2. Complete the following on continuous random variables. [10 points total] {a} X is a random variable that is uniformly distributed in the interval [1,7]. What is the probability of the random variable X taking on values less than 4.5? [3 points] (13} Suppose that X is an exponentially distributed random variable with parameter A = 2. Find the probability P(1 2). [2 points] 3. Answer the following on expected value and variance. [6 points] (a) Find the expected value, E[X], for the random variable X. [2 points] x 3 4 5 6 P(xx) .34 .18 .11 .37 (b) For a random variable X, suppose that E[X] = 5 and Var(X) = 3. Then, find E[(4 + X)~]. [4 points]