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## Main Question or Discussion Point

Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should

1) The variance is the

2) The

3) So shouldn't we always

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

*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, squared2) The

*expected*value of X is the mean3) 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?