Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 6 / a / iii

Table of contents
- Solution iii

Solution

The products

T U

and

U V

share

U

, so they are not independent. Using the definition of covariance and the independence of

T, U, V

,

Cov (T U, U V) = E (T U^{2} V) - E (T U) E (U V) = (E T) (E U^{2}) (E V) - 1 = 2 - 1 = 1.

By contrast,

T U

and

VW

depend on disjoint sets of independent random variables, so they are independent and have zero covariance. Hence

Cov (T U, U V) = 1, Cov (T U, VW) = 0.

 Ancestors (12)

 View article source

 Discussion (0)

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