W is true weight X and Y are two measured weights A and B ar

W is true weight. X and Y are two measured weights. A and B are two measurement errors. X = W + A and Y = W + B.

A and B are independent and normally distributed witih mean = 0 and variance = 0.1.

1: What is the mean of X and Y?

2: What is the variance of X and Y?

3: What is the correlation of X and Y, Corr(X,Y)?

Please show work.

Solution

x=W+A

Y = W + B.

Mean =0 var =0.1

1) Mean of X = W+ Mean of A

   Mean of Y = W + Mean of B

2) Var(X) = var(A) and Var(Y) = Var(B)

3) corr (x,y) = E(XY)-E(X)E(Y)

                  = 0 as x and y are independent.(when A and B are independent x,y are independent)