Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2....

Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2. LetV=X2−X3+X4 and W=X1−2X2+X3+ 4X4.

(a) Find E(V) and E(W).

(b) Find Var(V) and Var(W).

(c) Find Cov(V,W).(

d) Find the correlation coefficientρ(V,W). Are V and W independent?

Expert Solution

orchestra answered 2 years ago

Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2....

Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2. LetV=X2−X3+X4 and W=X1−2X2+X3+ 4X4. (a) Find E(V) and E(W). (b) Find Var(V) and Var(W). (c) Find Cov(V,W).( d) Find the correlation coefficientρ(V,W). Are V and W independent?

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Suppose that X1, X2, X3, X4 is a simple random (independent and identically distributed) sample of...

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Consider independent random variables X1, X2, and X3 such that X1 is a random variable having mean 1 and variance 1, X2 is a random variable having mean 2 and variance 4, and X3 is a random variable having mean 3 and variance 9. (a) Give the value of the variance of X1 + (1/2)X2 + (1/3)X3 (b) Give the value of the correlation of Y = X1- X2 and Z = X2 + X3.

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2...

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2 = X1 −X2, Y3 =X1 −X3. Find the joint pdf of Y = (Y1,Y2,Y3)′ using : Multivariate normal distribution properties.

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Question

Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2....

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Expert Solution

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