Binomial with Both Parameters Hidden
Six independent observations 2, 4, 5, 5, 3, 7 are drawn from a Binomial(N, p) distribution in which both the integer N and the probability p are unknown. What is the maximum likelihood estimate of N? (You may check the answer by evaluating the profile likelihood, in which p is replaced by its maximizer for each N, namely p = x̄/N.)
Related problems & prerequisites
Worth solving first
- Poisson Intervals with No Events 5.0/10
- How Many Trials Were There? 4.0/10
- Rates from Unequal Watching Times 4.0/10
Source: Classic joint estimation of the binomial parameters (Olkin, Petkau and Zidek discuss its instability); the data are original. Statement written for AxiomIQ.