... +t 2 x 2 2!+t3x33!+ ···(3.10 .20 )mx(t) = E[etx] = 1 + t E[x] +t 2 2!E[x 2 ] +t33!E[x3] + ···(3.10 .21 )ddtmx(t) = E[x] + t E[x 2 ] +t 2 2!E[x3] + ···(3.10 .22 )d 2 dt 2 mx(t) ... of thedie are 3, 2, 3, 3, 2, 3, therefore the average is46· 3 + 2 6· 2 = 2 23. Also optimal: (1) is it bigger than 2? (2) is it odd? (3) is it bi gger than 4? Gives 2, 2, 3, 3, 3, 3. Also ... nonnegative square root; (2) Expressold variab le in terms of new: z = u 2 , this is one-to-o ne on A (but not one-to-one on all of R);(3) then the derivative is 2u, which is n onne gati ve...