“The mean of Y is nβ. The variance of Y is the sum of the vj, which is less than nK2.” Been a while for me, but doesn’t this require the lotteries to be uncorrelated? If so, that should be listed with your axioms.
You know, I didn’t even realise I’d used “independence” both ways! Most of the time, it’s only worth pointing out the fact if the random variables are not independent.
No problem. (Don’t you love it when people use the same symbol for multiple things in the same work? I know as a mechanical engineer, I got so much joy from remembering which “h” is the heat transfer coefficient and which is the height!)
“The mean of Y is nβ. The variance of Y is the sum of the vj, which is less than nK2.” Been a while for me, but doesn’t this require the lotteries to be uncorrelated? If so, that should be listed with your axioms.
It requires the lotteries to be independent), which implies uncorrelated. Stuart_Armstrong specified independence.
Ugh, color me stupid—I assumed the “independence” we were relaxing was probability-related. Thanks RobinZ.
You know, I didn’t even realise I’d used “independence” both ways! Most of the time, it’s only worth pointing out the fact if the random variables are not independent.
No problem. (Don’t you love it when people use the same symbol for multiple things in the same work? I know as a mechanical engineer, I got so much joy from remembering which “h” is the heat transfer coefficient and which is the height!)