Suppose that a1 = 5 ft and az = 12 ft. (a) Find the expected value of the bending moment. (b) Find the standard deviation of the bending moment. (c) IE Y. and V are normall: dictributed uhat is the rprobahilitr that the handing mo ment uii11 excead 122 1-in 62

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Problem #9: 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 + azX2.
Suppose that X1 and X, are independent random variables with means 4 and 6 kips, respectively, and standard
deviations 0.7 and 1.3 kips, respectively. Suppose that aj = 5 ft and az = 12 ft.
(a) Find the expected value of the bending moment.
(b) Find the standard deviation of the bending moment.
(c) If X1 and X, are normally distributed, what is the probability that the bending moment will exceed 122 kip-ft?
Transcribed Image Text:Problem #9: 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 + azX2. Suppose that X1 and X, are independent random variables with means 4 and 6 kips, respectively, and standard deviations 0.7 and 1.3 kips, respectively. Suppose that aj = 5 ft and az = 12 ft. (a) Find the expected value of the bending moment. (b) Find the standard deviation of the bending moment. (c) If X1 and X, are normally distributed, what is the probability that the bending moment will exceed 122 kip-ft?
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