Consider $n$ random variables $X_i$ with $i=1,2,...,n$, each drawing values from identical normal distributions with mean $\mu=0$ and standard deviation $\sigma=const.$ so that expectation values are $\langle X_i\rangle=0$ and $\langle X_i^2\rangle=const.$ Is there a way to modify these distributions to additionally enforce
not just on average, but for each set of elements drawn? How can one generate and parameterize explicit distribution functions to numerically produce such sets of elements?
Naively, I suppose one could generate elements from the original distribution without the extra constraint and project to the subset of elements that satisfies the additional constraint... But that seems a bit unsatisfactory. Any analytical way to incorporate the constraint?