Exercise 3.1 (Discrete Convolution) Let X and Y be non-negative, discrete random variables with probability distributions p
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Exercise 3.1 (Discrete Convolution) Let X and Y be non-negative, discrete random variables with probability distributions pXi
= P{X = i} and pYi
= P{Y = i}, i = 0, 1, 2, . . . , respectively, and suppose that they are independent.
Prove that
Using this formula, prove that if X ∼ B(n, p), Y ∼ Be(p) and they are independent, then X + Y ∼ B(n + 1, p).
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Related Book For
Stochastic Processes With Applications To Finance
ISBN: 9781439884829
2nd Edition
Authors: Masaaki Kijima
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