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.

b) Let X be the random variable with the cumulative probability distribution:

0 x < 0 0 ≤x≤2
F(x) = {0, x<0
kx², 0 ≤ x < 2
1, x ≥ 2

Determine the value of k.

c) Let X be the random variable with the cumulative probability distribution:

F(x) = {0, x < 0
1 - e^-2x, x ≥ 0