In a town the number of buses that arrive at a certain bus stop is a Poisson variable with rate A buses per hour, where 1 > 0 is unknown. It is believed that A is distributed as a Gamma(4, 2.0) variable. Let Y be the number of buses that arrive in t hours, so that the conditional probability mass function P(Y|A) is Poisson with rate At 1. Give the value of the joint distribution for Y and A computed at y = 4, d= 2.1, t = 2 2. Give the marginal probability mass function of Y ,computed at y = 4, t = 2 3. Give the posterior mean E(|Y = y) at y = 4, t = 2 Give the posterior variance Var(A | Y = y) at y = 4, t = 2 4.

In a town the number of buses that arrive at a certain bus stop is a Poisson variable with rate A buses per hour, where 1 > 0 is unknown. It is believed that A is distributed as a Gamma(4, 2.0) variable. Let Y be the number of buses that arrive in t hours, so that the conditional probability mass function P(Y|A) is Poisson with rate At 1. Give the value of the joint distribution for Y and A computed at y = 4, d= 2.1, t = 2 2. Give the marginal probability mass function of Y ,computed at y = 4, t = 2 3. Give the posterior mean E(|Y = y) at y = 4, t = 2 Give the posterior variance Var(A | Y = y) at y = 4, t = 2 4.

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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