Suppose that g is an easy probability density function to generate from, and h is a non- negative function. Take a close look at the following algorithm pseudo-code: Step 1. Generate Y ~ g. Step 2. Generate E ~ Exp(1) in the way that E = - log(U), U ~ Unif(0,1). Step 3. If E > h(Y), set X = Y. Otherwise go to Step 1. Step 4. Return X. This is a rejection algorithm and we want to find the density function of the generated samples. (a) Note that E - Exp(1). What is the probability that P(E < t) for any constant t> 0? (b) Given Y = x, what is the probability that Y will be accepted? (c) What is the joint probability that P(Y
Suppose that g is an easy probability density function to generate from, and h is a non- negative function. Take a close look at the following algorithm pseudo-code: Step 1. Generate Y ~ g. Step 2. Generate E ~ Exp(1) in the way that E = - log(U), U ~ Unif(0,1). Step 3. If E > h(Y), set X = Y. Otherwise go to Step 1. Step 4. Return X. This is a rejection algorithm and we want to find the density function of the generated samples. (a) Note that E - Exp(1). What is the probability that P(E < t) for any constant t> 0? (b) Given Y = x, what is the probability that Y will be accepted? (c) What is the joint probability that P(Y
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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question (a) to (d)
Transcribed Image Text:Suppose that g is an easy probability density function to generate from, and h is a non-
negative function. Take a close look at the following algorithm pseudo-code:
Step 1. Generate Y ~ g.
Step 2. Generate E ~
Exp(1) in the way that E = - log(U), U ~ Unif(0,1).
Step 3. If E > h(Y), set X = Y. Otherwise go to Step 1.
Step 4. Return X.
This is a rejection algorithm and we want to find the density function of the generated
samples.
(a) Note that E -
Exp(1). What is the probability that P(E < t) for any constant
t> 0?
(b) Given Y = 2, what is the probability that Y will be accepted?
(c) What is the joint probability that P(Y < x,Y is accepted)?
(d) Note that the density function f(r) in the samples is the conditional prob. f(z|accepted).
Find f for X, subject to a constant.
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