1. Prove that the bootstrap estimate of the bias of the sample second
   central moment is sum(x_i - xbar)^2/2.  (Notice that here the x's are
   used to denote the realization of the random sample, rather than the
   random sample.)

2. Show that for the sample mean, both the bootstrap estimate of the
   bias and the Monte Carlo estimate of the bootstrap estimate of the
   bias using the mean resampling vector are 0.
   Is this also true for the ordinary Monte Carlo estimate?

3. Suppose it is desired to use Monte Carlo to estimate the difference
   in the variance of two estimators, T_1 and T_2, i.e., we wish to
   estimate V(T_1) - V(T_2).  Suppose it is known that both of these 
   estimators are unbiased (i.e., they have the same expectation).
   Why is it better to compute the Monte Carlo estimate as V(T_1-T_2),
   rather than as V(T_1) - V(T_2)?