1. (10 pts) Let U be a Standard Uniform random variable. Show all the steps required to generate

a. an Exponential random variable with the parameter = 3.0;

b. a Bernoulli random variable with the probability of success 0.65;

c. a Binomial random variable with parameters n = 12 and p = 0.6

d. a discrete random variable with the distribution P(x), where P(0) = 0.4, P(3) = 0.1, P(7) = 0.2, P(14) = 0.3;

e. a continuous random variable with the density f(x) = 4x 3 , 0 < x < 1;

f. a continuous random variable with the density f(x) = (1/18)x 2 , -3 < x < 3;

g. a continuous random variable with the density f(x) = (5/128)x 1/4 , 0 < x < 16