Suppose that g is an easy probability density function to generate from, and h is a nonnegative function. Consider 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 generatedsamples.(d) Note that the density function f(x) in the samples is the conditional prob. f(x|accepted).Find f for X, subject to a constant.(e) With the results, write the pseudo-code for the densityf(x) = c/x2 * e-(x^2)/2, x>1(Hint. Find g and h to generate f. For g, you may consider the inversion algorithm.) 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 generatedsamples.-Nete that E~Eæp(). Whatisthe probabitity that P(E < t) for any constantt> 0?Given Y- , what is the probability that Y will be-aecepted?What is the joint probability that P(YSI,Yis accepted)!(d) Note that the density function f(x) in the samples is the conditional prob. f(x|accepted).Find f for X, subject to a constant.(e) With the results, write the pseudo-code for the densityf(r) =2/2x > 1.(Hint. Find g and h to generate f. For g, you may consider the inversion algorithm.)

The simulation is the process in which the study is performed repeatedly to get an accurate result.…

Answered: Suppose that g is an easy probability…

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

Suppose that g is an easy probability density function to generate from, and h is a nonnegative function. Consider 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.

(d) Note that the density function f(x) in the samples is the conditional prob. f(x|accepted).
Find f for X, subject to a constant.

(e) With the results, write the pseudo-code for the density
f(x) = c/x² * e^{-(x^2)/2}, x>1
(Hint. Find g and h to generate f. For g, you may consider the inversion algorithm.)