Question

A drunk man is stumbling home from a bar. Each step he takes is equally likely to be one step forward or one step backward, independent of any other step.

the ith step is a random variable Zi, with p.m.f.

z	-1	1
f(z)	0.5	0.5

The drunkard’s position after n steps is Xn = Z1 + Z2 + .....Zn

1. What is the distribution of X2 (n = 2), the drunkard’s position after just 2 steps? Find these probabilties-

A. P(X2 = -2)

B. P(X2 = 0)

C. P(X2 = 2)

2. Calculate E[Zi] and Var[Zi].

3. Calculate E[X3] and Var[X3]

Answer 1