Last answered:

26 May 2020

Posted on:

09 May 2020

0

variance formula for any distribution

Where u get this formula?   variance = E(Y^2)-(mean)^2
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Instructor
Posted on:

26 May 2020

0
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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