# HG changeset patch # User Oleksandr Gavenko # Date 1459866722 -10800 # Node ID fa0dee44fe1fa217f9e9f9868aa4a3ae42e9977d # Parent 44779fa3053dad23370caf01afce780e1d2f69ba Law of total variance. diff -r 44779fa3053d -r fa0dee44fe1f probability-discrete.rst --- a/probability-discrete.rst Tue Apr 05 17:22:50 2016 +0300 +++ b/probability-discrete.rst Tue Apr 05 17:32:02 2016 +0300 @@ -261,6 +261,9 @@ .. math:: var(X|Y) = E[X²|Y] - (E[X|Y])² +Law of total variance +===================== + By applying expected value by :math:`Y` on both sides: .. math:: E[var(X|Y)] = E[E[X²|Y]] - E[(E[X|Y])²] = E[X²] - E[(E[X|Y])²]