6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left headlight) and Y (the right headlight) ze(y+1) for r> 0.y > 0 f(x, y) 0 otherwise (a) What is the probability that the lifetime X of the left headlight exceeds 2.8? (b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer (c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?

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6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left
headlight) and Y (the right headlight)
ze(y+1) for r> 0.y > 0
f(x, y)
0 otherwise
(a) What is the probability that the lifetime X of the left headlight exceeds 2.8?
(b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer
(c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?
Transcribed Image Text:6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left headlight) and Y (the right headlight) ze(y+1) for r> 0.y > 0 f(x, y) 0 otherwise (a) What is the probability that the lifetime X of the left headlight exceeds 2.8? (b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer (c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?
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