Sampling random numbers from a distribution

[TarskiMonster]

Let's say we have a given probability distribution. We sample two random numbers from this distribution, say x1 and x2. What is the probability that x1 > x2? Is it always 0.5? Does it even depend on the distribution? Sorry if it appears trivial. I just can't seem to wrap my mind around this.


Thanks!

 

[Ygggdrasil]

Well, you can make the easy argument from symmetry. Since there is nothing special about picking x1 first and x2 second, P(x1>x2) = P(x1<x2). If we assume P(x1=x2) is negligible, clearly P(x1>x2) = P(x1<x2) = 0.5.

 

[statdad]

It will always be $$0.5$$ as long as

$$\Pr(X_1 = X_2) = 0$$