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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...
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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.
- Winter '10