Chapter 1: Problem 63
Let \(X_{i}\) be an infinite set of independent stochastic variables with identical distributions \(P(x)\) and characteristic function \(G(k)\). Let \(r\) be a random positive integer with distribution \(p_{r}\) and probability generating function \(f(z)\). Then the sum \(Y=\) \(X_{1}+X_{2}+\cdots+X_{r}\), is a random variable: show that its characteristic function is \(f(G(k))\). [This distribution of \(Y\) is called a "compound distribution" in FELLFR \(L_{4}\) ch. XIL.]
Short Answer
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Key Concepts
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