Two components of a computer have the following joint pdf for their useful lifetimes X and Y: (a)…

Two components of a computer have the following joint pdf for their useful lifetimes X and Y: (a) What is the probability that the lifetime X of the first component exceeds 3? (b) What are the marginal pdfs of X and Y? Are the two lifetimes independent? Explain. (c) What is the probability that the lifetime of at least one component exceeds 3? You have two lightbulbs for a particular lamp. Let X =the lifetime of the first bulb and Y = the lifetime of the second bulb (both in thousands of hours). Suppose that X and Y are independent and that each has an exponential distribution with parameter λ =1. (a) What is the joint pdf of X and Y? (b) What is the probability that each bulb lasts at most 1000 h (i.e., X≤ 1 and Y ≤1)? (c) What is the probability that the total lifetime of the two bulbs is at most 2? [Hint: Draw a picture of the region A ={(x, y): x≥ 0, y≥ 0, x+y≤ 2} before integrating.] (d) What is the probability that the total lifetime is between 1 and 2? Apr 08 2022 03:21 PM

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