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*always*be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect:

1) The variance is the

*expected*difference from the mean, squared

2) The

*expected*value of X is the mean

3) So shouldn't we always

*expect*X to be the mean, and so (X - mean)^2 = 0^2 = 0?

But obviously it doesn't work out that way....it's so weird. Does anyone know an intuitive reason why Var[X]

*shouldn't*be zero? What's wrong with my logic?