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5. Let X and Y be i.i.d. U(0, 1). Let Z= min(X, Y) and W = X+Y. (a) Find the cumulative distribution function for Z and W.

5. Let X and Y be i.i.d. U(0, 1). Let Z= min(X, Y) and W = X+Y. (a) Find the cumulative distribution function for Z and W.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5. Let X and Y be i.i.d. U(0, 1). Let Z = min(X,Y) and W = X +Y. (a) Find the cumulative distribution function for Z and W. (b) For each of these two random variable Z and W, give two different algorithms to generate the random variates. One algorithm that uses exactly one random number per random variate, the other algorithm may use more than one random numbers per random variate.
Transcribed Image Text:5. Let X and Y be i.i.d. U(0, 1). Let Z = min(X,Y) and W = X +Y. (a) Find the cumulative distribution function for Z and W. (b) For each of these two random variable Z and W, give two different algorithms to generate the random variates. One algorithm that uses exactly one random number per random variate, the other algorithm may use more than one random numbers per random variate.
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