Let u be a fixed number in JR., and define the convex function

rp(x) = eux for all x E R Let X be a normal2random variable with mean

= lEX and standard deviation a = [IE(X - p,) ] i.e., with density

p,1

("-'2) f(x)= 1 e 2.. 2

(ii) Verify that Jensen's inequality holds (as it must): !Erp(X) rp(IEX).