Poisson variable w/ uni. dist. parameter

[shaggymoods]

Homework Statement

Let
$X\sim Poi(\lambda)$
and assume
$\lambda\sim Uni(0,5)$

Q: Find
$\mathbb{P}\{X \geq 3\}$

Homework Equations

For a Poisson r.v. with parameter lambda,
$\mathbb{P}\{X = k\}=\frac{\lambda^{k}e^{-\lambda}}{k!}$

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.

 

[rochfor1]

Condition on $$\lambda$$.