Let Sn denote the time of the nth event of the Poisson process 1 answer below »

Let Sn denote the time of the nth event of the Poisson process {N(t), t  width= 0} having rate λ. Show, for an arbitrary function g, that the random variable  width=g(Si ) has the same distribution as the compound Poisson random variable  width= g(Ui ), where U1,U2, . . . is a sequence of independent and identically distributed uniform (0, t ) random variables that is independent of N, a Poisson random variable with mean λt. Consequently, conclude that

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