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....

question (a) to (d)

Extracted 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="">