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variance formula for any distribution

variance formula for any distribution

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1
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Where u get this formula?
 
variance = E(Y^2)-(mean)^2

1 Answer

365 Team
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Hello!  
 
This is a formula that holds true for any distribution where the mean equals the expected value.
In Probability Theory we exclusively deal with such cases, so the two words are synonymous. You can prove this relationship yourself as well.   
 
V(X) = Sum((X-mu)^2 * P(X))
= E[(X – mu)^2]
= E[(X – E(X))^2]
= E[ X^2 – 2X*E(X) + E(X)^2]
= E(X^2) – E[2X * E(X)] + E[E(X)^2] 
= E(X^2) – 2*E(X)*E(X) + E[mu^2] 
= E(X^2) – 2E(X)^2 + mu^2  
= E(X^2) – 2E(X)^2 + E(X)^2
= E(X^2) – E(X)^2
 
Best, 
365 Vik

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