The discrete random variable X can take only the values 0, 1, 2, 3, 4, 5. The probability distribution of X is given by the following, where a and b are constants. PX-0) P(X-1) = P(X-2)-a P(X-3) PX-4)-P(X-5)-b PIX>2) 3P(X <2)

(a) Determine the values of a and

b,

(b) Show that the expectation of X is determine the variance of X. and

(c) Determine the probability that the sum of two independent observations from this distribution exceeds 7. (C)