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# CDF - Le arning Obje s ctive fine ulativedistribution...

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Learning Objectives Define cumulative distribution function Set up and use the cumulative distribution function of discrete and continuous random variables.

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CDF Cumulative distribution function (CDF) denoted F X (x) gives the P(X x) CDF defined for both continuous and discrete RV’s ( 29 ( 29 = = x k X X k p x X P x F ) ( ( 29 ( 29 dt t f x X P x F x X X - = = ) (
PDF & CDF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 x PDF CDF

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CDF F X (x)->0 as x->- F X (x)->1 as x->
CDF Monotonic, nondecreasing if x y , then F X x ( 29 F X y ( 29

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PMF CDF Sum PMF to get CDF Take differences of CDF to get PMF F X k (29 = p X i ( 29 i =-∞ k p X k ( 29 = PX k ( 29 - PX k - 1 ( 29

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CDF - Le arning Obje s ctive fine ulativedistribution...

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