Sampling random numbers from a distribution

  • #1

Main Question or Discussion Point

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!
 

Answers and Replies

  • #2
Ygggdrasil
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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.
 
  • #3
statdad
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It will always be [tex] 0.5 [/tex] as long as

[tex]
\Pr(X_1 = X_2) = 0
[/tex]
 

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