Assume $Y_1,$dots,$Y_n$ are uncorrelated random variables with $E(Y_i)={}_0+{}_1{x}_i$ and Var$(Y_i)={}^2,$ and that hat$({)}_0$ and hat$({)}_1$ are the LS estimates of ${}_0$ and ${}_1.$ Show each of the following: $($a$)E(hat({)}_0^2)={}_0^2+\frac{{}^2}{n}[1+n\frac{{\stackrel{}{x}}^2}{{\displaystyle \underset{?}{\overset{?}{}}}}(x_i-(\stackrel{}{x}){)}^2].$ Hint: Use general properties of variance and the results of Theorem $15\mathrm{.}3\mathrm{.}1.($b$)E(hat({)}_1^2)={}_1^2+\frac{{}^2}{{\displaystyle \underset{?}{\overset{?}{}}}}(x_i-(\stackrel{}{x}){)}^2.($c$)$