- #1

- 30

- 0

## Homework Statement

I look at the distribution ##(Y_1,Y_2,...,Y_n)##

where

##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1.

I need to find the the maximum likelihood estimator for μ and φ

## Homework Equations

## The Attempt at a Solution

I get to the Log likelihood funcion: ##L(Y_1,Y_2,...,Y_n;μ,φ)=∑μ+(1+φ x_i)+ε_i##

When I differentiate it get:

##d L / dμ =∑1/(μ+(1+φ x_i)+ε_i), d L / dφ =∑x/(μ+(1+φ x_i)+ε_i##. Right?

These equations doesn't allow me to set ##d L / dμ=0,d L / dφ=0## because you can't divide by zero. What is going wrong for me?