Let X have a continuous, strictly increasing CDF F. Let Y = F(X). Find the density of

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Let X have a continuous, strictly increasing CDF F. Let Y = F(X). Find the density of Y. This is called the probability integral transform. Now let U ti Uniform(0, 1) and let X = F-1(U). Show that X ti F. Now write a program that takes Uniform (0,1) random variables and generates random variables from an Exponential (/3) distribution.