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?