Variance Sum Law II
Prerequisites
Variance
Sum Law I
Learning Objectives
 State the variance sum law when X and Y are not assumed to be independent
 Compute the variance of the sum of two variables if the variance of
each and their correlation is known
 Compute the variance of the difference between two variables if the
variance of each and their correlation is known
Recall that when the variables X and Y are independent,
the variance of the sum or difference between X and Y can be written
as follows:
which is read "The variance of X plus or
minus Y is equal the variance of X plus the variance of Y.
When X and Y are correlated, the following formula
should be used:
where ρ is the correlation between X and Y
in the population.
If the variances and the correlation are computed
in a sample, then the following notation is used to express the
variance sum law:
.
