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The time of the nth point, Tn, of a Poisson process N of constant intensity on [0,) give rise to an
effect Xne(tTn) where Xn are independent and identically distributed with finite variance. Find i. the
mean and variance of the total effect N(T) W(t) = Xne(tTn) n=1 in terms of the first two moments of
the Xn ii. the covariance of W(t) and W(s) iii. the correlation between W(t) and W(s)

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The time of the nth point Tn of a Poisson process N of con.pdf

  • 1. The time of the nth point, Tn, of a Poisson process N of constant intensity on [0,) give rise to an effect Xne(tTn) where Xn are independent and identically distributed with finite variance. Find i. the mean and variance of the total effect N(T) W(t) = Xne(tTn) n=1 in terms of the first two moments of the Xn ii. the covariance of W(t) and W(s) iii. the correlation between W(t) and W(s)