An object has a weight W. When it is weighed with machine 1, a value X1 is obtained. When it is weighed with machine 2, a value X2 is obtained. The value X1 has a mean IV and a standard deviation 3. The value X2 has a mean W and a standard deviation 4. The values X1 and X2 are independent.
(a) Suppose that an engineer uses the value A = (X1 + X2)/2 to estimate the weight. What are the expectation and the standard deviation of A?
(b) Suppose that an engineer uses the value B = δX1 + (1 - δ)X2 to estimate the weight. What value of δ gives an estimate B with the smallest standard deviation? What is this smallest standard deviation?