Consider an experiment that consists of N players independently tossing fair coins. Let A be the event that there is an "odd" man (that is, either exactly one of the coins falls heads or exactly one of the coins falls tails). For r = 1, 2, ... let Xrbe the number of times the experiment is repeated until the event occurs for the rth time.
(i) Find the mean and variance of Xr.
(ii) Evaluate E[Xr] and Var[XT] for N = 3, 4,5 and r = 1, 2, 3.