Exercise 5.41 Compound distributions. If Y ~ Poisson(A) then E(Y)= \ and Var(Y)d. The Poisson distribution has only a single parameter so we cannot shift and scale the=distribution by different amounts, which limits its usefulness in certain practical applications.This problem can be addressed by allowing the parameter itself to be a random variable.1. Let Y ~ Poisson(X) where X ~ Exponential (0) and 0 > 0 is a fixed scale parameter.Use the laws of total expectation and total variance and the fact that E(X) = 0 andVar(X) = 0² to show that E(Y) = 0 and Var(Y) = 0(1+0).

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Answered: 1. Let Y Use the laws of total…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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1. Let Y Use the laws of total expectation and total variance and the fact that E(X) = 0 and Var(X) = 0 to show that E(Y) = 0 and Var(Y) = 0(1+0). Poisson(X) where X Exponential(0) and 0 > 0 is a fixed scale parameter.