Hello, I am reproducing the question in the hyperlink given in #1 of this thread so that the viewers of this MHB will conveniently read it.
Hello,I'd like to see some work from you on these. The third one in particular is extremely common and easy. The first is pretty straightforward if you know how to manipulate MGFs to get a martingale. As for the second one, since $S_n$ is even iff n is even, it should be relatively straight forward to attempt as well.
If I were in your shoes, I would start by writing out definitions and applying them to the third one. My guess is that you have foundational issues related to conditional expectations that are holding you back.