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var(x) = E[(x - E(x))2]
= E[(x - E(x)) (x - E(x))] <-------------Expand into brackets
= E[x2 - xE(x) - xE(x) + (E(x))2] <---Simplify
= E[x2 - 2xE(x) + (E(x))2]
= E(x2) + E[-2xE(x)] + E[(E(x))2]
= E(x2) - 2E[xE(x)] + E[(E(x))2] <---Bring (-2) constant outside
= E(x2) - 2E(x)E[E(x)] + E[(E(x))2] <--- E[xE(x)] = E(x)E(x)
= E(x2) - 2E(x)E(x) + [E(x)]2 <----------E[E(x)] = E(x)
= E(x2) - 2[E(x)]2 + [E(x)]2
var(x) = E(x2) - [E(x)]2
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The mathematician spent all day trying to derive the complex formula.
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The answer depends on what information you have.
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Favourable variance is that variance which is good for business while unfavourable variance is bad for business
