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

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

Show by defining appropriate random variables
September 6, 2018
Supposes that the price remains unchanged until a shock” occurs, at which time the price is..
September 6, 2018

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.transtutors.com/qimage/image09062014509.png” alt=” width=”>

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