The covariance is symmetric, because multiplication of real random variables is commutative. Expanding with the bilinearity just proved gives
(1)
Identical probability distributions imply equal second moments and equal means, hence equal variances. Therefore the assertion is true, with
(2)
The cancellation shows exactly why no assumption of independence is needed.

Ancestors (11)

  1. 3F
  2. Section I
  3. Paper 2
  4. ia
  5. 2004
  6. Past exam of the mathematics course of the University of Cambridge
  7. Mathematics course of the University of Cambridge
  8. Course of the University of Cambridge
  9. University of Cambridge
  10. List of universities
  11. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version