2.16 Bivariate Random Variables Discrete Case Continuous Case ...

More documents

Recommendations

Info

2.16 Bivariate RV’s Now let’s look at what happens when you consider 2 RV’s simultaneously. Example: Choose a person at random. Look at height and weight (X, Y ). Obviously, X and Y will be related somehow. 2
2.16 Bivariate RV’s Discrete Case Definition: If X and Y are discrete RV’s, then (X, Y ) is called a jointly discrete bivariate RV. The joint (or bivariate) pmf is f(x, y) = Pr(X = x, Y = y). Properties: (1) 0 ≤ f(x, y) ≤ 1. (2) ∑ x ∑ y f(x, y) =1. (3) A ⊆R 2 ⇒ Pr((X, Y ) ∈ A) = ∑∑ (x,y)∈A f(x, y). 3
Page 1: 2.16 Bivariate RV’s 2.16 Bivariat
Page 5 and 6: 2.16 Bivariate RV’s By the law of
Page 7 and 8: 2.16 Bivariate RV’s If A ⊆R 2 ,
Page 9 and 10: 2.16 Bivariate RV’s Example: Supp
Page 11 and 12: 2.16 Bivariate RV’s Properties: F
Page 13 and 14: 2.16 Bivariate RV’s Example: Supp
Page 15 and 16: 2.16 Bivariate RV’s Marginal Dist
Page 17 and 18: 2.16 Bivariate RV’s Example (disc
Page 19 and 20: 2.16 Bivariate RV’s Example: f(x,
Page 21 and 22: 2.16 Bivariate RV’s f X (x) = ∫

2.16 Bivariate Random Variables Discrete Case Continuous Case ...

Create successful ePaper yourself

Delete template?

Save as template?