Probability - Poisson Probability

[dkotschessaa]

Homework Statement

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

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

Homework Equations

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

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

 

[I like Serena]

Homework Statement

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

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

Homework Equations

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

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!

$p_k$ is just another way to write $f(k, λ)$.
What is $f(0, λ)$?
Can you express $f(k, λ)$ in terms of $f(k-1, λ)$?

 

[dkotschessaa]

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