# Poisson Distribution with two different expected value

#### Asano

##### New Member
Question:

Suppose there are number of accidents at location $$A$$ and location $$B$$ each day with Poisson Distribution with rate $$0.001$$ and the number of patients during each accident is Poisson distributed with rate $$0.1$$. Find the probability that the number of patients less than $$3$$ in one day.

Attempt:

So I did $$E(N)=0.001\times 0.1=0.0001$$ and then using this mean to find

P(X<3)=$$\sum_{0}^{2}Poi(0.0001)=1$$

and I got a value of $$1$$. I am sure this is the wrong answer. Where did it go wrong? I need some help. Thank you!

#### Mean Joe

##### TS Contributor
First thing, I would ask you to double-check the question: Is the question asking for <3 patients in one day or in one year? Is that rate of 0.001 per day or per hour?

#### Asano

##### New Member
Yes it is asking for <3. Also I think it is 0.001 per day. Thanks.