# Math Help - Probability for estimate/poisson distribution

1. ## Probability for estimate/poisson distribution

Hi

I've searched the forum for topic but I can't seem find one with the same problem, so here goes:

I have Xi given as the number of an occurrence pr quarter.

X1...Xn is independent and Xi~Poisson(a)

I have maximized a for the likelihoodfunction to be [LaTeX ERROR: Convert failed] as an estimation of a.

Now to my question:
For a=1.25 and n=10, what is the probability that a* equals respectively 1.1 and 1.25?

My paper is to be done in a couple of hours, so help would be very much appreciated..

Edit: Even though the couple of hours has gone by, I actually still need som help, so if anyone have a hint or two..?

2. Originally Posted by iljitj
Hi

I've searched the forum for topic but I can't seem find one with the same problem, so here goes:

I have Xi given as the number of an occurrence pr quarter.

X1...Xn is independent and Xi~Poisson(a)

I have maximized a for the likelihoodfunction to be $a*=\frac{1}{n}\sum{Xi}$ as an estimation of a.

Now to my question:
For a=1.25 and n=10, what is the probability that a* equals respectively 1.1 and 1.25?

My paper is to be done in a couple of hours, so help would be very much appreciated..

Edit: Even though the couple of hours has gone by, I actually still need som help, so if anyone have a hint or two..?
The sum of n Poisson iid RV's with parameter a, is a Poission RV with parameter na.

RonL

Correct me if I'm wrong, but does that mean that I should do it like this:

$P(X=1.1)=\frac{12.5^{11}}{11!}e^-12.5=0.109$

??

4. Originally Posted by iljitj
$P(X=1.1)=\frac{12.5^{11}}{11!}e^{-12.5}=0.109$