Best estimate for random values Due to work related issues I can't discuss the exact question I want to ask, but I thought of a silly little example that conveys the same idea.
Lets say the number of candy that comes in a package is a random variable with mean $\mu$ and a standard deviation $s$, after about 2 months of data gathering we've got about 100000 measurements and a pretty good estimate of $\mu$ and $s$.
Lets say that said candy comes in 5 flavours that are NOT identically distributed (we know the mean and standard deviation for each flavor, lets call them $\mu_1$ through $\mu_5$ and $s_1$ trough $s_5$).
Lets say that next month we will get a new batch (several packages) of candy from our supplier and we would like to estimate the amount of candy we will get for each flavour. Is there a better way than simply assuming that we'll get "around" the mean for each flavour taking into account that the amount of candy we'll get is around $\mu$?
I have access to all the measurements made, so if anything is needed (higher order moments, other relevant data, etc.) I can compute it and update the question as needed.
Cheers and thanks!

I find the question a bit unclear but since you have an estimate of the mean and standard deviation for a single package, assuming the candy in each package is independent why not use,  $E(X_1+X_2)=E(X_1)+E(X_2)$ and $Var(X_1+X_2) = Var(X_1) + Var(X_2) + 2*cov(X_1,X_2)$ ?
