Are the events mutually exclusive?
quote:quote:Going off of the general mood of the football board, this may be the case
I think by definition it would have to be. I guess which might be somewhat problematic if E[X]~0
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Seriously though, for means that are low numbers and for numbers close to the number of possible events I think that too much of the approximation will be sort of chopped off by the boundary, and I think that'll be the case for a lot of football teams.
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How difficult were they?
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Shouldn't the case where all the win probabilities are equal yield the most area behind 0 for any mean?
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Seriously though, for means that are low numbers and for numbers close to the number of possible events I think that too much of the approximation will be sort of chopped off by the boundary, and I think that'll be the case for a lot of football teams.
So I got curious about how well the normal distribution would approximate the answer to your question. Here are my results.The answer is for realistic situations I think the normal distribution is an apt approximation. One note: you may want to write your own simulation code just to make sure there are no errors in mine where the data might be skewed, but based on how well the simulation matches with the approximation I think I did everything correctly.