Question: Problem 5. For n = 1, 2, ..., let fn(x) be a probability density function, and let Pn be a sequence of non-negative numbers summing

Problem 5. For n = 1, 2, ..., let fn(x) be a probability density function, and let Pn be a sequence of non-negative numbers summing to one, i.e. sequence Pn forms a discrete probability distribution. Show that f (x) := >Pnin(2) n is a probability density function. 1

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