(d) Determine the probabilities of the following events: E1, E2, E3 E1 O E2 E1 U E2, and E2

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Answer letter d only.

Determine the following events:

Paragraph
Styles
A 20-ft cantilever beam is shown in the figure below. Load W, = 200 lb, or W,= 500 lb, or both may
be applied at the midpoint B or at the end of the beam C. The bending moment induces at the fixed support
A, MA, will depend on the magnitudes of the loads at B and C.
(a) Determine the sample space of MA-
(b) Determine the following events:
E, = (MA> 5,000 ft – lb)
E2
(1000 < MA < 12,000 ft – lb)
E3 = (2,000, 7,000 ft – lb)
Are the events E1 and E2 mutually exclusive? Explain why.
%3D
(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
Assuming that the positions of W1 and W2 are statistically independent; what are the
respective probabilities associated with each of the possible values of MA ?
(d) Determine the probabilities of the following events:
E1, E2, E3 E1 0 E2 E1 U E2, and E2
Transcribed Image Text:Paragraph Styles A 20-ft cantilever beam is shown in the figure below. Load W, = 200 lb, or W,= 500 lb, or both may be applied at the midpoint B or at the end of the beam C. The bending moment induces at the fixed support A, MA, will depend on the magnitudes of the loads at B and C. (a) Determine the sample space of MA- (b) Determine the following events: E, = (MA> 5,000 ft – lb) E2 (1000 < MA < 12,000 ft – lb) E3 = (2,000, 7,000 ft – lb) Are the events E1 and E2 mutually exclusive? Explain why. %3D (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 Assuming that the positions of W1 and W2 are statistically independent; what are the respective probabilities associated with each of the possible values of MA ? (d) Determine the probabilities of the following events: E1, E2, E3 E1 0 E2 E1 U E2, and E2
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