Unformatted text preview: n and p . Suppose that we want to generate a random variable Y whose probability mass function is the same as the conditional mass function of X given that X ≥ k , for some k ≤ n . Let α = P ( X ≥ k ) and suppose that the value of α has been computed. (a) Give the inverse transform method for generating Y . (b) Give a second method for generating Y . (c) For what values of α , small or large, would the algorithm in (b) be ineﬃcient? 6. Give a method for generating a random variable having density function f ( x ) = e x / ( e-1) , ≤ x ≤ 1 7. Extra credit: If Z is a standard normal random variable, show that E [ | Z | ] = ± 2 π ² 1 / 2...
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- Spring '10
- Probability theory, probability density function, Cumulative distribution function, binomial random variable, random variables U1, Prof. Mariana Olvera-Cravioto