1. Suppose Xi for i=1, 2, 3... has Uniform (0,1) distribution.
A. Let M = min (n: X1 + X2 + ... + Xn> 1). Find E (M) by simulation.
B. Let N = min (n+1: Xn > Xn+1). Find E (N) by simulation.
2. Toss a pair of fair dice. If you get any double stop and lose. Otherwise keep tossing. If any sum gets repeated before getting any doubles stop and win.
A. Find the probability of winning
B. Find the expected number of tosses per game.