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Unformatted text preview: F ( b ) = 0 since { b n } n ≥ 1 was an arbitrary sequence of values decreasing to∞ . 4. F is right continuous. Proof. Let b ∈ R and { b n } n ≥ 1 be a decreasing sequence of values that converges to b . Thus lim n →∞ F ( b n ) = F ( b ). So, F is right continuous. Notes: • Let a,b ∈ R where a < b . We can write { X ≤ b } as { X ≤ b } = { X ≤ a } ∪ { a < X ≤ b } . Thus P ( a < X ≤ b ) = F ( b )F ( a ), for all a < b . • P ( X < b ) = = = lim n →∞ F ± b1 n ² ....
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 Spring '10
 ClionaGolden
 Math, Statistics, Probability, Probability distribution, Probability theory, Cumulative distribution function

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