(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x[tex]^{y}[/tex] (1-x)[tex]^{n-y}[/tex] for y = 0, 1,..., n.

2. Relevant equations

FInd E(y) and the distribution of Y.

3. The attempt at a solution

f(x) = [tex]\frac{1}{b-a}[/tex] = [tex]\frac{1}{1-0}[/tex] =1

E[Y] = E [E[Y|X=x]

= [tex]\int[/tex] E[Y|X=x] f(x) dx where the integral is from o to 1

= [tex]\int[/tex] [[tex]\Sigma[/tex] y f(y|x)] f(x) dx

= [tex]\int[/tex] [[tex]\Sigma[/tex] y nCy x[tex]^{y}[/tex] (1-x)[tex]^{n-y}[/tex]] f(x) dx

...but I do not know anymore what to do next...please help.

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# Homework Help: Iterative expectation of continuous and discrete distributions

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