A company manufacturing bike helmets wants to estimate the proportion
p of helmets with a certain type of flaw. They decide to keep inspecting
helmets until they find r = 5 flawed ones. Let X denote the number of
helmets that were not flawed among those examined.
a) Write the log-likelihood function and find the MLE of p.
b) Find the method of moments estimator of p.
c) If X = 47, give a numerical value to your estimators in (a) and
(b)above