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Assuming that we have a model that outputs these (binomial) probabilities for 10 independend events: 0.89, 0.69, 0.41, 0.92, 0.43, 0.52, 0.90, 0.98, 0.56, 0.85

I would like to know if there is a way to find the expected number of events happening, as in: "if the model is calibrated correctly, it should result in 'X' hits and '10-X' misses".

I do know that I can find the range of hits by running a simulation and constructing a histogram, however I was wondering whether there is a more elegant way.

Thank you.

Ann-Marie
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  • This is a good question. It actually is a simpler version of the question that asks how to obtain the full probability distribution of the number of events. If you're interested in that, please see http://stats.stackexchange.com/questions/41247 and http://stats.stackexchange.com/questions/5347. However, by asking for the expectation you have greatly simplified the problem: what do you know about the expectation of a sum of variables? – whuber Feb 29 '16 at 14:08

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