0
votes
1answer
110 views

geometric sum - weighted random walk

I am trying to model the following sum: $\sum_{i=0}^{n}{W_i \alpha^{i}}$ where $\alpha \in[0, 1) $ and $W_n$ takes values 0 or 1 and may be modeled as a markow chain or for simplicity as a binary ...
3
votes
1answer
101 views

Limit of a probability regarding a random walk

Consider a random walk on the integers starting at 0, where in each step you move either 1 or 2 meters (back or forth alike). As soon as you reach either the $N$ or $N+1$ meter mark, you stop. What is ...