Question: Exercise 1.6. Let u be a fixed number in R, and define the convex function up(ar) = e for all r E R. Let X

Exercise 1.6. Let u be a fixed number in R, and define the convex function up(ar) = e" for all r E R. Let X be a normal random variable with mean u = EX and standard deviation o = E(X - u)2 2, i.e., with density H (2-4) 2 f(x) = e 202 oV2TT (i) Verify that Eeux = quuthu202 (ii) Verify that Jensen's inequality holds (as it must): Ep(X) 2 4(EX)

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