In general, how do you find the distribution given x>c for some c? For example, what's the distribution of an exponential distribution given $\displaystyle \lambda = .1$ and $\displaystyle x>12$? Thanks
Use Bayes formula of conditional pdf (which is equivalent to that of conditional probabilities)
I'm not sure I'm guessing correctly what you mean... the distribution of what given X>c ?
Basically, I'm trying to find $\displaystyle E(X|X>c)$ for some constant c where X is exponential. I thought maybe figuring out the distribution would help. Thanks
So you just have to translate the conditioning as "such that X>c", which gives $\displaystyle \int_c^\infty x f_X(x) ~dx$, where $\displaystyle f_X$ is the pdf of X.