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by krcz
4818 days ago
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Using uniform distribution definition from Wikipedia ("all intervals of the same length on the distribution's support are equally probable") we get
P(X \in [0,1)) = P(X \in [1, 2)) = P(X \in [2, 3)) = ... By countable additivity
P(\Omega) = P(X \in [0, \infty)) = P(X \in [0, 1)) + P(\X \in [1, 2)) + ... = P(X \in [0, 1)) + P(X \in [0, 1)) + ... And this evaluates to 0 if P(X \in [0, 1)) = 0 and to \infty if P(\X \in [0, 1)) > 0. |
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