2. (Total: 15 points) (a) (4 points) The density function of a random variable X is given by {p+qx, for 0 x 1; f(x) = otherwise. If E(X) = 0.6, find p and q. (b) Suppose that Y follows a Poisson distribution. (i) (2 points) If Pr(Y = 0) = Pr(Y = 1), determine E(Y). (ii) (2 points) If Pr(Y = 1) = Pr(Y = 2), determine E(Y). (c) (3 points) Suppose that Z follows a standard normal distribution, determine Pr(Z > -0.56|Z < 1.07). (d) (4 points) A discrete random variable W takes the value a with probability p and takes the value b with probability 1 -p where 0 < p < 1. Find the variance of W in terms of a, b and p.