Questions tagged [conditional]

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Calculate conditional probability using sample from 3variate normal distribution

I am working in R and have a matrix (200X3) named X where I have simulated data from a 3variate normal distribution given its parameters (variance-covariance matrix & and mu). My task is to ...
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Scenario Analysis with a GARCH model - conditional forecasts with hard restrictions on dependent variables?

Waggoner and Zha (1999), see reference below, developed an approach to produce conditional forecasts for VAR models with hard restrictions on the variables using Gibbs Sampling. As an example, they ...
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32 views

How to compute the CDF of summation of two time series? (Using Copula)

My question is about the time series. For modeling the multivariate time series based on the conditional copula. I read two book “Copulas and their applications in water resources engineering”, and “...
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1answer
29 views

Conditional expectations and variance - OLS

Apologies for starting a new post for such basic problems but I have an exam tomorrow and struggle to sort out two answers from last year's exam (2. and 3.). I gave as much context as possible: The ...
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25 views

Conditional and density probability (normal distribution)

I am trying to solve the following problem: Suppose that $\mu\sim N(1,4)$ and $Y|\mu\sim N(\mu,1)$. Show that: $$\begin{bmatrix}Y \\ \mu \end{bmatrix} \sim N\bigg(\begin{bmatrix}1 \\ 1 \end{bmatrix},...
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38 views

A trivial question about EM algorithm theory

In "The EM Algorithm and Extensions", second edition, from Geoffrey J. McLachlan and Thriyambakam Krishnan, X is the latent variable, and Y is de observed (incomplete) variable I'm little confuse ...
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23 views

Conditional expectation of (degenerate) trivariate normal?

Say $A$ and $B$ are both independent, normally distributed. $A\sim\mathcal{N}(\mu_{A},\sigma^{2}_{A})$ and $B\sim\mathcal{N}(0,\sigma^{2}_{B})$ define $C=A+B$. Then $(A,B,C)'$ are degenerate, joint ...
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1answer
20 views

Inference problem, having issues translating problem from words into probabilistic terms

This is the question: There are particular readers for swipe cards, Under normal operating conditions, there is a small probability of 0.02 that swiping a card fails to open the entrance - some of ...
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49 views

How does conditional probability relate to mathematical operators? How to know when to define events as conditional?

I noticed in my introductory statistics course that most operators like AND/OR relate to mathematics operators like multiplication and addition. Is there any relation between conditional probability ...
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39 views

conditional distribution for normal distribution

Assume $X = (X_1, X_2 , ... ,X_n )$ is observed, where the $X_i$ are (independently) $N(\theta , 1)$. find the conditional distribution of $X_1,....X_{n-1}$ given $\bar{X}$. I am having a problem in ...
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61 views

How can I use Bayes' Theorem or analog to compute two dimensional conditional probabilities?

I have Y categories with X divisions and given two marginal probabilities and one conditional probability Given two marginal likelihoods: $\sum_{j=1}^{Y}P(C_j)=1$ $\sum_{i=1}^{X}P(D_{ij})=1$ And ...
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62 views

What is the posterior mean of $\mu$ given a randomly stopped i.i.d. observations from a Normal

Let's imagine I have a machine giving me an independent random number from a normal distribution $N(\mu,1)$ whenever I push a button. I have a stopping rule to decide how many samples to collect - I ...
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18 views

Independent variables in conditional probability

So I am reading this paper about reasoning(Hall, Ali, Chater, & Oaksford, 2016). Consider this conditionals. ...
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10 views

Correct terminology to refer to a collection of conditional probability distributions

I would like your help to find the correct terminology to refer to a collection of conditional probability distributions. Consider two random variables $Y$ and $X$, with supports $\mathcal{Y}$ and $\...
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25 views

Conditional Expectation - confused as how to deal with Et[zt+1] - only know how to do Et-1[zt]

Consider the following MA(2) process: zt = ut + α1ut−1 + α2ut−2, where ut is a zero-mean white noise process with variance σ 2 (a) Calculate the conditional and unconditional means of zt, that is, Et[...
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42 views

Conditional Covariance Problem

Suppose we have independent (not necessarily identical) normally distributed random variables X, Y. If we're given that, upon sampling each variable, X is some multiple a of Y (i.e. x = ay), what is ...
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1answer
33 views

Computing conditional probabilities on multivariate data from covariances

I am struggling to implement some Bayesian algorithm which I hope you may help me with. I am required to compute all probabilities of the form: $$P(Z_i\le z_i\;|\;Z_1=z_1, \dots, Z_{i-1}=z_{i-1}) \;\...
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20 views

Conditional expectation in Basic Linear Unobserved Effects Panel Data Model

I want to see that $ E[u_t|X_t,c] \Rightarrow E[X_t' u_t]$ in a Panel Data Models
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30 views

Probability of picking a white ball

the problem: I have a vase with a ball in it which I know to be either white or black with equal probabilities. I throw a white ball in the vase, shake, and take out a ball without looking, which ...
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Conditional sorts as an alternative for regression models

I have the following regression model R=a+bX+cZX where R is the return and X is a control variable and Z is the variable of interest. As an alternative approach to the use OLS, often conditional ...
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1answer
67 views

Conditional probability with chain rule and marginalisation

I have the following exercise, and I don't understand its solution (the picture): Consider a student who has the choice to buy or not buy a textbook for a course. We’ll model this as a decision ...
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23 views

Conditional dependence between two ordinal variables

I really hope that this question was not answered in any way before, but I couldn't find an appropriate solution to my problem - most probably due to my lack of statistical knowledge. I am trying to ...
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378 views

Conditional expectation on exponential distribution

How can I compute the conditional expectation C-X in the following formula E[C-X|X$<$C]; where C is a constant and X a random variable following exponential distribution?
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37 views

$k$-th order statistics when the value of $j$-th one is known

Suppose there are $n$ random variables $X_i,~i\in\{1,\cdots,n\}$ which are independently drawn according to a CDF $F$ and pdf $f$. Suppose also that we know one of the realization, say $X_{(j)}=x_{(...