- #1
Mark53
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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