variance formula for any distribution
Where u get this formula?
variance = E(Y^2)-(mean)^2
1 answers ( 0 marked as helpful)
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