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I would like to find the conditional bivariate normal distribution. … I found the conditional expectation of $X$ given that $Y$ is bigger than $M$: $E(X|Y>M)= \mu + \rho \sigma \frac{\phi(\frac{M-\mu}{\sigma})}{1-\Phi(\frac{M-\mu}{\sigma})}$. …

I am now searching for the conditional expectation $$ E(s_1|s_1>r_1,\ s_2>r_2) $$ where $r_1$ and $r_2$ are constants. …

For that I need to know the conditional expectation and variance. … I found the conditional expectation of $X$ given that $Y$ is bigger than $M$ is $E(X|Y>M)= \mu + \rho \sigma \frac{\phi(\frac{M-\mu}{\sigma})}{1-\Phi(\frac{M-\mu}{\sigma})}$. …

I am struggling with some finding expectation value question . the question is to find $E[Y|X]$ from the result $P(Y|X)$ with given mean and covariance $$\mu=[\mu_x, \mu_y]^T$$ $$\Sigma=\begin{bmatrix} …

In the previous question, we were given that X and Y form a bivariate normal distribution and I derived the marginal distribution for X and Y. I am stuck as to how to proceed with this question. … Is it safe to assume that Y|X form a linear relationship and thus the expectation? …

I am working on a paper in which I'd need to use the two following conditional expectations: $E(X_{1}|a \leq X_{2} \leq b)$ $E(X_{1}|a \leq X_{2} \leq b, a \leq X_{3} \leq b)$ where $X_{1}, X_{2}, … Could anyone help me derive these conditional expectations, or else point me to any good reference(s) I may have missed? …

What would be the conditional expectation $\mathbb{E}[B|C]$? … (b) Does it even make sense to use the formula for the conditional expectation of the bivariate normal by just using $1$ for $\rho=1$? …

Suppose $X \sim N(0, \sigma^2)$, is it possible to evaluate $E[\Phi(\frac{aX + b}{c}) | X > k]$ in closed form, where $\Phi$ is the standard normal cdf? … But not sure if something similar holds for the conditional expectation case. …

I want to evaluate a conditional expectation of log-normal distribution. Let $y$ be a log-normal distributed random variable. So $\log(y)\sim N(\mu,\sigma^2)$. …

coming up with the conditional joint density to use in the above expectation. … I am little confused due to the conditional expectation and the normal log normal mixture? …

So what I did first was to get the conditional expectation value for X and the conditional variance. … Here are the formulas that I used to get the variance and the expectation value. …

Suppose $(X_1, X_2, X_3)^T$ is multivariate normal. What is the conditional expectation $E(X_1 \mid X_2, I(X_3 > 0))$? … If this is true, one could proceed using properties of conditional distributions for multivariate normal vectors to get more specific expressions. …

Let $(X,Y,Z)$ have a multivariate normal distribution: \begin{align} (X, Y, Z) \sim N\left(\begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 & \rho_{xy} & \rho_{xz} \\ \rho_{xy} & 1 & \rho_{ … yz} \\ \rho_{xz} & \rho_{yz} & 1 \end{pmatrix}\right) \end{align} I'm trying to find the conditional expectation of the following: $$E[X| Y > \tau_Y, Z > \tau_Z]$$ where $\tau_X$ and $\tau_Y$ are constants …

from a multivariate normal, conditional on known values for another subset of variables, is a multivariate normal distribution." … Then, I could take the Expected Value of " Prob (Var_3 | Var_1 = a and Var_2 = b) " to answer my question? E.g when "Var_1 = a and Var_2 = b", Var_3 is most likely to be equal to "c"? …

If a man's height places him at the 60th percentile, at what percentile would you expect his weight to be?" … If there's an exact largest value and smallest value for the conditional expectation, that (and for preference, the circumstances in which each occurs*) would be good to know about. …