A drunken man at any time takes a step forward with pr. 1/2, 2 steps backward with pr. 1/4 and stays in place otherwise. He starts at x = 0 at time t = 0 and goes on till time t = T when he passes out. The time T at which he passes out is 1 with probability 1/3, 2 with probability 1/3 and 3 with probability 1/3. (a) Find the exp. of the total number of steps (in any direction) he has taken. (b) Let S be the random variable corresponding to his position when he passes out. Find E[S°).

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.