Let x, y , z be three random variables which satisfy the following conditions: var(x) = 4, var(y ) = 9, var(z) = 16. cov(x, y ) = −2, cov(z, x) = 3, and y and z are independent. find: (a) cov(x + 2y, y − z). (b) var(3x − y ). (c) var(x + y + z)

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Step-by-step explanation:

Given that X, Y , Z be three random variables which satisfy the following conditions:

Var(X) = 4, Var(Y ) = 9, Var(Z) = 16. Cov(X, Y ) = −2, Cov(Z, X) = 3,

Var(y,z) =0 since given as independent

To find

b)

c) Var(X + Y + Z)

Note:

Var(x+y) = var(x) + Var(Y) +2cov (x,y)

Var(x+2y) = Var(x) +4Var(y)+4cov (x,y)

ab will be equal to