Expected Value of Convolution

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#1
I am interested in estimating E[g(h(X))] where...
- X ~ Normal(mu,sigma)
- h(.) = CDF of Standard Normal distribution
- g(.) = inverse CDF of Beta distribution with known parameters alpha and beta

Any suggestions as to how to proceed? Taylor approximation?

Any help appreciated.
Jesse
 

Dason

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#2
You should be able to figure out the exact distribution of g(h(X)). First consider h(X) - what distribution does this have?
 

Dason

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#4
Yes but I asked about h(X). What happens when you apply the cdf of a random variable to the random variable itself?
 
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