3.1 Solve the below problem Let Y,, Y2, and Y3 be random variables, where E(Y) = 1, E(Y2) V (Y,) = 1,V(Y,) = 3,V(Y;) = 5, Cov (Y,, Y2) = -0.4, Cov(Y,, Y3) = 1/2, and Cov(Y2, Y3) = 2. 2, E (Y3) = -1, = %3D %3D 3.1.1 Find the expected value and variance of U = 2Y, - 3Y 2 + 2Y3. %3D 3.1.2 If W = 2Y, + 2Y2, find Cov(U, W) and state if U and W are independent. %3D

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3.1 Solve the below problem
Let Y,, Y2, and Y be random variables, where
E (Y,) = 1, E(Y,) = 2, E (Y;) = -1,
V (Y,) = 1,V(Y2) = 3,V(Y;) = 5,
Cov (Y,, Y2) = -0.4, Cov(Y1, Y3) = 1/2, and Cov(Y2, Y3) = 2.
3.1.1 Find the expected value and variance of U =
2Y - 3Y 2 + 2Y3.
3.1.2 If W =
2Y, + 2Y2, find Cov(U, W) and state if U and W are independent.
Transcribed Image Text:3.1 Solve the below problem Let Y,, Y2, and Y be random variables, where E (Y,) = 1, E(Y,) = 2, E (Y;) = -1, V (Y,) = 1,V(Y2) = 3,V(Y;) = 5, Cov (Y,, Y2) = -0.4, Cov(Y1, Y3) = 1/2, and Cov(Y2, Y3) = 2. 3.1.1 Find the expected value and variance of U = 2Y - 3Y 2 + 2Y3. 3.1.2 If W = 2Y, + 2Y2, find Cov(U, W) and state if U and W are independent.
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