Hi! I have a problem to solve:
y/x 0 1_

0__ 5 15
 1 _10 20
_
Above are the observations of which a dataset consists (N=50). I hope that you can read the table: (there are 5 observations with x=0 and y=0, 15 with y=0 and x=1, etc) Both x and y are binary and I need to plug these into a logit model and find the MLE. I start out by defining the likelihood function:
L =
After this I go on with the usual MLEprocess. I take the log of the expression above, I then calculate the first derivative with respect of beta_0 and thereafter beta_1. I then maximize these expressions with respect to the actual parameter. My problem is that I don't know how to use these observations above to receive a numerical MLE. Can someone please help me with this? Thank you.