A professor wishes to make up a true-false exam with n questions. She assumes th

A professor wishes to make up a true-false exam with n
questions. She assumes that she can design the problems in such a way that a
student will answer the jth problem correctly with probability pj and that the
answers to the various problems may be considered independent experiments. Let
Sn be the number of problems that a student will get correct. The professor
wishes to choose pj so that E(Sn)=.7nand so that the variance of Sn is as large
as possible. Show that to achieve this she should choose pj = .7 for all j;
that is she should make all the problems have the same difficulty.