(a) A discrete probability distribution of K is given as follows: k2 p[K=k) = a for k: 4,2,a,3,5 where a is an unknown positive value of k (i) Determine the value of a. Round off your answer to one decimal place. (3 marks] (ii) Calculate the expected 1value of K . (3 marks] (b) In a game, a player is required to roll two dice at the same time. If he gets a sum of 5, he wins $15. If the person gets a sum of 4, 8 or 12 he wins $8. Else he gets nothing. (i) If the player need to pay $4 to play the game, what is the expected net wim'loss of the player? (4 marks] (ii) For the game to be fair, how much should the player pay to play the game? (4 marks]