Pitman’s text doesn’t include MLEs because we typically teach it as part of statistics courses, not probability. In Prob 140, the lectures, discussion and homework together cover the MLE in the contexts that are typically covered in an introduction. Work through all the examples and you’ll be fine.
Pitman x.y.z means Exercise z of Section x.y and x.rev.z means Exercise z of the Review Exercises at the end of Chapter x.
Pitman 6.3.1, 6.3.8, 6.3.9, 6.3.11, 6.3.13, 6.3.15 (just notice that it is essentially all done in Ch 21)
Let $X_1, X_2, \ldots, X_n$ be i.i.d. Poisson $(\mu)$. Find the MLE of $\mu$.