{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment04Sol

# Assignment04Sol - Columbia University IEOR 4404 Simulation...

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

Columbia University IEOR 4404: Simulation Fall 2009 Solutions to Assignment 4 1. (Exercise 5.2) Let X denote the random variable with the given density function f ( x ). We use the acceptance-rejection method in order to gen- erate X . Note that f ( x ) 1 / 2 for all 2 x 6. Let Y be a random variable uniformly distributed on [2 , 6], with density g ( x ) given by g ( x ) = 1 4 for 2 x 6 . It follows that f ( x ) g ( x ) 2 for 2 x 6 . (1) With this, we can implement the acceptance-rejection method to generate X . The value of the constant c in the algorithm is given by c = 2 by (1). The steps of the algorithm are the following: STEP 1. Generate a random number U 1 , uniform on (0 , 1). Set Y = 4 * U 1 + 2 (this makes Y uniform on (2,6)). STEP 2. Generate a random number U 2 , uniform on (0 , 1). STEP 3. If U 2 f ( Y ) 2 g ( Y ) , set X = Y . Otherwise return to STEP 1. 2. (Exercise 5.4) We can use the inverse transform method. From the explicit form of the distribution function, we can get the inverse of this function as F - 1 ( y ) = [ - 1 α log(1 - y )] 1 β

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.
• Spring '10
• C
• Probability theory, Cumulative distribution function, random number, Inverse transform sampling, inverse transform method

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern