{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

10SimHw4

# 10SimHw4 - IEOR 4404 Simulation Prof Mariana...

This preview shows pages 1–2. Sign up to view the full content.

IEOR 4404 Assignment #4 Simulation February 20, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #4 – due February 26th, 2010 1. Let X be an exponential random variable with mean 1. Give an efficient algorithm for simulating a random variable whose distribution is the conditional distribution of X given that X < 0 . 05. That is, its density function is f ( x ) = e - x 1 - e - 0 . 05 , 0 < x < 0 . 05 Generate 1000 such variables and use them to estimate E [ X | X < 0 . 05]. Then determine the exact value of E [ X | X < 0 . 05]. 2. Suppose that we want to generate a random variable X whose density function is f ( x ) = 1 2 x 2 e - x x > 0 by using the rejection method with an exponential density having rate λ (mean 1 ). Find the value of λ that minimizes the expected number of iterations of the algorithm used to generate X . ( Hint: Recall that from Assignment #3 the expected number of rejections is c - 1, so the expected number of iterations is c .) 3. Write a computer program that, when given a probability mass function { p j : j = 1 , . . . , n } as an input, gives as an output the value of a random variable having this mass function.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}