Lecture-24

Lecture-24 - Lecture 24. See Chapter 10, section 2....

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Unformatted text preview: Lecture 24. See Chapter 10, section 2. Definition. Suppose X and Y are random variables on the same probability space. The covariance of X and Y is: Cov(X, Y ) := E X − E(X ) Y − E(Y ) . Fact. Cov(X, Y ) = E(XY ) − E(X )E(Y ). Fact. Var(aX + bY ) = a2 Var(X ) + b2 Var(Y ) + 2abCov(X, Y ) Problem. Given a pair of random variables X , Y with joint pmf as follows, find Cov(X, Y ) X=1 Y =1 Y =2 .1 .2 X=2 X=3 .1 .3 Homework. Problems 2, 5, 10, 12, 19, 20 in 10.2. .2 .1 ...
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