Assume that Y1 Y2 and Y3 are random variables with the follo

Assume that Y1, Y2, and Y3 are random variables, with the following: E(Y1) = l.7 E(Y2) = -1.3 E(Y3) = 4 Var(yx) = 3.6 Var(Y2) = 2.4 Var(Y3) = 4.9 Cov(Y1,Y2) = 0.2 Cov(Y2,Y3)=-o.5 Cov(Y1,Y3) = 0.3

Solution

var (5Y1 + 8Y2 - 11Y3) = var(5Y1) + var(8Y2) + var(11Y3) + 2*5*8*cov(Y1,Y2) + 2*5*(-11)*cov(Y1,Y3) + 2*8*(-11)*cov(Y2,Y3)

= 5^2*var(Y1) + 8^2*var(Y2) + 11^2*var(Y3) + 80*cov(Y1,Y2) - 110*cov(Y1,Y3) - 176*cov(Y2,Y3)

= 25*var(Y1) + 64*var(Y2) + 121*var(Y3) + 80*cov(Y1,Y2) - 110*cov(Y1,Y3) - 176*cov(Y2,Y3)

= 25*(3.6) + 64*(2.4) + 121*(4.9) + 80*(0.2) -110*(0.3) -176*(-0.5)

= 90 + 153.6 + 592.9 + 16 - 33 + 88

= 907.5