Problem $2$

Let $x_{i}Poisson(),$iin$1,$dots,$n$ with $=5.$ Recall that the MLE hat$()$ for a Poisson

distribution is equal to the sample mean $\stackrel{}{x}.$

Part A$)$

The data being created into prob$\mathrm{.}2.$a$.$data is $12$ random samples from the Poisson$(5)$

distribution. Calculate the observed MLE, as well as the theoretical variance and bias for the

MLE. $($Your variance and bias calculations will have nothing to do with the generated data.$)$

Store the your answers in mle,mle.var and mle.bias respectively.

set. seed $(0)$

lambda $=5$

$n=12$

prob$\mathrm{.}2.$a$.$data $,$ lambda$)$

prob$\mathrm{.}2.$a$.$data

$8,4,4,5,8,3,8,9,6,6,2,3$

mle $=$ NA mle.var $=-1$ mle. $*$ bias $=$ NA

# your code here