Question

Let 3,2,0,2 are four independent random samples from a Poisson distribution with mean= , use maximum likelihood estimation to estimate ?.

Answer 1

Let us suppose we have a sample of size n, X₁, X₂,....., X_n.. from Poisson() distribution

then the joint pdf is

From this, we can find the maximum likelihood estimation (MLE) to estimate ?.

To find this,

Likelihood is

So taking log we will get log-likelihood as

Now taking derivative w.r.t ? we get,

To get MLE we equate above with zero

that is

that is

so for passion(?), the MLE will be sample mean.

In our problem

samples are

(3,2,0,2 ) so n=4 sample and the mean is

=1.75

so 1.75 is the MLE for ?.