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6 months ago in Probability Theory By Ezra

Can you have a uniform distribution over an infinite set?

InfiniteSet

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By Kabir Answered 3 months ago

They don't. That's the problem. If every integer has the same probability p, and there are infinitely many of them, the sum is either zero (if p = 0) or infinite (if p > 0). Neither equals 1. So it's not a valid probability distribution. In Bayesian statistics, we sometimes use this as an improper prior a mathematical convenience but it's not a real PMF. For a proper uniform distribution, the support must be finite.

 

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