A criminologist is searching through FBI les to document the

A criminologist is searching through FBI les to document the prevalence of a rare double-whorl ngerprint. Among six consecutive sets of 100,000 prints scannedbyacomputer,thenumbersofpersonshavingthe abnormality are 3, 0, 3, 4, 2, and 1, respectively. Assume that double whorls are Poisson events. Use the method of moments to estimate their occurrence rate, . How would your answer change if were estimated using the method of maximum likelihood

Solution

A criminologist is searching through FBI les to document the prevalence of a rare double-whorl ngerprint.

Among six consecutive sets of 100,000 prints scannedbyacomputer,thenumbersofpersonshavingthe abnormality are 3, 0, 3, 4, 2, and 1, respectively.

Assume that double whorls are Poisson events.

Use the method of moments to estimate their occurrence rate,

The first moment is nothing but the sample mean.

The first moment using method of moment is,

mu1\' = E(X) = sum of observations / total observations

m1\' = 2.1667

And maximum likelihood estimator of poisson distribution is also sample mean which is 2.1667.