(a) The geometric random variable X which gives the probability of first success in the xth trial of a binomial distribution is: P(X = x) =q p, x=123. Determine: 1) the moment generating function M (t) ofX (6 Marks) 11 ) E(X) and V(X). (2 +4 Marks) (b) In many board games it is necessary to throw a six with an ordinary die before a player can start the game. Find the probability that a player requires more than five or less than eight attempts before starting. What is the mean number of throws required to obtain a six. (3 + 4 Marks)