A rock specimen is randomly selected and weighed two different times. Let w denote the true weight (a number) of the rock, and let X1 and X2 be the two measured weights. Then, X1 = w + E1, and X2 = w + E2, where E1 and E2 are the two measurement errors. Suppose that E1 and E2 are independent, and distributed normally with mean 0 and variance equal to 0.1 (ie, E1, E2~ N(0,0.1)).
a) What is the mean of X1? What is the mean of X2?
b) What is Var(X1)? What is Var(X2)?
c) What is Corr(X1,X2)?