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) fi(x) = 1/*(1+x?), (i) f2(@) = 1e- (=] (iv) fa(x) = = (1+x2/3)-2, Only examine variance reductions of the mean and the median. Calculate E(X ) and the me- dian (the value of # such that [" (x)dx = }) using the antithetic variable strategy Answer for i, ii, and iv