Problem 3 In this problem, we aim to design a device that generates a random variable with a desired CDF. 1 (a) If X is a random variable with a CDF F(x), show that Y = F(X) is uniformly distributed, i.e., Y ~U(0,1). Suppose the inverse function F-1 of F(x) exists. (b) Suppose we are given a random number generator, which emits random numbers drawn according to the uniform distribution U(0,1). Using this device, describe how to generate a random variable X with CDF F(). Another way to interpret the problem is as follows. Suppose Y ~U(0,1). Can you find a function G(Y) such that the random variable X = G(Y) has the CDF F(). Problem 3 In this problem, we aim to design a device that generates a random variable with a desired CDF. 1 (a) If X is a random variable with a CDF F(x), show that Y = F(X) is uniformly distributed, i.e., Y ~U(0,1). Suppose the inverse function F-1 of F(x) exists. (b) Suppose we are given a random number generator, which emits random numbers drawn according to the uniform distribution U(0,1). Using this device, describe how to generate a random variable X with CDF F(). Another way to interpret the problem is as follows. Suppose Y ~U(0,1). Can you find a function G(Y) such that the random variable X = G(Y) has the CDF F()