(Solved): Let x1,x2,,xN be iid (independent and identically distributed) random variables with E( ...

Let $$x_1,x_2,\dots ,x_N$$ be iid (independent and identically distributed) random variables with $$\mathrm{E}\left(x_i\right)=?$$ and $$\mathrm{Var}\left(x_i\right)={?}^2<?$$. Consider the following estimators of $$?$$ : $$\begin{array}{rl}{\widehat{?}}_1& =\frac{1}{N?5}\underset{i=1}{\overset{N}{?}}{x}_i\\ {\widehat{?}}_2& =\frac{1}{3}{x}_1+\frac{2}{3(N?1)}\underset{i=2}{\overset{N}{?}}{x}_i\end{array}$$ a. Compute the expected value of each of the estimators above. Which of them are unbiased estimators of $$?$$ ? b. Compute the probability limit (plim) of each of the estimators above. Which of them are consistent estimators of $$?$$ ? Make any assumptions you find necessary.