(a) An experiment involves tossing two dice and observing the total of the upturned faces.
Find: (i) The sample space S for the experiment.
(ii) Let X be a discrete random variable representing the total of the upturned faces. Find the discrete density function of X, denoted by f(x).
(iii) The cumulative distribution function of X.
(b) Suppose that the die is biased or loaded so that the probability of each face landing upper- most is proportional to the number on the face, i.e. P(k)= ck, k= 1,..., 6 for some constant c.
Find: (i) The constant c.
(ii) The probability that an even number appears.
