I. PowER DERIVATIVES WITH THE LOG-NoRMAL DISTRIBUTION Consider a non-dividend-paying stock S. Given S has price S, at date t, the return on has a log-normal distribution at T under Q with mean-?2(T-)/2 and variance ?2(T-t), In this question we study the date t price X of a derivative that pays off Xr ST at maturity T for some number a. This is called a power derivative. Throughout we fix the risk-free rate r = 0. 1. Here we study the Qmean of the distribution and verify that the FTAP prices S correctly. I. PowER DERIVATIVES WITH THE LOG-NoRMAL DISTRIBUTION Consider a non-dividend-paying stock S. Given S has price S, at date t, the return on has a log-normal distribution at T under Q with mean-?2(T-)/2 and variance ?2(T-t), In this question we study the date t price X of a derivative that pays off Xr ST at maturity T for some number a. This is called a power derivative. Throughout we fix the risk-free rate r = 0. 1. Here we study the Qmean of the distribution and verify that the FTAP prices S correctly