A naive way to implement the antithetic variable scheme is to use both U and 1 - U in an inver- sion simulation. Examine empirically whether this method leads to variance reduction for the distributions (i) (x) = 1/(1+x), (ii) 2(x) = e|| (iv) f(x)=(1+x/3), Only examine variance reductions of the mean and the median. Calculate E(X) and the me- dian (the value of such that f(x)dx = ) using the antithetic variable strategy Answer for i, ii, and iv