Question 1 [11 marks] a) The discrete probability distribution is given by X 0 1 2 3 P(X = x) m 2m 3m 2m i. Show that m = [2] ii. Find the mean of the probability distribution. [2] iii. Calculate P(X > H) [2] b) A bag contains 10 cards, of which 2 are marked two, 1 is marked three, 4 are marked four and 3 are marked five. IN 4 3 4 2 4 5 UT Construct a probability distribution table, showing X, the number on the card. [2] ii Use your table in i) to find the variance of this probability distribution. [3]