What' s $E[Y] = E[f(X)]$? $X\sim N(\mu,\sigma^2)$ and $f()$ is cdf of std normal rv?
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How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
78386
Finding the moment generating function of the product of two standard normal distributions
48811
Characteristic function of product of normal random variables
141685
Why is expectation defined by $\int xf(x)dx$?
79773
What is $P(X > 0 \mid X + Y > 0)$ given that $X, Y$ are i.i.d standard normal?
128440
If $X_1,\ldots,X_n\sim Uniform(0,1)$ and $Y=\max[X_1,\ldots,X_n]$, find $E(Y)$
5350
Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
29227
Why the CDF for the Normal Distribution can not be expressed as a closed form function?
98060
Mean and variance of inverse of a normal RV
118866
How are the Error Function and Standard Normal distribution function related?
27788
Why is the expected value $E(X^2) \neq E(X)^2$?
157517
Simple homework question about normally distributed variables
109311
Integral of a CDF
92054
$X$ and $Y$ i.i.d., $X+Y$ and $X-Y$ independent, $\mathbb{E}(X)=0 $ and $\mathbb{E}(X^2)=1$. Show $X \sim N(0,1)$
150667
Given the normal distribution X=N(1,2), what is E[X^3]?
35454
Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?
156901
Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely