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====== Covariance Properties ======

  - The covariance of two constants, c and k, is zero. \\ $Cov(c,k) = E[(c-E(c))(k-E(k)] = E[(0)(0)] = 0$
  - The covariance of two independent random variables is zero. \\ $Cov(X, Y) = 0$ When X and Y are independent.
  - The covariance is a combinative as is obvious from the definition. \\ $Cov(X, Y) = Cov(Y, X)$
  - The covariance of a random variable with a constant is zero. \\ $Cov(X, c) = 0 $
  - Adding a constant to either or both random variables does not change their covariances.  \\ $Cov(X+c, Y+k) = Cov(X, Y)$
  - Multiplying a random variable by a constant multiplies the covariance by that constant. \\ $Cov(cX, kY) = c*k \: Cov(X, Y)$
  - The additive law of covariance holds that the covariance of a random variable with a sum of random variables is just the sum of the covariances with each of the random variables. \\ $Cov(X+Y, Z) = Cov(X, Z) + Cov(Y, Z)$
  - The covariance of a variable with itself is the variance of the random variable.  \\ $Cov(X, X) = Var(X) $


For additional info see [[http://prob140.org/textbook/content/Chapter_13/02_Properties_of_Covariance.html]]