Recovering small quantities of calcium in the presence of magnesium can be a difficult problem for an analytical chemist. Suppose the amount of calcium Y to be recovered is uniformly distributed between 4 and 7 mg. The amount of calcium recovered by one method is the random variable
W1 =0.2281+ (0.9948) Y + E1
Where the error term E1 has mean 0 and variance 0.0427 and is independent of Y. A second procedure has random variable
W2=−0.0748+ (1.0024) Y + E2
Where the error term E2 has mean 0 and variance 0.0159 and is independent of Y.
The better technique should have a mean as close as possible to the mean of Y (=5.5), and a variance as small as possible. Compare the two methods on the basis of mean and variance.