Let N be a Poisson (1) random variable. We observe N, say it equals n, we then throw a p-biased coin n times and let X be the number of heads we...
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# Let N be a Poisson(λ) random variable. observe N, say it equals n, then throw a p-biased coin n times and let X

be the number of heads we get. Show that X is a Poisson(pλ) random variable. (You can use the following identity: ∑ ∞ k=0 y^k / k! = e^y

4. Let N be a Poisson (1) random variable. We observe N, say it equals n, we then throw
a p-biased coin n times and let X be the number of heads we get. Show that X is a
Poisson (pA) random variable. (You can use the following identity: EX-o k! = ey.)

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