Consider an 7-sided coin and suppose that on each flip one of the sides appears side i with probability P., numbers r,,n,, let N, denote the number of flips required until side i has appeared for the n, time, i = 1,.,r, and let N = min N, P. 1 For given Thus N is the number of flips required until side i has appeared n, times for some 1, r

(a) What is the distribution of N,?

(b) Are the N, independent? Now suppose that the flips are performed at random times generated by a Poisson process with rate A 1 Let 7, denote the time until side i has appeared for the n, time, i = 1,,r and let T = min T 1-1. F

(c) What is the distribution of T,"

(d) Are the 7, independent?

(e) Derive an expression for E[T]

(f) Use

(e) to derive an expression for E[N]