2 Attachment(s)

Describe the sampling distribution of the maximum likelihood estimator...

Okay, I literally have no idea with this, so I'm just gonna give you all the info I have and see if anyone can help. (I've attached the PDF with my whole assignment on, but this post's referring only to section A, question 1 part a).

*Describe the sampling distribution of the maximum likelihood estimator for the Geometric parameter $\displaystyle \pi$ for samples of size 5 obtained from a Geom(0.01) distribution.*

Now basically this question involes a program called R (don't know how many people know what it is) and I've typed the following code in...

m<-1000

n<-5

gsim<-matrix(nrow=n,ncol=m)

for (i in 1:m)

{

gsim[,i]<-rgeom(n,0.01)

}

gmle<-vector()

for (i in 1:m)

{

gmle[i]<-1/(mean(gsim[,i])+1)

}

hist(gmle)

...where m is the number of data sets, n is the size of said data sets, and this is all from the Geom(0.01) distribution, so $\displaystyle \pi=0.01$. It might also be useful to tell you that we're using $\displaystyle Pr(X=x)=(1-\pi)^{x}\pi, x=0,1,2,...$ as well, as apparently this is the Geometric distribution favoured by R.

The histogram I obtain from running all of the above code is attached to the post (any code I type in will be in Courier New).

So yeah, does anyone have any idea what the question means? I thought it was asking for a comment on what the histogram looks like, but that's parts (c) and (d), not (a) (Worried) I think I've given all the information needed... I've given everything I have written here, anyway.