Question 4 (a) A fair coin is rolled until 2 heads (not necessarily consecutively!) are shown. Let X denote the roll in which the second head is obtained. (i) Determine the support of X [1 marks] (ii) Determine the probability mass function of X. [2 marks] (b) Let c E R and p: R - R be a function defined as p(k) = Jce-kl, for ke Z otherwise . Hint: Notice that in the first case k ranges over all integers, so that for integers k 5 0, p(k) = cek while for k 2 0, p(k) = ce-k.] (i) After stating the conditions under which p is a probability mass function, determine the value of c for which this is indeed the case. [2 marks] [If unable to determine the value of c, leave it as 'c' in the next question. } For the value of c determined above, let X be the random variable whose probability mass function is p. (ii) For every m E Z, determine P(X > m). [Hint: consider separately the cases m 2 0 and m