Homework SourseSuppose Ex2 Varx9 EY0 VarY4 CorrX Y14 Determine e Cov2X 3Y1
Suppose E(x)=2, Var(x)=9, E(Y)=0, Var(Y)=4, Corr(X, Y)=1/4. Determine:
(e) Cov(2X, 3Y-1)
(f) Cov(5x+1, 2x-1)
(g) Cov(x+y, x-y)
(i) Cov(2x+1/4y, 1/2x+3y)
Solution
E.
As
cov (x, y) = cor (x, y) sqrt [var(x) var(y)]
And
cov (2x, 3y - 1) = 2(3) cov (x, y) = 6 cov (x, y)
Then
cov (2x, 3y - 1) = 6 cor (x, y) sqrt [var(x) var(y)]
= 9 [ANSWER]
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F.
As
cov (x, x) = var (x)
And
cov (5x + 1, 2x - 1) = 5(2) cov (x, x) = 10 cov (x, x)
Then
cov (5x + 1, 2x - 1) = 10 var (x) = 90 [ANSWER]
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g)
As
Cov(x + y, x - y) = Cov (x, x) - Cov (x, y) + Cov (y, x) - Cov (y, y)
As Cov (x, y) = Cov (y, x), then
= Var(x) - Var (y)
= 9 - 4
= 5 [ANSWER]
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I)
Cov (2x + 1/4y, 1/2x + 3y) = Cov(x, x) + 6Cov (x, y) + 1/8 Cov (y, x) + 3/4 var (y)
= Var(x) + 6.125 Cov (x, y) + 3/4 Var(y)
= 9 + 6.125(1.5) + 3/4 (4)
= 21.1875 [ANSWER]
