3. Let X have probability density function k: 1

3. Let X have probability density function I < a: < 02 O; otherwise [21 a. Find the constant k. Determine E (X) and Vat' (4] b. You are required to generate a random variable X with the probability density function f You have available to you a computer program that will generate a random variable U having a distribution. What function of U will provide a random variable with the p.d..f f (x)? [4) c. Using R, generate 100000 values of the random variable X, and compare the sample mean and variance with the theoretical values you obtained in Plot the empirical c.d.f. Of these values as you did in question l.