Probability - Poisson Probability

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

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Homework Helper

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)##?

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