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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 )
Y =2 .1
.2 X=2 X=3
.3 Homework. Problems 2, 5, 10, 12, 19, 20 in 10.2. .2
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