1. Let the random variable Y have an uniform distribution with minimum value theata 1=0 and maximum value theata 2 = 1 and let the random variable U have the form aY + b, where a and b are both constants and a > 0.
(a) Using the transformation method, find the probability density function for the random variable U when a = 2 and b = -4. What distribution does the random variable U have?
(b) Using the transformation method, find the probability density function for the random variable U for general values of a and b. What distribution does the random variable U have?