Likelihood function

• Feb 20th 2009, 03:30 AM
Ond
Likelihood function
Hi there!

I have the following problem:

The following probability mass function is given:
http://i42.tinypic.com/15nn2va.jpg
It's convenient to write beta0 + beta1*xi = x'i (i should be subscript)*beta, where x' = (1 xi) and beta' = (beta0 beta1).

a) Find the log-likelihood function
b) Find the first order conditions for the maximum likelihood estimation.
c) Find the second derivative (the Hessian matrix) for the log-likelihood function.

• Feb 21st 2009, 01:30 PM
matheagle
this isn't clear
It looks like the y's given the x's are bernoulli's
• Feb 22nd 2009, 05:07 AM
Ond
Yes, I believe they are bernoulli's. However, that information is not given beforehand.

Anything else that's perhaps not clear?
• Feb 22nd 2009, 06:40 AM
matheagle
I still don't get the beta's.
I understand that
\$\displaystyle P\{Y_i=0|X_i\}=q_i\$
and
\$\displaystyle P\{Y_i=1|X_i\}=p_i\$
But how can \$\displaystyle P\{Y_i=1|X_i\}\$ also equal that equation with the beta's?
I think the first line is wrong.
It's just a function of the \$\displaystyle X_i\$'s or a marginal or something else.