03. Simulation of random variables

03. Simulation of random variables - University of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics 100B Instructor: Nicolas Christou Simulating a continuous random variable Many times computer simulations are used to evaluate proposed statistical techniques. Typ- ically, these simulations require that we obtain observed values of random variables with a prescribed distribution. Most computer systems contain a subroutine that provides ob- served values of a uniform random variable on the interval [0 , 1]. Let X 1 ,X 2 , ··· ,X n be a random sample from this distribution. How can we use these values to generate n obser- vations Y 1 ,Y 2 , ··· ,Y n from an exponential distribution with parameter λ , Y ∼ exp ( λ )? As a reminder the probability density function (pdf) of an exponential random variable Y is f ( y ) = λe- λy ,y ≥ 0, and the cumulative distribution function (cdf) is F ( y ) = 1- e- λy ,y ≥ 0. Example: Suppose we want to generate 100 values form the exponential distribution with parameter...
View Full Document

This note was uploaded on 01/14/2011 for the course STATS 100B 100B taught by Professor Christou during the Winter '10 term at UCLA.

Page1 / 3

03. Simulation of random variables - University of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online