Chapter 16, Problem 46SE

a.

To determine

Prove that $E\left(W_t\right)=\mu$

b.

To determine

Prove that ${\sigma }_t^2=\left(\frac{\alpha \left[1-{\left(1-\alpha \right)}^{2t}\right]}{2-\alpha }\right)\left(\frac{{\sigma }^2}{n}\right)$

c.

To determine

Construct a control chart for the example 16.9 using ${\mu }_0=40$.