5. LetXbe a discrete random variable whose probability at each of the valuexis given by

[14 marks]

[2] [3] [3] [2]

[4]

P(X=x) = for some positive real numberk.

5. Let X be a discrete random variable whose probability at each of the value a: is given by P(X : m) : km for :I: =I1,2,...,c (where c > 2), 0 Otherwlse. for some positive real number k. [20 marks] " 1 (a) Express k: in terms of c. [Hint: You may use the identity Ex : % for all positive integers 11.] [6] 12:1 (b) It is knwon that the two events {1 S X S 3} and {X > 2} are indepedent. Find the values of k and c. [6] (c) Calculate E(X). " 1 2 1 [Hint: You may use the identity 21:2 = W 01\" all positive integers "-l [6] 33:1 (d) Calculate E(3X 2). [2]