(b) 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 value of K . (3 marks] 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 winfloss of the player? (4 marks) (ii) For the game to be fair, how much should the player pay to play the game? (4 marks)