# Probability of extrema given uncertain measurements

by greendolphin   Last Updated August 13, 2019 20:19 PM - source

Detecting extrema under uncertainty?

I realized that my question was not asked very clearly. So here is another way to phrase the question:

I have ten objects. With a different independent scale for each object, I measure their weights 100 times each (1000 measurements in total). I can compute the variance $$\sigma^2_i$$ of each of the scales based on the distribution of the measurements of each object.

Given my measurements and my $$\sigma^2_i$$, what is the probability for each of the objects being, in fact, the heaviest?