2 problems

Let $c>1$, and let $U_c$ be the Choquet simplex of probability distributions solving the size-bias scaling relation associated with $c$. Write $c=\exp(\sigma^2/2)$, and let $Z$ be…

Let $c=\exp(\sigma^2)$ with $\sigma>0$, and let $\ell(b,c)$ denote the single-orbit discrete distributions supported on $\\{\ldots,b/c^2,b/c,b,bc,bc^2,\ldots\\}$ that have the logn…