We choose a random integer from {1,2,3}, each having the same chance to be chosen. Denote this random number by N. Then we will roll N independent six-face fair dice, and denote by X1, ..., XN their outcomes. Let X = max{X1,...,XN}. (a) Given X = 1, is N uniformly distributed (i.e. does each possible outcome have the same chance)? Prove or disprove it. (10 marks) == (b) Given N = 3, is X uniformly distributed? Prove or disprove it. (10 marks) (c) Are X and N independent? Prove or disprove it. (5 marks)