Consider a Bayesian model with a parameter having a prior distribution ~ x² (4), and one observation Y|0 Poi(0). That is, has a chi-squared distribution with 4 degrees of freedom and Y|0 has a Poisson distribution with mean E(Y|0) = 0. s (a) Derive the marginal probability mass function (pmf) of Y. Note: this is the uncondi- tional pmf of Y. (b) Let V = Y + 2. Derive the pmf of V and show that it is a negative binomial pmf as
Consider a Bayesian model with a parameter having a prior distribution ~ x² (4), and one observation Y|0 Poi(0). That is, has a chi-squared distribution with 4 degrees of freedom and Y|0 has a Poisson distribution with mean E(Y|0) = 0. s (a) Derive the marginal probability mass function (pmf) of Y. Note: this is the uncondi- tional pmf of Y. (b) Let V = Y + 2. Derive the pmf of V and show that it is a negative binomial pmf as
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 6
Consider a Bayesian model with a parameter having a prior distribution 0 ~ x² (4), and
Ꮎ
one observation Y|0 ~ Poi(0). That is, has a chi-squared distribution with 4 degrees of
freedom and Y|0 has a Poisson distribution with mean E(Y|0) = 0.
(a) Derive the marginal probability mass function (pmf) of Y. Note: this is the uncondi-
tional pmf of Y.
(b) Let V = Y + 2. Derive the pmf of V and show that it is a negative binomial pmf as
defined in the Chapter 17 lecture slides. Specify the values of the negative binomial
parameters r and p.
(c) Let V = Y + 2. Calculate E(2V² + 3V – 10).
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