# A function of two cumulative probability distributions with same first 2 moments

Let $\Phi_1$ and $\Phi_2$ be cumulative probability distribution functions with domain $[L, \infty)$, $L\geq 0$, both distributions having the same expectation $\mu$ and the same second moment (hence finite second moment, $\textbf{a modification and added constraint to the earlier post}$), and the kurtosis of the distribution behind $\Phi_2$ is higher than that of $\Phi_1$ (new constraint).