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--- statistical_review [2017/12/11 09:08] – hkimscil
+++ statistical_review [2023/10/05 17:30] (current) – [Rules for the Covariance] hkimscil
@@ Line 1: / Line 1: @@
 ====== Rules for Variance ======
-The variance of a constant is zero.
+see [[:expected value and variance properties]]
-Adding a constant value, c to a variable does not change variance (because the expectation increases by the same amount).
-$ \sigma_{x+c} = Var(X+c) = E[((X_{i} + c)-E(\overline{X} + c))^{2}] = Var(X) $
-Multiplying a constant value, c to a variable increase the variance by square of the constant, c.
-$ \sigma_{c*x} = Var(cX) = c^{2}Var(X)$
-The variance of the sum of two or more random variables is equal to the sum of each of their variances only when the random variables are independent.
-$ Var(X+Y) = Var(X) + 2 Cov(X,Y) + Var(Y)$
-and $ Cov(X,Y) = 0 $
 ====== Rules for the Covariance ======
-The covariance of two constants, c and k, is zero.
+see [[:covariance properties]]
-$Cov(c,k) = E[(c-E(c))(k-E(k)] = E[(0)(0)] = 0$