I have a random walk with the following rules:
- It starts at 2
- At each step it goes up by 1 with chance .4, down by one with chance .4 and up by 2 with chance .2
- The walk ends if it reaches 0
I want to know two things...
- Firstly is this guaranteed to terminate at some point - I believe it is but confirmation would be nice. If not can a probability be given to it not finishing?
- What is the probability of the walk having a given maximum value (eg what is the probability of it getting to 10 but no higher before terminating at zero).
And just so you know I used to study maths at university but that was a while ago now so best to assume that I know basic stuff but try not to assume too much knowledge on my part in an answer. :) I also was never great at statistics. ;-)
I tried solving the problem using a difference equation but I got stuck trying that. I'm not sure that was the right way to go really...