Students are given addition items and the number of items the students get wrong prior to getting their 25th correct item is recorded. If X is the number of incorrect items, then it has a negative binomial distribution with pdf (seen in attachment). Consider a random sample X1, ..., Xn from this distribution:
a. Find the maximum likelihood estimator of p.
b. Find the maximum likelihood estimator of the log-odds log (p/1-p)
c. Find the method of moments estimator of the log-odds.
d. Find the fisher information about p.
e. Find an approximate standard error of the MLE of p based on the Fisher information.
f. Find an approximate standard error of the MLE of the log-odds.
The solution gives detailed steps on determining method of moments, method of maximum likelihood and fisher information. All formulas and calculations are shown and explained.