Differences

This shows you the differences between two versions of the page.

--- statistical_review [2017/12/11 08:54] – 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]]
+====== Rules for the Covariance ======
-Adding a constant value, c to a variable does not change variance (because the expectation increases by the same amount).
+see [[:covariance properties]]
-$$ \sigma_{x+c} = VAR(X+c) = E[((X_{i} + c)-E(\overline{X} + c))^{2}] = VAR(X) $$
-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.
-$$ VAR(X+Y) = VAR(X) + 2 COV(X,Y) + VAR(Y)$$