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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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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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solveIn random sampling from the exponential distribution, f(x) =1 θθe x− , x > 0, θ> 0, find the maximum likelihood estimator of θ and obtain the asymptotic distribution of this estimator
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