fp(p) = 12 p²(1-p), 0

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
Section13.3: Special Probability Density Functions
Problem 26E
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FInd E(X) and Var (X). Find marginal PMF of X.  

Let the conditional distribution of X given P = p be Geometric(p) with pmf
fx|p(x|p) = (1 − p)-¹p, 0<p<1, x = 1, 2, 3, ...
Further assume that P has a Beta(3, 2) distribution with pdf
fp(p) = 12 p²(1 − p), 0<p<1.
(a) Calculate E(X).
(b) Obtain Var (X).
(c) Find the marginal pmf of X.
Transcribed Image Text:Let the conditional distribution of X given P = p be Geometric(p) with pmf fx|p(x|p) = (1 − p)-¹p, 0<p<1, x = 1, 2, 3, ... Further assume that P has a Beta(3, 2) distribution with pdf fp(p) = 12 p²(1 − p), 0<p<1. (a) Calculate E(X). (b) Obtain Var (X). (c) Find the marginal pmf of X.
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