Correction of Hwk11-Problem 4-ii

Hwk 11 (4-ii)'s solution is wrong.
I must show that for all F.
(New Answer: Fix arbitrary F. Then from Jensen's inequality,
E[u(x)] = E[-x^2 + 6x +1] = E[-x^2] + 6(E[x]) +1
< -(E[x])^2 + 6(E[x]) +1 = u(E[x]).)