(A universal random number generator.) Let X have a continuous, strictly increasing cdf F . Let Y…

(A universal random number generator.) 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 ~ Uniform(0, 1) and let

X = F -1(U ). Show that X ~ F . Now write a program that takes

Uniform (0,1) random variables and generates random variables from an Exponential (ß) distribution

the probability integral transform. Now let U ~ Uniform(0, 1) and let

X = F -1(U ). Show that X ~ F . Now write a program that takes

Uniform (0,1) random variables and generates random variables from an Exponential (ß) distribution

(A universal random number generator.) Let X have a continuous, strictly increasing cdf F . Let Y…