conditional distribution

**brogers** · February 21st 2011, 02:04 PM

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

**Moo** · February 22nd 2011, 11:53 AM

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 ?

**brogers** · February 22nd 2011, 06:37 PM

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

**Moo** · February 23rd 2011, 12:54 PM

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.

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