Consider the potential outcomes framework from Appendix 13.3. Suppose \(X_{i}\) is a binary treatment that is independent of the potential outcomes \(Y_{i}(1)\) and \(Y_{i}(0)\). Let \(T E_{i}=Y_{i}(1)-Y_{i}(0)\) denote the treatment effect for individual \(i\).

a. Can you consistently estimate \(E\left[Y_{i}(1)\right]\) and \(E\left[Y_{i}(0)\right]\) ? If yes, explain how; if not, explain why not.

b. Can you consistently estimate \(E\left(T E_{i}\right)\) ? If yes, explain how; if not, explain why not.

c. Can you consistently estimate \(\operatorname{var}\left[Y_{i}(1)\right]\) and \(\operatorname{var}\left[Y_{i}(0)\right]\) ? If yes, explain how; if not, explain why not.

d. Can you consistently estimate \(\operatorname{var}\left(T E_{i}\right)\) ? If yes, explain how; if not, explain why not.

e. Do you think you can consistently estimate the median treatment effect in the population? Explain.