- #1

shaggymoods

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## Homework Statement

Let

[itex]X\sim Poi(\lambda)[/itex]

and assume

[itex]\lambda\sim Uni(0,5)[/itex]

Q: Find

[itex]\mathbb{P}\{X \geq 3\}[/itex]

## Homework Equations

For a Poisson r.v. with parameter lambda,

[itex]\mathbb{P}\{X = k\}=\frac{\lambda^{k}e^{-\lambda}}{k!}[/itex]

and the probability that lambda is in the interval (0,5) is 1/5 and 0 otherwise.

## The Attempt at a Solution

I know that I first need to write out P(X<=2) and use the fact that P(X>=3)=1 - P(X<=2). However, how do I use the fact that lambda is uniform over (0,5)? I can't seem to think about it correctly.

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