1. ## actuarial exam question

Hi,
I have just sat a paper that a failed big time!
Because on on question I couldn't get started on and it was worth 21 marks.

So could some one put my mind at rest as to the answer to this question.

If X1,....Xi is distributed poison with E[Xi]=lamda then if

lamda(estimate)=1/n * sum[Xi]

What is the expected value and variance of lamda(estimate)

Bobisback

2. ## Re: actuarial exam question

Originally Posted by bobisback
Hi,
I have just sat a paper that a failed big time!
Because on on question I couldn't get started on and it was worth 21 marks.

So could some one put my mind at rest as to the answer to this question.

If X1,....Xi is distributed poison with E[Xi]=lamda then if

lamda(estimate)=1/n * sum[Xi]

What is the expected value and variance of lamda(estimate)

Bobisback
The formulas you need are undoubtedly in your class notes and textbook. Otherwise, you will certainly find them using Google eg. AP Statistics: Combinations of Random Variables

3. ## Re: actuarial exam question

im really sorry but i came to the forum asking for help not a smart ass comment about the fact you know where you can find it. Not all of us are maths genius's but we come here to ask for some help.
When working on this I kept getting the a return of Lamda(estimate) = Lamda

This is because E[1/n*sum(Xi)]=1/n*Sum(E[Xi]) =1/n*sum(lamda)=1/n*n*lamda=lamda

Can you now explain where i am going worry. I dont understand how you link helps me

4. ## Re: actuarial exam question

Originally Posted by bobisback
im really sorry but i came to the forum asking for help not a smart ass comment about the fact you know where you can find it. Not all of us are maths genius's but we come here to ask for some help.
When working on this I kept getting the a return of Lamda(estimate) = Lamda

This is because E[1/n*sum(Xi)]=1/n*Sum(E[Xi]) =1/n*sum(lamda)=1/n*n*lamda=lamda

Can you now explain where i am going worry. I dont understand how you link helps me
1. The questions can be answered using standard formulae for the mean and variance of a sum of random variables. And as I said, these formulae will be found in either your textbook or class notes or you can use Google to find them. Why should we re-invent the wheel when a little effort on your part is all that's needed.

2. Had you posted your working and answer in your original post, I could have said "Yes, your answer for the expected value is correct". Why should we spend time typing out a solution you already have when simple confirmation is all that's required?

3. You do not say whether of not the random variables are independent. The answer for the variance depends on knowing this. But either way, you will find the required formulas if you make an effort to find them. Then it is simply a matter of applying them.

4. It's not my fault you might have failed an exam.