Probability of extrema given uncertain measurements

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

I recently asked this question:

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?

Thank you for your help!



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