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I am wondering what is the probability density function for the normal cdf $\Phi (aX+b)$, where $\phi$ is the usual standard normal cumulative distribution function

I want to calculate $\mathbb{E}[\Phi(aX+b)]$ but i am stuck on how to get the distribution. thank you =]

note: X is normally distributed

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    What does $X$ stand for? Where does the problem come from?2011-10-22
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    X is a random variable, I thought it up, trying to calculate the expected value of a cumulative distribution2011-10-22
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    The expected value of a *function* $f(X)$ of a random variable $X$ depends in general on the distribution of $X$, and not only the mean of $X$. There was no specification made in the post about the distribution of $X$, only about what $f$ was.2011-10-22
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    oops hehe, thanks for reminding me =]2011-10-22
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    X is normally distributed2011-10-22
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    Convnetionally the capital $\Phi$ is the cdf and the lower-case $\varphi$ is the density function. This posting says "where $\phi$ is the[...]cumulative distribution function", after an expression that uses $\Phi$, not $\phi$.2011-10-22

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