Assignment 1:

We throw a coin, where the probability of obtaining head in a throw is p, where p ]0,1[. We let the random variable X denote the number of throws until we get the results headtail in the given succession (thus we have X = n, if the pair headtail occurs for the rst time in the experiments of numbers n1 and n). Find the generating function of X and use it to nd the mean and variance of X. For which value of p is the mean smallest?