# Questions tagged [conditional-expectation]

A conditional expectation is the expectation of a random variable, given information on another variable or variables (mostly, by specifying their value).

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### Conditional distributions of correlated normal random variables

Suppose that $X$ and $Y$ are normally distributed with mean zero and nonzero covariance. I want to know the distributions of $X | X - Y > c$ and $Y | X - Y > c$, which I believe should be ...
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### Expectation of structural equation

I am trying to learn about structural equations, and in this post here Correlation, regression and causal modeling I am having difficulties trying to prove the answer. The problem is, given structural ...
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I am building a predictor for $y = f(x)$ using training samples ${(x_i, y_i)}$ (assume) drawn i.i.d from some distribution $p(x,y)$, by optimising the empirical L2-loss: $f(x) = argmin_f \; \sum_i ||... 1answer 34 views ### Gauss Markov Theorem and zero conditional mean/mean independent assumption So I read online that one of the assumptions of Gauss Markov Theorem is: $$E[\epsilon_i]=0$$However, we also know that one of the assumptions for linear regression is the zero conditional mean: $$E[\... 1answer 16 views ### Iterated expectation over different sets of variables For some random variables Y, X, Z, and Q, can we simplify E[E[Y|X,Z]|Z,Q]? Is it correct that E[E[Y|X,Z]|Z,Q] = E[Y|X,Q] (idea being that Z is averaged out)? In general, for some sets of ... 0answers 9 views ### What is the maximum entropy distribution given *conditional* means and MADs? I know the maximum entropy distribution given the mean and MAD (Mean Absolute Difference) around the mean (it's the Laplace distribution, a proof here for example). I also know the maximum entropy ... 3answers 1k views ### Poisson random variable self-study question You are invited to a party. Suppose the times at which invitees arrives are independent uniform(0,1) random variables. Suppose that aside from yourself the number of other people who are invited is a ... 2answers 73 views ### Expected value of sum of two gaussian random variables conditional on their difference Given two standard normally distributed random variables x_1 and x_2. y = x_1 + x_2 I would now like to calculate the following:$$\mathop{\mathbb{E}}[y | x_1 -x_2 = 0]$$My idea was to do it as ... 1answer 28 views ### Conditional expectation versus correlation Consider two random variables X and Z. Suppose E(X)=3 and E(X|Z=z)=0 for some realisation z of Z. Does this imply that X and Z are correlated? Does this imply that X and Z cannot ... 0answers 120 views ### Alternating Conditional Expectations: Multiple regression transform Alternating Conditional Expectations (ACE) is a non-parametric algorithm for multiple regression transform selection. It finds a set of transformed response variables that maximizes R^2 using ... 0answers 21 views ### Expected value of X given Y is less than some constant [duplicate] Here is the problem I'm trying to work out: Let v_b,v_s be jointly normally distributed random variables with pdf f(v_b,v_s). I want to work out E[v_b|v_s\leq\pi] for some constant \pi. Here ... 0answers 28 views ### Expectation of an Expectation I need to solve two exercises: Calculate V[ui|xi] using E[yi|xi] and ui = yi - E[yi]. Calculate E[y^2|xi]. Information given for the exercise: E[u^2|xi] = V[yi|xi] E[u^2|xi] = V[yi|xi] ... 0answers 21 views ### conditional expectation with updated information Let$$\epsilon_{t+1} = \rho\epsilon_t + \eta_{t+1}E_t[r_{t+k}|\eta_t] = \phi^k \eta_t$$Can we say that$$E_t[r_{t+1}] = \sum_{k=0}^\infty \phi^k \eta_{t-k}$$Are there any conditions for this ... 1answer 17 views ### Deriving reward functions in Sutton & Barto Does anyone know how the equations have been derived, I'm still learning probablity theory and expectations 0answers 24 views ### Truncated expectation of sum of independent random variables Take three random variables X, Y, Z s.t. E[X]>0, E[Y|X]=0, Z = X+Y. What can I say about E[x| x> k] vs. E[z| z>k] where k>0? Intuitively, the latter should be bigger ... 1answer 145 views ### How to generate data that have given conditional mean and conditional quantile using R? Suppose I want to generate independent data (y_{i},x_{i}) such that the conditional mean of y_{i} given x_{i} is a quadratic function in x_{i} and the .25 conditional quantile of y_{i} ... 0answers 16 views ### Conditional expectation of functions of two random variables with inequality conditions Consider general case first. Let X and Y be independent continuous random variables with known pdfs. What is expectation of Z = \begin{cases} g_1(X, Y), & Y \geq X,\\ g_2(X, Y), & Y < ... 1answer 35 views ### Where is the error? I am trying to compute expectation of X\mathbb I_{[X+Y\le a]} where a is a fixed positive integer, X is discrete uniform random variable taking values from 1 to a, and Y another random ... 3answers 33k views ### A generalization of the Law of Iterated Expectations I recently came across this identity:$$E \left[ E \left(Y|X,Z \right) |X \right] =E \left[Y | X \right]$$I am of course familiar with the simpler version of that rule, namely that$E \left[ E \...
Consider two random variables, $x$ and $y$. Denote the correlation between them by $\rho$. Assume that $E[x]$ is also a function of some parameter $\pi$ and is increasing in $\pi$. So if we increase \$\...