Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should(adsbygoogle = window.adsbygoogle || []).push({}); alwaysbe 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 theexpecteddifference from the mean, squared

2) Theexpectedvalue of X is the mean

3) So shouldn't we alwaysexpectX 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'tbe zero? What's wrong with my logic?

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# Intuitively, shouldn't variance always be 0?

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