Question

A 20-ft cantilever beam is show in the figure below. Load W1 = 200 lb, or W2 = 500 lb, or both may be applied at the mid-point B or at the end of the beam C. The bending moment induced at the fixed support A, MA, will depend on the magnitudes of the loads at B and C. 10 ft 10 ft A B C (a) Determine the sample space of MA. (b) Define the following events: E1 = {MA > 5,000 ft-lb} E2 = {1,000 <= MA < 12,000 ft-lb} E3 = {2,000 ft-lb; 7,000 ft-lb} Are the events E1 and E2 mutually exclusive? Explain why. (c) Assume the following respective probabilities for the positions of the two loads: P[W1 at B] = 0.25 P[W1 at C] = 0.60 P[W2 at B] = 0.30 P[W2 at C] = 0.50

          A 20-ft cantilever beam is show in the figure below. Load W1 = 200 lb, or W2 = 500 lb, or both may be applied at the mid-point B or at the end of the beam C. The bending moment induced at the fixed support A, MA, will depend on the magnitudes of the loads at B and C.

10 ft 10 ft
A B C

(a) Determine the sample space of MA.
(b) Define the following events:
E1 = {MA > 5,000 ft-lb}
E2 = {1,000 <= MA < 12,000 ft-lb}
E3 = {2,000 ft-lb; 7,000 ft-lb}
Are the events E1 and E2 mutually exclusive? Explain why.
(c) Assume the following respective probabilities for the positions of the two loads:
P[W1 at B] = 0.25
P[W1 at C] = 0.60
P[W2 at B] = 0.30
P[W2 at C] = 0.50

A 20-ft cantilever beam is show in the figure below. Load W1 = 200 lb, or W2 = 500 lb, or both may be applied at the mid-point B or at the end of the beam C. The bending moment induced at the fixed support A, MA, will depend on the magnitudes of the loads at B and C.

10 ft 10 ft
A B C

(a) Determine the sample space of MA.
(b) Define the following events:
E1 = MA > 5,000 ft-lb
E2 = 1,000 <= MA < 12,000 ft-lb
E3 = 2,000 ft-lb; 7,000 ft-lb
Are the events E1 and E2 mutually exclusive? Explain why.
(c) Assume the following respective probabilities for the positions of the two loads:
P[W1 at B] = 0.25
P[W1 at C] = 0.60
P[W2 at B] = 0.30
P[W2 at C] = 0.50

Added by Luis L.

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