Let (Ω, ℱ, P) be a probability space, and (E, ℰ) a measurable space. Then an (E, ℰ)-valued random variable is a function X: Ω→E, which is (ℱ, ℰ)-measurable. That is, such function that for every subset B ∈ ℰ, its preimage lies in ℱ: X −1(B) ∈ ℱ, where X −1(B) = {ω: X(ω) ∈ B}.
(Wikipedia: Random Variable: Formal Definition)
Thought I’d share one the few things that brought a smile to my face today. I love and miss math.
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