A used car salesman is willing to assume the number of sales he makes, per day, is a Poisson random variable with parameter µ. Over the past 30 days, he made 0 sales on 20 days and one or more sales on each of the remaining 10 days. What are the method of moments and maximum likelihood estimates for µ?
My question is really about how to compute the Method of Moments estimator for this question.
All I can think doing is setting the first sample moment, M1, as being greater than or equal to 1/3 and then setting M1 = µ. So overall µ >= 1/3.
For the ML estimator I got µ = -ln(2/3) which is roughly equal to 0.4055 so this fits with my MM estimation of µ.