A certain random variable X has the probability density function (pdf) given by (x + 1, l1-x, -1≤x≤0 0≤x≤1 fx(x) = and fx (x)=0, otherwise. (a) Find the cumulative distribution function (cdf) of X and give an algorithm to generate X from a standard uniform random variable U. Find the pdf of Y = X². (b) (c) Determine the probability P(X>0|X< 1/2).
A certain random variable X has the probability density function (pdf) given by (x + 1, l1-x, -1≤x≤0 0≤x≤1 fx(x) = and fx (x)=0, otherwise. (a) Find the cumulative distribution function (cdf) of X and give an algorithm to generate X from a standard uniform random variable U. Find the pdf of Y = X². (b) (c) Determine the probability P(X>0|X< 1/2).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:A certain random variable X has the probability density function (pdf) given by
(x + 1,
l1-x,
-1≤x≤0
0≤x≤1
fx(x) =
and fx (x)=0, otherwise.
(a) Find the cumulative distribution function (cdf) of X and give an algorithm to
generate X from a standard uniform random variable U.
Find the pdf of Y = X².
(b)
(c) Determine the probability P(X> 0|X < 1/2).
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