MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Say $\boldsymbol{\beta}$ is a random n-vector having the multivariate normal distribution with mean $\boldsymbol{b}$ and covariance matrix $\boldsymbol{S}$. And let $\boldsymbol{x}_1$ and $\boldsymbol{x}_2$ be two row vectors with n elements each. Then we know the distribution of $\frac{exp(\boldsymbol{x_1\beta})}{1+exp(\boldsymbol{x_1\beta})}$ and $\frac{exp(\boldsymbol{x_2\beta})}{1+exp(\boldsymbol{x_2\beta})}$. Then can we determine the joint distribution of these two random variables?

share|cite|improve this question
Where does this question come from? – Igor Rivin Dec 25 '11 at 18:10
what does "can we determine the joint distribution of these two random variables"? You can indeed find an ugly formula for it. – Alekk Dec 25 '11 at 19:27
up vote 2 down vote accepted

If $A$ is the matrix with rows $x_1$ and $x_2$, then $A \beta$ has a bivariate normal distribution with mean $A b$ and covariance matrix $A S A^T$. From that you can get the joint distribution of your two random variables.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.