2.16 Bivariate Random Variables Discrete Case Continuous Case ...

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2.16 Bivariate RV’s Bivariate cdf’s Definition: The joint (bivariate) cdf of X and Y is F (x, y) ≡ P (X ≤ x, Y ≤ y), for all x, y. F (x, y) = ⎧ ⎪⎨ ⎪⎩ ∑∑ s≤x,t≤y f(s, t) discrete ∫ y −∞ ∫ x −∞ f(s, t) ds dt continuous 10
2.16 Bivariate RV’s Properties: F (x, y) is non-decreasing in both x and y. lim x→−∞ F (x, y) = lim y→−∞ F (x, y) =0. lim x→∞ F (x, y) =F Y (y) =Pr(Y ≤ y) lim y→∞ F (x, y) =F X (x) =Pr(X ≤ x). F (x, y) is cts from the right in both x and y. 11
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2.16 Bivariate Random Variables Discrete Case Continuous Case ...

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