Heating oil futures and natural gas futures for the various regions are tied to the average temperature since oil/gas heating usage is tied to temperature acros

Heating oil futures and natural gas futures for the various regions are tied to the average temperature since oil/gas heating usage is tied to temperature across days and not just the min or max. So to go back to your excellent analogy, I am certainly asking for the average middle (the first moment) and not a point prediction. ps: you should write more, we need better scientific explanations!