We are trying to solve a problem and right now it boils down to a complex data analysis problem.
Let's assume that $x$ is a random variable and we know the probability density function for that $(W(x))$.
Now we are going to perform the experiment for $10^{6}$ times.
The problem is, for each experiment, the instrument can't give us the exact $x$ value. Rather it will give us roughly $10^{2}$ $x$ values and say that the actual $x$ value will be one of those.
So, $10^{6}$ trails will give us $10^{6}$ data sets and each data set will contain roughly $10^{2}$ $x$ values in which only one value is the true value. Now in a straight forward way we can choose a random combination (where one $x$ value from each data set will be chosen randomly) and after plotting the histogram we can calculate statistical error for that and we can say for sure that the exact true combination will minimize statistical error. But I can't check all the combinations because the total number of combinations that I have to check is $({10^2})^{10^6}$.
Hence my question is, Is there any other way to approach this problem?
Image added here, https://ibb.co/eZcSGQ