Im wondering if anyone has looked at this problem while practicing problems like I am.
Without going into too much detail for the entire problem, is the information stated in parts (i) and (ii) not necessary? I usually expect problems too give you minimally sufficient information in order for you to solve the problem (for the most part that is). I was under the impression that you know the distribution behavior (poisson|gamma) then you should estimate the parameters by the method of moments which leads me to a variance calculation as if it were biased (dividing by n). I got the correct answer but not the same exact number. the solutions I think used an unbiased sample variance (dividing by n-1).
Is my assumption that I know the frequency distribution behavior false????
If you look at the solutions, they have a slightly different answer than mine. The difference I see is that their Var[N] is equal to 0.932432 which to me suggests they just computed it by finding the (unbiased) sample variance from the data in part (iii) and completely ignoring information from part (i) and (ii).
Am I making a false assumption somewhere??? I feel like if you know the distribution for the frequency and have a sample, you would compute their expectations and variances by first estimating their parameters. If I was only given sample data and did not know the distribution, then I would have been ok here and done exactly what the solutions did.