Do these models cover the same hypothesis space of distributions? In other words, given any choice of $\{\backslash$mu i$,\backslash$sigma i$\}$ni$=1,$ does there always exist a choice of $\{\backslash$mu $$i$,\backslash$sigma $$i$\}$ni$=1$ such that pf $=$ pr$?$ If yes, provide a proof. Else, provide a concrete counterexample, including mathematical definitions of the modeled functions, and explain why.