Answer all questions. Show all working. Question 1 [11 marks] a) The discrete probability distribution is given by i. Show that m=81 [2] ii. Find the mean of the probability distribution. [2] iii. Calculate P(X>) [2] o) A bag contains 10 cards, of which 2 are marked two, 1 is marked three, 4 are marked four and 3 are marked five. i. 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. Answer all questions. Show all working. Question 1 [11 marks] a) The discrete probability distribution is given by i. Show that m=81 [2] ii. Find the mean of the probability distribution. [2] iii. Calculate P(X>) [2] o) A bag contains 10 cards, of which 2 are marked two, 1 is marked three, 4 are marked four and 3 are marked five. i. 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