I have a geometric r.v. p(1-p)^(n-1), n = 1, 2, 3, 4, ...
I was able to figure out the conditional mean conditioned on X > a. My answer to this is E[X] + a. I am pretty sure that is correct but if not can anyone let me know where I went wrong.
I am not able to find the conditional pmf for the same condition. Any pointers that can help? Thanks
Write $X \sim \operatorname{Geo}(p)$ as your RV. Bayes's theorem: $$ P(X=r \mid X>a ) = \frac{P(X>a \mid X=r)P(X=r)}{P(X>a)}. $$ The first term in the numerator is just $1$ when $r>a$. Can you see how to do the rest?