Calculate the conditional distribution

Reference no: EM131005827

Shocks occur according to a Poisson process with rate λ, and each shock independently causes a certain system to fail with probability p. Let T denote the time at which the system fails and let N denote the number of shocks that it takes.

(a) Find the conditional distribution of T given that N = n.

(b) Calculate the conditional distribution of N, given that T = t, and notice that it is distributed as 1 plus a Poisson random variable with mean λ(1 - p)t.

Reference no: EM131005827

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