Probability - Poisson Probability

  • #1
1,049
780

Homework Statement



Show that the Poisson probabilities [itex] p_{0}p_{1},... [/itex]can be estimated recursively by [itex] p_{0} = e^{-\lambda} [/itex] and

[itex]
p_{k}=(\lambda/k)*p_{k-1} [/itex] k=1,2,...


Homework Equations



I know the Poisson distribution [itex] f(x, \lambda) = e^{-\lambda}\lambda^{x}/x! [/itex]

But I haven't the faintest idea what is even being asked for here. It was never covered in class, our book, or any of the books I've looked through.

-Dave K
 

Answers and Replies

  • #2
I like Serena
Homework Helper
6,579
177

Homework Statement



Show that the Poisson probabilities [itex] p_{0}p_{1},... [/itex]can be estimated recursively by [itex] p_{0} = e^{-\lambda} [/itex] and

[itex]
p_{k}=(\lambda/k)*p_{k-1} [/itex] k=1,2,...


Homework Equations



I know the Poisson distribution [itex] f(x, \lambda) = e^{-\lambda}\lambda^{x}/x! [/itex]

But I haven't the faintest idea what is even being asked for here. It was never covered in class, our book, or any of the books I've looked through.

-Dave K

Hi dkotschessaa! :smile:

##p_k## is just another way to write ##f(k, λ)##.
What is ##f(0, λ)##?
Can you express ##f(k, λ)## in terms of ##f(k-1, λ)##?
 
  • #3
1,049
780
Thank you, that was extremely helpful . I was also able to use this to get a value for P(X≤4) which was the next part of the question!

Regard,

Dave K
 

Related Threads on Probability - Poisson Probability

  • Last Post
Replies
3
Views
772
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
2
Views
11K
Replies
15
Views
4K
  • Last Post
Replies
8
Views
5K
Replies
1
Views
662
Replies
3
Views
1K
Replies
1
Views
3K
Top