Bivariate normal distribution , link $\Bbb E(Y\mid X=x)$ and $\Bbb E(X\mid Y=y)$
81547
Effect of switching response and explanatory variable in simple linear regression
88860
The product of two lognormal random variables
64319
Deriving the canonical link for a binomial distribution
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
30060
Decomposing the normal distribution
118534
Find the distribution of (X, X+Y) when X and Y have a given joint Normal distribution
100916
Finding $\mathrm{Cov}(X,Y)$ and $E(X\mid Y=y)$ given the joint density of $(X,Y)$
43833
How to parameterize the ratio of two normally distributed variables, or the inverse of one?
156901
Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely
156965
Expected value of $\max\{X,Y\}$ when $(X,Y)$ is bivariate normal
29407
Distribution of multivariate Gaussian conditional on value of linear function
99024
Let $\,E=\{(x,y) \in \Bbb R^2: |x| \le 1,|y|\le 1\}.$
127662
Integrating product of multivariate normal and univariate normal to find marginal
30561
The conditional normal distribution
103876
Covariance between a normally distributed variable and its exponent
74054
Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely