- #1

Mark53

- 93

- 0

## Homework Statement

Define a simple random walk Yn on a finite state space S = {0, 1, 2, . . . , N} to be a random process that

• increases by 1, when possible, with probability p,

• decreases by 1, when possible, with probability 1 − p, and

• remains unchanged otherwise.

(a) Specify the transition matrix for Yn.

(b) Assume that N = 2 and initially, the process is evenly distributed across S. Calculate the probability the process is in state 0 after 2 steps.

## The Attempt at a Solution

\begin{pmatrix}

1-p & p & 0 \\ 1-p & 0 & p \\ 0 & 1-p & p

\end{pmatrix}\quad

would this matrix be correct not sure about the first entry

b)

Just need to calculate P^2 and see what the probability is in state 0.

Need the correct matrix to do this first