If the conditional distribution of Y, given X with parameter x and if the unconditional distribution of X is an Erlang distribu- tion with parameters A(> 0) and k(> 2), prove that the conditional distribution of X, given Y = y, is an Erlang distribution with parameters 2 + y and k +1 . = x, is an exponential distribution %3D

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 46E
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If the conditional distribution of Y, given X = x, is an exponential distribution
with parameter x and if the unconditional distribution of X is an Erlang distribu-
tion with parameters (> 0) and k(> 2), prove that the conditional distribution of
X, given Y = y, is an Erlang distribution with parameters
and k +1.
6.
Transcribed Image Text:If the conditional distribution of Y, given X = x, is an exponential distribution with parameter x and if the unconditional distribution of X is an Erlang distribu- tion with parameters (> 0) and k(> 2), prove that the conditional distribution of X, given Y = y, is an Erlang distribution with parameters and k +1. 6.
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