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.

In $[8]$: set. seed $(0)$

lambda $=5$

$n=12$

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

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

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

In $[10]$: mle $=$

mle. var $=0\mathrm{.}417$

mle. bias $=0$

# your code here

mle

mle.var

mle.bias

$4\mathrm{.}583$