Chapter 12.3, Problem 17E

a.

To determine

Calculate the value of $E\left(Y_{ij}\right)$.

b.

To determine

Prove that $Y_{1j}\text{'}\text{s}$, for $j=1,2,\mathrm{...},n$ are not normally distributed.

c.

To determine

Prove that $\text{Cov}\left(Y_{1j},Y_{2j}\right)=\frac{1}{3}$ for $j=1,2,\mathrm{...},n$.

d.

To determine

Prove that $D_j=Y_{1j}-Y_{2j}\text{are independent, normally distributed random variables}\text{.}$

e.

To determine

Provide another example that illustrates the same phenomenon.