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Two components of a minicomputer have the following joint pdf for their lifetimes ? and ?:...

Two components of a minicomputer have the following joint pdf for their lifetimes ? and ?: ?(?, ?) = { ??? −?(1+?) ? ≥ 0, ? ≥ 0

0 otherwise

(a) Find the value of ?.

(b) What is the probability that the lifetime ? of the first component exceeds 3?

(c) What are the marginal pdf’s of ? and ?? Are the two lifetimes independent? Explain.

(d) What is the probability that the lifetime of at least one component exceeds 3?

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