For Wednesday, you can skip Problem 4. I think it is too time-intensive for the lesson I wanted you to learn. The punchline is shown in the figure below, which was generated by Jon Swift (of Swift & Beaumont 2009).
The point is that the least-squares approach underestimates the power-law index for all values of N. So the next time you see a power-law fit in the literature, be suspicious!
For Wednesday, do Problem 3. In addition to what is written, estimate the power-law index for the exoplanet masses using MLE, and compare your answer to the value you find from a least-squares fit as discussed in Problem 4. For the least-squares fit, you can ignore mass bins containing zero planets.
Turn in a figure showing the pdf for alpha, and a figure illustrating the best-fitting powerlaws from both methods compared to a histogram of the planet masses. For the two figures, write captions describing what is plotted.
ETC: less than 2 hours
Reading assignment due Wed is still Sivia Chapter 4.1