申論題

6. (35%) Let w_T denote the terminal wealth of a uni-dollar investment after T periods. Consider two possible cumulative distribution functions (CDFs) for w_T as follows.
where N(μ, σ²) represents the normal distribution with the mean to be u and the variance to be σ². For any utility function U'(•) ≥ 0, the expected utility under F or G is

Last，Φ(c)≡dx is the CDF for the standard normal distribution. 

6.1 (5%) Find such that