# Thread: Conditional distribution of a uniformly distributed random variable

1. ## Conditional distribution of a uniformly distributed random variable

Let $U$ denote a random variable uniformly distributed over $(0,1)$. Compute the conditional distribution of $U$ given that
$U>a$
where $0

So if I understand this correctly, we desire

$f_{U|U>a}(U|U>a)=\frac{f(U, U>a)}{f_{U>a}(U>a)}$

How do I proceed from here, assuming I'm correct?

2. ## Re: Conditional distribution of a uniformly distributed random variable

Hello,

You're applying the formula for the conditional density in a bizarre way. It's the conditional density of a random variable with respect to another random variable, not with respect to an event. And here, {U>a} is an event. You can't write that. It makes no sense to take the "density" of U>a !

U>a should remind you of the cumulative density function. And it's like a density because it determines the distribution of a random variable. And since it works with probabilities, it will be better

So we're looking for P(U<x|U>a). Of course, the value will depend on whether x>a or not, and if it's in (0,1). But it's not an insurmountable obstacle. And if you want the pdf, you know what to do once you get the conditional cdf