Let N follow a geometric distribution with probability p. After the success of the experiment we define X, a uniform distribution from 1 to N. Both distributions are discrete. Find E[X|N].
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1What is the formula for $E[X|N]$? Please state it, so we can confirm you know it. – Sarvesh Ravichandran Iyer Apr 05 '19 at 07:45
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Since E[N]=1/p I have assumed that X is uniformly distributed from 1 to 1/p thus E[X|N]=p+1/2*p – EmKal Apr 05 '19 at 09:17
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Guide:
Find $\mathbb E[X\mid N=n]$.
This is an expression in $n$ and if we set $f(n)=E[X\mid N=n]$ then $\mathbb E[X\mid N]=f(N)$.
drhab
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