Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 7 / a / i

Table of contents
- Solution i

Solution

Multiplying the beta distribution density by

x

gives a constant multiple of the normalized density with parameters

(p + 1, q)

:

x f_{p, q} (x) = \frac{p}{p + q} f_{p + 1, q} (x) .

Integrating and using the fact that the latter probability density function integrates to one gives

E [X] = \frac{p}{p + q} .

This is a normalization-ratio argument, requiring no explicit integration of the polynomial density.

 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