We have two random variables X and Y. Also, introduce two constants a and b. What is true about the expectation and the variance of
We have two random variables X and Y. Also, introduce two constants a and b. What is true about the expectation and the variance of aX + bY?
1. E(aX + bY) = a2E(X) + b2E(Y) and Var(aX + bY) = aVar(X) + bVar(Y).
2. E(aX + bY) = aE(X) + bE(Y) and Var(aX + bY) = a2Var(X) + b2Var(Y) + 2abCov(X, Y).
3. E(aX + bY) = aE(X) + bE(Y) and Var(aX + bY) = aVar(X) + bVar(Y) + abCov(X, Y).
4. E(aX + bY) = aE(X) + bE(Y) and Var(aX + bY) = a2Var(X) + b2Var(Y).
5. E(aX + bY) = a2E(X) + b2E(Y) and Var(aX + bY) = a2Var(X) + b2Var(Y) + 2abCov(X, Y).
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Authors: Leland Blank, Anthony Tarquin
7th Edition
9781259027406, 0073376302, 1259027406, 978-0073376301
