1. Let X ~Poisson(A) and Y ~Poisson(u). Assume that X and Y areindependent. Use probability generating functions to find the distribu-tion of X + Y.

Solution: Let X~Poisson ( λ) The probability generating function of X is PX(t)= e-λ(1-t) If…

Answered: Let X ~ Poisson(A) and Y independent.…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places.

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Let X ~ Poisson(A) and Y independent. Use probability generating functions to find the distribu- tion of X + Y. Poisson(u). Assume that X and Y are