# Maximum liklihood estimator

1. May 15, 2014

### cutesteph

1. The problem statement, all variables and given/known data
y=x+z
where the pdf of z is exp(-v-2) for v >= 2 and 0 otherwise and x is just an unknown constant

what is the MLE of z which maximizes the condition density f_v(y-x)

2. Relevant equations

3. The attempt at a solution
f_v(y-x) = integral of -2+x to infinity of exp(-y+x-2) dy = exp(2x) but maximizing this would mean x = infinity?

Last edited: May 15, 2014
2. May 15, 2014

### haruspex

Do you mean "integral from -2+x to infinity of exp(-y+x-2) dy"? I don't get e2x for that.