Point Estimate Question

Hi,

May I confirm if my answers to the questions are correct?

For Q1) I used the following limits for my integral

$\displaystyle \int_{x_{0}}^{0} \alpha x_{0}^{\alpha}\ x^{-\alpha-1}\ dx = 1$

Q2) My final answer is:

$\displaystyle \alpha = \frac{\mu_{1}}{\mu_{1} - x_{0}}$

Q3) My answer after solving the derivative of the log likelihood

$\displaystyle \alpha = \frac{1}{\log \left( \frac{x}{x_{0}} \right)}$

Thank you in advance

Linda