a) A merchant receives a shipment of five photocopying machines, two of which are defective. He randomly selects three of the machines and checks them for faults. Let the random variable X be number of faulty machines in his selection. Find the probability distribution of random variable X in the table form. (6) b) Let X be the random variable with the cumulative probability distribution: x < 0 PGD - feat. F(x)=kx², 0 ≤ x < 2 x 22 Determine the value of k. (6) c) Let X be the random variable with the cumulative probability distribution: x < 0 F(x) = {₁-e²²x x 20 Determine the expected value of X. (5) d) The random variable X has a Poisson distribution such that P(X = 0) = P(X= 1). Calculate P(X= 2).