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Suppose Y is a continuous random variable with support Ry In addition, its cdf Fy is strictly increasing, so that Fy' exists and Fy(Fyl(y)) = ! for any y Ry _ ...

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Suppose Y is a continuous random variable with support Ry In addition, its cdf Fy is strictly increasing, so that Fy' exists and Fy(Fyl(y)) = ! for any y Ry _ Let U = Fy(Y) Use the cdf technique to show that U Unif (0,1); i.e U follows standard uniform distribution_

Suppose Y is a continuous random variable with support Ry In addition, its cdf Fy is strictly increasing, so that Fy' exists and Fy(Fyl(y)) = ! for any y Ry _ Let U = Fy(Y) Use the cdf technique to show that U Unif (0,1); i.e U follows standard uniform distribution_



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Suppose that $X$ is a random variable that has a uniform distribution on the interval [0,1] . (See Problem 20 .) The point (1, $X$ ) is plotted in the plane. Let $Y$ be the distance from $(1, X)$ to the origin. Find the CDF and the PDF of the random variable $Y$. Hint: Find the CDF first.


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