Consider an observable $X$ which follows some unknown statistical distribution $P$, with elements $x\in X$ in the interval $-1<x<1$.
Consider also an observable $Y$ which follows a uniform random distribution, with elements $y\in Y$ in the interval $-1<y<1$.
Let's say we make a sequence of observations $O$, which consist of elements $(z,p)$, such that:
- $z\in X$ with probability $p$
- $z\in Y$ with probability $1-p$
Is there a way to use Mathematica to obtain some sort of "best fit" for the probability distribution $P$ of observable $X$ from the "$Y$ contaminated" observations $O$?
For example, given the particular sequence of observations
what is a best fit for probability distribution $P$?