7. 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 a = 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®].

7. 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 a = 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®].

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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