2.16 Bivariate Random Variables Discrete Case Continuous Case ...

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2.16 Bivariate RV’s Continuous Case Definition: If X and Y are cts RV’s, then (X, Y )isa jointly cts RV if there exists a function f(x, y) such that (1) f(x, y) ≥ 0, ∀x, y. (2) ∫∫ R 2 f(x, y) dx dy =1. (3) Pr(A) =Pr((X, Y ) ∈ A) = ∫∫ A f(x, y) dx dy. In this case, f(x, y) is called the joint pdf. 6
2.16 Bivariate RV’s If A ⊆R 2 ,thenPr(A) is the volume between f(x, y) and A. Think of f(x, y) dx dy ≈ Pr(x
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2.16 Bivariate Random Variables Discrete Case Continuous Case ...

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