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1 year ago in Probability Theory By Ezra

Can you have a uniform distribution over an infinite set?

InfiniteSet

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By Kabir Answered 10 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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