Suppose that the random variables X and Y are independent, and that X has the Poisson distribution with parameter A and Y has the Poisson distribution with parameter µ. (a) Show that the sum Z = X + Y has the Poisson distribution with naramotor

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 43CR
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Suppose that the random variables X and Y are independent, and that X has
the Poisson distribution with parameter A and Y has the Poisson distribution
with parameter u.
(a) Show that the sum Z = X + Y has the Poisson distribution with
parameter A+ µ.
(b) Find the conditional probability P(X = k | Z = n) for k = 0, 1,...,n,
and give a name for this distribution.
Transcribed Image Text:Question Suppose that the random variables X and Y are independent, and that X has the Poisson distribution with parameter A and Y has the Poisson distribution with parameter u. (a) Show that the sum Z = X + Y has the Poisson distribution with parameter A+ µ. (b) Find the conditional probability P(X = k | Z = n) for k = 0, 1,...,n, and give a name for this distribution.
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