Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have the following problem:

A mail server, sends emails with rate $7.5/\text{hour}$.

What is the probability that it will send exactly $5$ emails in one hour?

To solve it, I did the following using a Poisson distribution:

$$\frac{7.5^5 e^{-7.5}}{5!}$$

or with sage math:

def dpoi(x):
  return (7.5^x * (e^-7.5)) / factorial(x)

dpoi(5) 
0.109374594682555$$

is that right?

share|improve this question
1  
Yes, that's correct. –  Eckhard Dec 30 '12 at 15:39
    
Hey @Eckhard. You should read it meta.math.stackexchange.com/questions/6883/… you can add your comment as answer and I do accept it. –  VP. Dec 30 '12 at 15:51
add comment

2 Answers 2

up vote 1 down vote accepted

As suggested I repeat my comment as an answer:

Yes, that's correct.

share|improve this answer
add comment

This is a mere generalization of Eckhard's answer.

If $X \sim Poisson(\lambda)$, then the pdf of $X$ is $P(X=k)=\frac{e^{-\lambda} \lambda^{k}}{k!}$, and this is the same as asking 'what is the probability that exactly $k$ events happen in a given time interval'

share|improve this answer
    
thank you for improving the knowledge base :-) –  VP. Dec 31 '12 at 9:32
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.