A six-sided die has an unknown number of faces marked with a six. Let k be this unknown number, which we would like to estimate. Our prior distribution for k is P(k = j) = (5/8, j = 1 |1/16, j= 0,2,3,4,5,6. When the die is thrown each face has an equal chance of showing. The observed data is that the die was thrown twice, and it showed a six exactly once. (a) Write down the likelihood for the observed data. What is the maximum likelihood estimate for k? (b) Derive the normalized posterior distribution for k. What is the posterior mean for k? (c) Find the posterior predictive probability that if the die is thrown again, it will not show six.
A six-sided die has an unknown number of faces marked with a six. Let k be this unknown number, which we would like to estimate. Our prior distribution for k is P(k = j) = (5/8, j = 1 |1/16, j= 0,2,3,4,5,6. When the die is thrown each face has an equal chance of showing. The observed data is that the die was thrown twice, and it showed a six exactly once. (a) Write down the likelihood for the observed data. What is the maximum likelihood estimate for k? (b) Derive the normalized posterior distribution for k. What is the posterior mean for k? (c) Find the posterior predictive probability that if the die is thrown again, it will not show six.
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:A six-sided die has an unknown number of faces marked with a
six. Let k be this unknown number, which we would like to estimate. Our prior distribution
for k is
P(k = j) =
5/8, j = 1
1/16, j= 0,2,3,4,5,6.
When the die is thrown each face has an equal chance of showing. The observed data is that
the die was thrown twice, and it showed a six exactly once.
(a) Write down the likelihood for the observed data. What is the maximum likelihood
estimate for k?
(b) Derive the normalized posterior distribution for k. What is the posterior mean for k?
(c) Find the posterior predictive probability that if the die is thrown again, it will not show a
six.
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