82. Let X1,X2,... be independent positive continuous random variables with a common density function f , and

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82. Let X1,X2,... be independent positive continuous random variables with a common density function f , and suppose this sequence is independent of N, a Poisson random variable with mean λ. Define N(t) = number of i  N : Xi  t Show that {N(t),t 0} is a nonhomogeneous Poisson process with intensity function λ(t) = λf (t).

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