A obtain the moment-generating function of the random, Basic Statistics

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A obtain the moment-generating function of the random

Suppose that {N(t), t ≥ 0} is a Poisson process with rate λ > 0 and that S is a random variable having a uniform distribution on the interval [0,2].

(a) Obtain the moment-generating function of the random variable N{t + S). Indication. If X has a Poisson distribution with parameter a, then Mx(t) = exp{α(e^t - 1)}.

(b) Calculate the mean and the variance of N{t + S).

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Basic Statistics: A obtain the moment-generating function of the random

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