Question-90

poisson
mle

A research team is analyzing customer complaints per day for a new service. The number of complaints \(X\) follows a Poisson distribution with an unknown average rate \(\lambda\). The number of complaints observed over a period of 10 days are as follows:

\[ 3,\ 5,\ 2,\ 4,\ 6,\ 3,\ 4,\ 7,\ 5,\ 4 \]

Find the maximum likelihood estimate of \(\lambda\). Enter your answer correct to one decimal place.

\(4.3\)

The MLE of \(\lambda\) for a Poisson distribution is the sample average. Therefore, \(\hat{\lambda} =( 3+5+2+4+6+3+4+7+5+4) /10=4.3\).