Let X₁, X₂ and X3 be mutually independent random variables with Poisson distributionshaving means 2, 1, and 4, respectively.(a) Find the moment generating function of the sum Y = X₁ + X₂ + X₂.(b) How is y distributed?(c) Compute P(3≤Y≤9).

X~Pois(λ) P(X=x)=e-λ λx/x! x=0,1,2,3,..,..

Answered: Let X₁, X₂ and X3 be mutually…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X₁, X₂ and X3 be mutually independent random variables with Poisson distributions having means 2, 1, and 4, respectively. (a) Find the moment generating function of the sum Y = X₁ + X₂ + X3. (b) How is y distributed? (c) Compute P(3≤Y≤9).