One More Formula for the Variance

Authors: Sabiou Inoua

This short paper establishes one more formula for the variance. Consider a random variable X whose possible values are x1, …, xn with probabilities p1, …, pn of occurring, respectively. Pick two of these possible values successively (each xi having the probability pi of being chosen). Compute the difference between the two chosen values. Square the difference. Claim: you are expected to get (twice) the variance of X. This formula makes the variance appear an even more natural measure of dispersion than usually thought.

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[v1] 2013-06-05 07:25:19

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