def. Covariance. Covariance measures the joint variability of two R.V.s; let .

  • When show similar behavior,
  • When show opposite behavior,
  • When , then ; but does not imply
  • Covariance is a generalization of Variance:

thm. Relationship between Covariance and Variance. let . then:

  • When then

thm. Bilinearity of Covariance.

thm. Summed Variance. let . Then

E.G. second summation has terms: