The following questions relate to the maximum likelihood estimators for the unknown parameters in two standard distributions.

Question: Single binomial value

In a series of \(n\) independent success/failure trials with probability \(\pi\) of success, \(x\) successes were observed. What is the maximum likelihood estimator of \(\pi\) and what are its bias and standard error?

Question: Geometric random sample

If \(\{x_1, x_2, \dots, x_n\}\) is a random sample from a geometric distribution with parameter \(\pi\), what is the maximum likelihood estimator of \(\pi\) and what are its bias and standard error?

(Both solved in full version)