# Questions tagged [conditioning]

Conditioning is a probabilistic operation that consists in examining the probabilistic properties of a random variable (or of an event) given the realised value of another random variable (or of an event)

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### Variance of Bernoulli when success probability varies

Say the success probability $X$ is a random variable with mean $\mu$ and Variance $\sigma^2$ which takes values in $[0,1]$. How can I compute the variance of a random Variable $Y$ which is 1 with ...
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### If $e_0$ are the OLS residuals, what is random in $\hat{\beta}_{OLS}|f(e_0) < \hat{\beta} < f^*(e_0)$?

This is a follow up question to the question I've posted here. Suppose $Y \sim N(X\beta, \sigma^2I)$, where $y \in \mathbb{R}^n$. Let $X \in \mathbb{R}^{n \times p}$ denote a full rank design matrix. ...
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### Test for conditional dependence

I am trying to find out whether two variables are conditionally dependent on each other. I would like to have a test for B implies A (B->A) or not and one for A implies B (A->B) or not. It is ...
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### Gaussian Processes as weighted averages?

I've been wondering if a "weighted average" is a valid means to consider the Gaussian Process, specifically in the context of GP Regression. The kernel (I'll be referring to the common ...
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### Expected value of max of two discrete random variables

I'm reading this paper An Efficient PTAS for Stochastic Load Balancing with Poisson Jobs. Which is solving a makespan minimizing job-shop problem for Poisson job sizes. Basically, schedule the minimum ...
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### Markov transition matrix row sums to 1

I am trying to learn a little bit of Markov Chains through Dobrow's "Introduction to Stochastic Processes with R", but i am struggling with the following: The entries of every Markov ...
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### Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$?

I understand that $E(Y|X)$ and $E(Y)$ are different, but difference sources, when $Y$ is a function of other random variables such as $X$, use $Y|X$ and $Y$ to describe this relationship. I'm not sure ...
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### Why condition on either the r.v. $X$ or $Y$ and integrate over a product of pdfs rather a single pdf to find this probability density?

Let $X$ have the probability density $f_{X}(x)=\lambda e^{-\lambda x}, \;\; x>0$ and let $Y$ have the probability density $f_{Y}(y)=\lambda e^{-\lambda x},\;\; y>0.$ Find the probability ...
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281 views

### conditioning for deep neural networks

What is the best way to do conditioning when working with deep neural nets? For example, say we we want to condition a VAE on the class i.e. CVAE. There exists different ways of adding the class to ...
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### What is E[X|Y>c] where Y=X+Z, and X, Z are normally distributed rvs? [duplicate]

Suppose X, Z are normally distributed random variables and independent ($X$ follows $N(\mu,\sigma^{2})$ and $Z$ follows $N(0,\sigma_{z}^{2})$), and that Y=X+Z. What is E[X|Y>c], where c is just a ...
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### Find conditional pdf given joint

Let the joint pdf of $X$ and $Y$ be $f(x,y) = 12e^{-4x-3y}, x>0, y>0$. What is the marginal cdf of $X$? of $Y$? Am I just supposed to integrate f(x,y) with respect to $x$ or $y$ to get the ...
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### Meaning of “for each value $X = x$, the random variable Y can be represented in the form $Y = \beta_0 + \beta_1 x + \epsilon$” in linear regression

In what follows assume $Y: \ \Omega \to \mathbb R$ and $X: \ \Omega \to E$ The following quoute is from page 700 in DeGroot and Schervish - Probability and statistics, introducing a simple linear ...
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### When can we use fixed design regression results for the random design setting? [closed]

Suppose I have an independent vector $X$ and a dependent scalar random variable $Y$ and I wish to construct a regression model to predict $Y$ using $X$ given data $\{(x_i,y_i)\}_{i=1}^{n}$. For ...
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### What does “Normal distribution conditioned on $x \mod 1$” mean?

I understand what $Pr[X = x | Y = y]$ means, however, on this paper (Lemma 10 in Appendix A), we have the following: Let $D_r$ denote the continuous Gaussian distribution of parameter $r$,i.e., the ...
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### Consistent estimator for conditional expectation

Take sequence of random vectors $(Y_i, X_i)_{i=1}^N$ i.i.d. $X_i$ has finite support. Let $x$ be a point in the support of $X_i$. Consider $E(Y_i|X_i=x)$. Suppose it exists and is finite. Is it ...
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### Suppose $X,Y,Z$ are random variables such that $Y,X$ are perfectly correlated. Does it hold that $P(Z|X,Y) = P(Z|Y)$?

Suppose $X,Y,Z$ are random variables such that $Y,X$ are perfectly correlated. I am wondering if it holds that $P(Z|X,Y) = P(Z|Y)$? It would seem that $X$ would then be a substitute of $Y$. Is there a ...
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### Are normal prior and posterior random variables dependent?

Consider the usual normal Bayesian model. The prior $X=\mu_0+\sigma_0\epsilon_0$, where $\epsilon_0$ follows a standard normal distribution. The data $Y=X+\sigma_1\epsilon_1$, where $\epsilon_1$ ...
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### notation: precedence of conditional when multiple variables

In expressions such as $P(X,Y|Z)$ and $I(X; Y|Z)$ (mutual information) there are two interpretations for a student, and the correct one does not seem to be mentioned in textbooks. "joint ...
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### How does conditional expectation relate to sufficiency?

In what follows, I will disregard all "measure-theoretic niceties about conditioning on measure-zero sets", as my professor calls it. I just want to know if the following general idea, or ...