# conditional distribution

• February 21st 2011, 02:04 PM
brogers
conditional distribution
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 $\lambda = .1$ and $x>12$? Thanks(Nod)
• February 22nd 2011, 11:53 AM
Moo
Hello,

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 ?
• February 22nd 2011, 06:37 PM
brogers
Basically, I'm trying to find $E(X|X>c)$ for some constant c where X is exponential. I thought maybe figuring out the distribution would help. Thanks (Wink)
• February 23rd 2011, 12:54 PM
Moo
Okay.

So you just have to translate the conditioning as "such that X>c", which gives $\int_c^\infty x f_X(x) ~dx$, where $f_X$ is the pdf of X.