Here's a result I'm trying to get as part of a larger problem I'm solving: The random variables $A_1,B_1...J_1$ and $A_2,B_2,...J_2$ can take integer values between 0 and 100 such that $A_1+...+J_1=100$, $A_2+...+J_2=100$ and random variables with the same letter (e.g. $C_1,C_2$) must be identically distributed.
What is the distribution that minimises the expected weighted sum of ties, where the weights are given as "A : 1", ... "J: 10"? Intuitively, it should be the distribution with the highest variance. Is this right?