Rolling a die that follows a poisson distribution and computing it's mean

Question

Roll a fair, 4-sided die N times where N is a Poisson random variable with parameter λ>0, let X be the number of 3's rolled in this experiment. Find E(x)

What I have figured out is that E(X) seems to be N/4. But am doubting this since we have been given the factor of Poisson.

score 0 · Answer 1 · answered Apr 22 '16 at 19:32

0

Hint: the conditional expectation $\mathbb E[X \mid N=n] = n/4$.

answered Apr 22 '16 at 19:32

Robert Israel

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How do I now incorporate Poisson distribution into this. I have been thinking of N/4 but by the fact that it is Poisson am confused – Ben Apr 22 '16 at 19:46
$\mathbb E[X] = \mathbb E[\mathbb E[X \mid N]]$. What is $\mathbb E[N/4]$ if $N$ has a Poisson distribution? – Robert Israel Apr 22 '16 at 22:19

Rolling a die that follows a poisson distribution and computing it's mean

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