Question

Suppose that E(X) = 2, Var(X) = 9, E(Y) = 0, Var(Y) = 4, and Corr(X, Y) = 0.25. Find: (i) Var(X + Y). (ii) Cov(X, X + Y). (iii) Corr(X + Y, X - Y). (iv) Corr(2X + 3Y, 5X + Y).

          Suppose that E(X) = 2, Var(X) = 9, E(Y) = 0, Var(Y) = 4, and Corr(X, Y) = 0.25. Find:
(i) Var(X + Y).
(ii) Cov(X, X + Y).
(iii) Corr(X + Y, X - Y).
(iv) Corr(2X + 3Y, 5X + Y).

Added by Nathan H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/06/2023

Step 1

We know that Var(X+Y) = Var(X) + Var(Y) + 2*Cov(X,Y). Since Corr(X,Y) = Cov(X,Y) / (SD(X) * SD(Y)), we can find Cov(X,Y) as follows: Cov(X,Y) = Corr(X,Y) * SD(X) * SD(Y) = 0.25 * sqrt(9) * sqrt(4) = 0.25 * 3 * 2 = 1.5 Now, we can find Var(X+Y): Var(X+Y) = Show more…

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Suppose that E(X) = 2, Var(X) = 9, E(Y) = 0, Var(Y) = 4, and Corr(X, Y) = 0.25. Find: (i) Var(X + Y). (ii) Cov(X, X + Y). (iii) Corr(X + Y, X - Y). (iv) Corr(2X + 3Y, 5X + Y).