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--- statistical_review [2017/12/11 08:45] – 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]]
-    * $ \sigma_{c} = VAR(c) = 0 $
+====== 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.
-    * $\text{VAR}(X+Y) = \text{VAR}(X) + 2 \text{COV}(X,Y) + \text{VAR}(Y) $
-    * because X and Y are independent to each other Covariance X and Y is 0.
-    * $\text{VAR}(X+Y) = \text{VAR}(X) + \text{VAR}(Y) $
-  -