MathDB
Problems
Contests
Undergraduate contests
Arnold's Trivium
1991 Arnold's Trivium
97
97
Part of
1991 Arnold's Trivium
Problems
(1)
Problem 97
Source:
7/1/2010
A particle performing a random walk on the integer points of the semi-axis
x
≥
0
x \ge 0
x
≥
0
moves a distance
1
1
1
to the right with probability
a
a
a
, and to the left with probability
b
b
b
, and stands still in the remaining cases (if
x
=
0
x = 0
x
=
0
, it stands still instead of moving to the left). Determine the steady-state probability distribution, and also the expectation of
x
x
x
and
x
2
x^2
x
2
over a long time, if the particle starts at the point
0
0
0
.
probability