Help Urgent: Poisson Question

• Dec 5th 2006, 09:43 AM
Billy2007
Help Urgent: Poisson Question
Dear Friends,

I have this there discrete stochastic vector

$P(X=x, Y=y) = \left\{ \begin{array}{cccc} \frac{1}{3} \cdot e^{-\lambda} \frac{\lambda^y}{y!} \mbox{x \in {-1,0,1} \mathrm{and} y \in {0,1,\ldots}} \\ 0 \mbox{elsewhere.} \end{array}$

where $\lambda>0$

My question I know that $\sum_{n=0}^{\infty} e^{-\lambda} \frac{\lambda^n}{n!} = 1$

But does $\sum_{n=0}^{\infty} \frac{1}{3} e^{-\lambda} \frac{\lambda^n}{n!} = 1$ also do this??

If yes this doen't this prove that

$P(X=x) = \left\{\begin{array}{ccx} \frac{1}{3} \mbox{x \in {-1,0,1}} \\ 0 & \mathrm{elsewhere.} \end{array}$

and

$P(Y=y) = \left\{ \begin{array}{cccc} e^{-\lambda} \frac{\lambda^y}{y!} \mbox{y \in {0,1,\ldots}} \\ 0 \mbox{elsewhere.} \end{array}$

are the probability functions P_x and P_y for X and Y respectively??

Sincerely Yours and God bless You all
Billy

p.s. Is latex broken here? I heard that one had to use , but if I do that I get a post then build arrays error! Therefore I use . Hope thats allright.
• Dec 5th 2006, 10:11 AM
ThePerfectHacker
Quote:

Originally Posted by Billy2007

p.s. Is latex broken here? I heard that one had to use , but if I do that I get a post then build arrays error! Therefore I use . Hope thats allright.

I am not familar with probabilty. So I might be missing what you are saying.
Whay can you not simple multiply by $1/3$. If the infinite sum adds to 1 then 1/3 of the infinite sum adds to 1/3.

Also the code is not it is 
• Dec 5th 2006, 10:21 AM
Billy2007
Quote:

Originally Posted by ThePerfectHacker
I am not familar with probabilty. So I might be missing what you are saying.
Whay can you not simple multiply by $1/3$. If the infinite sum adds to 1 then 1/3 of the infinite sum adds to 1/3.

Also the code is not it is 

Dear Hacker and all,

But doesn't a probability sum have to add up to 1 ??? Because if doesn't add up one? then its not a probability sum is it?

Best Regards
Billy