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3. The number of mahjong games played in a given family on the Lunar New Year can be modeled as a Geometric() random variable, where the value of the parameter varies from family to family. Assume a Uniform(0, 1) prior on . (a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt games t years ago. Show that the posterior is a Beta(a, 3) random variable. What are a and B? (b) Bob observed that x₁ = 22 and 2 = 41. What is the expected number of games that his family will play this year?

3. The number of mahjong games played in a given family on the Lunar New Year can be modeled as a Geometric() random variable, where the value of the parameter varies from family to family. Assume a Uniform(0, 1) prior on . (a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt games t years ago. Show that the posterior is a Beta(a, 3) random variable. What are a and B? (b) Bob observed that x₁ = 22 and 2 = 41. What is the expected number of games that his family will play this year?

MATLAB: An Introduction with Applications
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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3. The number of mahjong games played in a given family on the Lunar New Year can be modeled as a Geometric (0) random variable, where the value of the parameter varies from family to family. Assume a Uniform (0, 1) prior on 0. (a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt games t years ago. Show that the posterior is a Beta(a, ß) random variable. What are a and 3? (b) Bob observed that x₁ 22 and x₂ = 41. What is the expected number of games that his family will play this year? -
Transcribed Image Text:3. The number of mahjong games played in a given family on the Lunar New Year can be modeled as a Geometric (0) random variable, where the value of the parameter varies from family to family. Assume a Uniform (0, 1) prior on 0. (a) Suppose Bob's family played x₁ games on the 2020 festival, x2 games in 2019, up to xt games t years ago. Show that the posterior is a Beta(a, ß) random variable. What are a and 3? (b) Bob observed that x₁ 22 and x₂ = 41. What is the expected number of games that his family will play this year? -
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