MathDB

A particle performing a random walk on the integer points of the semi-axis

x \ge 0

moves a distance

1

to the right with probability

a

, and to the left with probability

b

, and stands still in the remaining cases (if

x = 0

, it stands still instead of moving to the left). Determine the steady-state probability distribution, and also the expectation of

x

and

x^2

over a long time, if the particle starts at the point

0

Problem Statement