Let x be a discrete random variable that takes on the values i æ 0, 1, 2, . . with probability mass function (pmf): p(x æ i ) æ c ¸i i ! (1) where ¸ è 0 is a fixed and known positive number and c is a (yet to be determined) real number. (a) find the value of c which makes p(x æ i ) a valid probability function. remember we need the probability of all outcomes to be equal to 1. or more specifically: 1 æ 1x iæ0 p(x æ i ). (b) determine p(x æ 0) (c) determine p(x è 2). hint: it might be to use the law of total probability which tell us that 1 æ p(x · 2)åp(x è 2).