1. ## Poisson precess exercise

I'm struggling with this problem, I tried different ways but failed. I would appreciate your help.

2. ## Re: Poisson precess exercise

If you have been struggling with this problem and have tried different ways, surely you can show us what you have tried so we will know what help you need. What is a "Poisson process"?

3. ## Re: Poisson precess exercise

The independent rates add so you want to solve

$CDF[Poisson[(3+2)t],400]=0.9$

You can use the Normal approximation to the Poisson distribution to get a reasonably accurate answer.

$Poisson[\lambda] \text{ is approximately modelled by }Normal[\lambda,\sqrt{\lambda}]$

As a ballpark guess you would expect 400 cars passing with a rate of 5 cars/minute to pass in approximately $\dfrac{400}{5} = 80~min$

I get 75.1 minutes as an answer. Is the 85.1 a typo?

4. ## Re: Poisson precess exercise

Thank you!

The solution written in the book is 85.1 min.

I would like to ask how you come up to 75.1 minutes? Also P(T_400<=a)=0.90, isn't this an exponential distribution since it's about the distribution of the time 400 cars have passed?

I appreciate the help.