1. ## Likelihood function

Hi there!

I have the following problem:

The following probability mass function is given:

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.

2. this isn't clear
It looks like the y's given the x's are bernoulli's

3. Yes, I believe they are bernoulli's. However, that information is not given beforehand.

Anything else that's perhaps not clear?

4. I still don't get the beta's.
I understand that
$P\{Y_i=0|X_i\}=q_i$
and
$P\{Y_i=1|X_i\}=p_i$
But how can $P\{Y_i=1|X_i\}$ also equal that equation with the beta's?
I think the first line is wrong.
It's just a function of the $X_i$'s or a marginal or something else.