Let Sn denote the time of the nth event of the Poisson process

Let Sn denote the time of the nth event of the Poisson process {N(t), t .transtutors.com/qimage/image09062014506.png” alt=” width=”> 0} having rate ?. Show, for an arbitrary function g, that the random variable .transtutors.com/qimage/image09062014508.png” alt=” width=”>g(Si ) has the same distribution as the compound Poisson random variable .transtutors.com/qimage/image09062014508.png” alt=” 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 ?t. Consequently, conclude that

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