(a) A random variable X-U(0,1), is standard uniformly distributed in the interval [0,1], having a constant density over

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A A Random Variable X U 0 1 Is Standard Uniformly Distributed In The Interval 0 1 Having A Constant Density Over 1 (71.37 KiB) Viewed 30 times

(a) A random variable X-U(0,1), is standard uniformly distributed in the interval [0,1], having a constant density over the interval [0,1], i.e., the probability (density) function p(x)=1 in 0<x<1, otherwise p(x)=0. In addition we have an exponential distributed random variable Y-E(T) having the probability density function. 1e-y/ y > 0 p(y) - { y < 0 Plot the probability density functions and the cumulative distribution functions. Now consider areas are of the same size, i.e., F(x)=F(y) or P(Xsx)=P(Y<y). Use this condition to find the relation y(x). [Hint: See transformation of random number (chapter 2, Computational Physics II]