Maximum Likelihood Estimator for a function

[ych22]

Homework Statement

Consider the following density function:
f(x) = A^BB/x^B+1; A<= x, zero elsewhere, where A > 0 and B> 0

Homework Equations

The Attempt at a Solution

f(x₁,...,x_n)= A^BnBⁿ(x₁...x_n)^B+1

ln f(x₁,...,x_n)= Bn ln A + n ln B + (B+1)ln((x₁...x_n)

After differentiating with respect to A and setting to 0, Bn/A= 0. Therefore there is no maximum likelihood estimator for A?

 

[HallsofIvy]

Where did all of the different "x"s come from? You seem to have your original density function to a power. Why?

Also please state the entire problem. Are you asking for the "maximum likelihood estimator of A?