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(Nod)

Printable View

- Feb 21st 2011, 02:04 PMbrogersconditional 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 $\displaystyle \lambda = .1$ and $\displaystyle x>12$? Thanks(Nod)

- Feb 22nd 2011, 11:53 AMMoo
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 ? - Feb 22nd 2011, 06:37 PMbrogers
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 (Wink)

- Feb 23rd 2011, 12:54 PMMoo
Okay.

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.