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 A > 0 is unknown.It is believed thatis distributed as a Gamma(4, 2.0)variable.Let Ybe the number of buses that arrive in t hours, so that the conditional probability mass function P(Y|A)is Poisson with rate AtGive the value of the joint distribution for Yand A computed at y = 4,1= 2.1, t = 21.Give the marginal probability mass function of Y, computed at y = 4, t = 22.3.Give the posterior mean E(AY = y)at y = 4, t = 2Give the posterior variance Var(A |Y = y)at y = 4, t = 24.

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 A > 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|X) is Poisson with rate At 1. Give the value of the joint distribution for Y and A computed at y = 4, = 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(A | 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 A > 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|X) is Poisson with rate At 1. Give the value of the joint distribution for Y and A computed at y = 4, = 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(A | 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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Estimation

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Question

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 A > 0 is unknown.
It is believed that
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
Give the value of the joint distribution for Y
and A computed at y = 4,1= 2.1, t = 2
1.
Give the marginal probability mass function of Y
, computed at y = 4, t = 2
2.
3.
Give the posterior mean E(AY = y)
at y = 4, t = 2
Give the posterior variance Var(A |Y = y)
at y = 4, t = 2
4.

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