6. Suppose X is a continuous random variable with a strictly positive probability density function f(r);and let F(r) be the corresponding cumulative distribution function. Let U be a random variable uniformon the interval (0, 1).Show that Y = F-1(U) has the same distribution as X.Mathematical StatisticsMidterm Part OnePage 3 of 4

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A First Course in Probability (10th Edition)

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6. Suppose X is a continuous random variable with a strictly positive probability density function f(r); and let F(r) be the corresponding cumulative distribution function. Let U be a random variable uniform on the interval (0, 1). Show that Y = F-(U) has the same distribution as X.