Let X follows the Poisson, P. (2) distribution and the conditional distribution of Y given X=x is binomial, b(x, p). Derive the probability density function (pdf) of Y. (Hint: If U P (2), the pdf of Uis P(U=u) = ² . Also, if T~ b(n, p), the pdf of T ea qu u! is P(T=1)=(")p'(-p)~')
Let X follows the Poisson, P. (2) distribution and the conditional distribution of Y given X=x is binomial, b(x, p). Derive the probability density function (pdf) of Y. (Hint: If U P (2), the pdf of Uis P(U=u) = ² . Also, if T~ b(n, p), the pdf of T ea qu u! is P(T=1)=(")p'(-p)~')
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 4CR
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Transcribed Image Text:Let X follows the Poisson, P. (2) distribution and the conditional distribution of Y given
X=x is binomial, b(x, p). Derive the probability density function (pdf) of Y.
(Hint: If U P (2), the pdf of U is P(U=u) = ⋅ . Also, if T~ b(n, p), the pdf of T
e-2 qu
u!
is P(T-1)-(*) p'(1-p)*¹)
= t) =
n
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