# Let X1,X2, . . . be independent positive continuous random variables with a common density function 1 answer below »

Let X_{1},X_{2}, . . . 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

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Let X1,X2, . . . be independent positive continuous random variables with a common density function
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Show that {N(t), t 0} is a nonhomogeneous Poisson process with intensity function λ(t) = λf (t ).