Question 3 a) Check whether the function given by f ( x) = - x - 1 x = 2,3,4,5,6 10 Can serve as the probability distribution of a discrete random variable? b) I roll a fair die twice and obtain two numbersZ 1 = result of the first roll andZ 2 =result of the second roll. Given that I know Z1 + Z2 = 9 , what is the probability that Z1 = 3 or Z2 = 3? c) A fair coin is tossed twice. Let Y be the number of heads that are observed. i) Construct the probability distribution of Y. ii) Find the probability that at least one head is observed. iii) Also construct a histogram that graphically illustrates the probability distribution d) A pair of fair dice is rolled. Let Y denote the sum of the number of dots on the top faces. i) Construct the probability distribution of Y for a pair of fair dice. ii) Find P() > 9). iii) Find the probability that Y takes an even value