# poisson with given

• Dec 14th 2010, 10:32 AM
mathcore
poisson with given
i know the poisson formula but how does a given condition affect it?

i.e. E(X)=3, find P(X=2|X>1).

i have X>1, as 1 - 4e^-3, and i can work out the normal P(X=2) but how does the given X>1 affect it? i dont know what to do
• Dec 14th 2010, 11:38 AM
mr fantastic
Quote:

Originally Posted by mathcore
i know the poisson formula but how does a given condition affect it?

i.e. E(X)=3, find P(X=2|X>1).

i have X>1, as 1 - 4e^-3, and i can work out the normal P(X=2) but how does the given X>1 affect it? i dont know what to do

You're expected to understand conditional probability: $\displaystyle \Pr(A | B) = \frac{\Pr(A \cap B)}{\Pr(B)}$.

Note that $\Pr(X = 2 \cap X > 1)$ is equivalent to $\Pr(X = 2)$ ....
• Dec 14th 2010, 12:26 PM
mathcore
so this will just be p(x=2)/p(x>1) then? just divide my own calculations

i get 0.28 is thAT RIGHT
• Dec 14th 2010, 07:30 PM
mr fantastic
Quote:

Originally Posted by mathcore
so this will just be p(x=2)/p(x>1) then? just divide my own calculations Mr F says: Yes.

i get 0.28 is thAT RIGHT

If you have calculated each probability correctly and then done the arithmetic correctly then your answer will be correct.
• Dec 15th 2010, 02:46 AM
mathcore
yesh but thats what im asking if i did it correctly or not... is my result correct or not...?
• Dec 15th 2010, 03:51 AM
CaptainBlack
Quote:

Originally Posted by mathcore
i know the poisson formula but how does a given condition affect it?

i.e. E(X)=3, find P(X=2|X>1).

i have X>1, as 1 - 4e^-3, and i can work out the normal P(X=2) but how does the given X>1 affect it? i dont know what to do

Bayes' theorem can be used here:

$P(x=2|X>1)=\dfrac{P(X>1|X=2)P(X=2)}{P(X>1)}=\dfrac {P(X=2)}{1-(P(X=0)+P(X+1))}$

where:

$P(X=k)=\dfrac{3^ke^{-3}}{k!}$

To two significant firures this gives $0.28$ which is your answer, but you should give more digits (even if they are zeros)

CB