Maximum Likelihood Estimation for Constant x and Exponential Distribution of z

[cutesteph]

Homework Statement

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)

Homework Equations

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?

 

[haruspex]

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?

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