
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 loglikelihood function
b) Find the first order conditions for the maximum likelihood estimation.
c) Find the second derivative (the Hessian matrix) for the loglikelihood function.
Help anyone? Thanks in advance.

this isn't clear
It looks like the y's given the x's are bernoulli's
please clarify

Yes, I believe they are bernoulli's. However, that information is not given beforehand.
Anything else that's perhaps not clear?

I still don't get the beta's.
I understand that
$\displaystyle P\{Y_i=0X_i\}=q_i$
and
$\displaystyle P\{Y_i=1X_i\}=p_i$
But how can $\displaystyle P\{Y_i=1X_i\}$ 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.