Two related questions here....
Consider a random sample X1,X2, . . . ,Xn from a Poisson(μ) distribution. Using the log–likelihood function, show that the maximum likelihood estimator
for μ is given by ˆμ = ¯X . (That is meant to say "moo hat = X bar"
Suppose the number of buses arriving each rush–hour (8am – 9am) at a bus–
stop in Chicago is thought to follow a Poisson(μ) distribution. In five consecutive daily rush–hours, the numbers of buses arriving at the bus–stop are:
22, 14, 23, 15, 16.
Find the maximum likelihood estimate for μ. What assumption have you made
about the five measurements?