Supplementary Exercise 4.73 of IPS7e
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Two scales for measuring weight. For an item with true weight
of 2 g, the scales give results:
  X with mean 2.000 g and std.dev. 0.002 g,
  Y with mean 2.001 g and std.dev. 0.001 g.
Also, X and Y are independent.

Note that in the terminology to be introduced in Session 5, the estimate Y
is more precise than X, but less accurate.

(a) Z = Y-X.
    EZ = EY-EX = 2.001-2.000 = 0.001 g
    VarZ = VarY+VarX = 0.002^2 + 0.001^2 = 0.000005 g^2
    sdZ = sqrt(VarZ) = 0.00224 g

(b) Z = (X+Y)/2
    EZ = (EX+EY)/2 = (2.000+2.001)/2 = 2.0005 g
    VarZ = 0.5^2 *(VarX+VarY) = 0.25*(0.002^2 + 0.001^2)
         = 0.00000125 g^2
    sdZ = sqrt(VarZ) = 0.00112 g

Therefore the average, Z, is more variable than Y, but its mean is closer to
the true value. In the above terminology, we could say Z is more accurate
than Y, but less precise.