The number of users registering their names for Covid-19 vaccination using the CoWin

app follows a Poisson distribution with mean per minute. Consider randomly se-

lecting 5 such 1-minute intervals. Suppose the observed number of registrations are

respectively 4.1, 3.2, 1.9, 2.8, 3.4 (in '00s).

(a) Find the method of moments estimate of . [5 points]

(b) Find the maximum likelihood estimate of the standard error of the method of

moments estimator of . [5 points]

(c) What is the maximum likelihood estimate of the mean time gap between two

registrations?