A fair die with k faces (k 2), numbered.. ,k, is rolled n times, with each roll being independent of all other rolls. Let X be a random variable for the number of times the ith face shows up. For each of the following parts, your answers should be in terms of n and k 

(a) What is the size of the sample space? (How many possible outcomes are there?) 

(b) What is the distribution of X, for 1 SiSk? 

(c) What is the joint distribution of Xi,X5 ,X? 

(d) Are Xi and X2 independent ran?