I hope the below link will be helpful...
Bertrand's ballot theorem - Wikipedia, the free encyclopedia
I am having a lot of trouble with the following question:
A point starts at the origin on the real line and takes unit steps to the right with probability p or to the left with probability q = 1 - p. Assuming that the steps are independent, find the expected value of the squared distance from the origin after n steps.
I'm not really sure about how to attempt the question. I think it is asking for the variance though? Any help would be appreciated.
I hope the below link will be helpful...
Bertrand's ballot theorem - Wikipedia, the free encyclopedia