The midpoint rule can be transformed using any distribution function F by evaluating at F −1  2i−1 2n  with n equally weighted points. Apply this transformed midpoint rule to the logistic distribution...

The midpoint rule can be transformed using any distribution function F by evaluating at F −1  2i−1 2n  with n equally weighted points. Apply this transformed midpoint rule to the logistic distribution with F(x) = 1/(1 + e−x ). Compare your computation of the variance to your result in Exercise 10.2.