Events (or random variables) are independent when information on some of them tells you nothing about the probability of occurrence (/ distribution) of the others. Please DO NOT use this tag for independent variable use [predictor] instead.

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Showing independence between two functions of a set of random variables

I've been working on the following problem and I'm confused about how to get started: Let $X_1, X_2,..., X_n$ denote $i$.i.d. real valued random variables, each absolutely continuous with an ...
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Post-hoc for independent t-tests for a total scale score and subscale scores

I'm comparing two groups on scores on the Dissociative Experiences Scale, and its subscales, using independent-samples t-tests. The DES is a 28 item questionnaire yielding a total DES score. There are ...
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30 views

Paired independent sample t-test?

I have two methods of processing certain data, where one is a more advanced version of the other. After processing the data, the output is scored from -1 to 1. I have a set of 7 distinct data points ...
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72 views

Does zero correlation mean no causation? [duplicate]

If I demonstrated that there is no correlation between two random variables, does that mean that there is no cause and effect relation between them ?
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30 views

Probability question regarding independence of events

The question was posed in this way: Suppose John and Jan read a book separately. Each person has a probability of $.5$ to catch a typo and the each event to catch a typo is independent. Let $A = ...
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1answer
23 views

Statistical independence of US presidential primaries occurring on the same day

A new market recently appeared on PredictIt, for the chance of Trump winning 50% of the vote in each of the April 26th primaries. This market seemed overvalued to me. I tried to get a handle on how ...
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1answer
103 views

Independence of two decks of cards, each with a different numbers of cards

I am trying to get an intuitive feel for what independence 'is.' My initial guess was that variables are independent if they can't casually affect each other. I was discussing this on a hacker news ...
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14 views

Independence of ordered statistics part 2

In relation to my previous question, I have a second problem. How to show that $U_1+U_2$ is independent of $Y_3$? I can find out the pdf of $U_1+U_2$, as well as of $Y_3$, however please help me ...
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103 views

Independence and Order Statistics

I have a problem at hand, which I am not being able to proceed. Can someone help me begin? $Y_1<Y_2<Y_3$ :An order statistic of size 3 from distribution having pdf $$ f(x)=2x\ \ \ ...
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1answer
44 views

Probability Question - Mutual Exlusive/Independent (To the power)

A bridge has to be designed for a region which is subject to the influence of both floods and earthquakes. Its expected design life is 120 years. At the particular site, the probability of a flood ...
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6 views

Number independent components in ICA

I'm a student working on my bachelor thesis performing independent component analysis (ICA) on some fMRI data using MELODIC FSL. I would like to ask some questions regarding the results of ICA. ...
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How to evaluate the quality of Bayesian network sampling?

I have generated a sample from a Bayesian network by applying Forward Sampling. I learn the parameters of the network (the same structure) from this sample so as to evaluate the quality of the sample ...
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Proving that the estimators of coefficients and variance in GLS model are independent

I have come across this question in a textbook: I have a linear model $Y=Xb+u$ with for instance autocorrelation, in order to introduce GLS $Y^*=X^*b+u^*$ (with $Z^* = \Omega^{-1/2}Z$). Then an ...
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How to check if functions of i.i.d random variables are dependent or independent?

i'm new to this forum and the science of statistic.This is my question: Let's say that we have two i.i.d random variables X and Y, which both follow a Rayleigh distribution. Then, we define two new ...
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23 views

Assumptions on Multiple Comparison - Bonferroni and others

I was asked for an alternative procedure to multiple comparisons which does not require independence of the multiple tests being applied. I´ve found some readings where Bonferroni´s correction is said ...
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2answers
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How is mean independence defined?

Suppose $X$ and $Y$ are random variables. As I understood it, mean independence is defined as follows $Y$ is mean-independent of $X$ iff $\Bbb E[Y|X] = \Bbb E[Y]$ But my professor in class gave ...
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23 views

All possible tables in fisher exact test

The table contain results of a study comparing radiation therapy with surgery in treating cancer of the larynx. Use Fisher's exact test to test $H_0:\theta=1$ vs $H_a:\theta>1$ I have ...
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How to determine if events are joint or disjoint?

Two events recorded for two dice throws : 1. odd,even (P = 1/2) 2. 1,2,3,4,5,6 (P = 1/6) As these events are joint the probability of dice1 being odd and dice2 ...
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1answer
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OLS when both independent and dependent variable are multiplied by another variable

I was given the following problem involving OLS: Suppose we have $(y_i,x_i,z_i)_{i=1}^n$ iid sequence, such that $x_i$ is a vector with K entries and $y_i$ and $z_i$ are scalars. Suppose $z_i$ is ...
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Autocorrelation of concatenated independent AR(1) processes

Let $\left\{X_t\right\}$ be a stochastic process formed by concatenating iid draws from an AR(1) process, where each draw is a vector of length 10. In other words, $\left\{X_1, X_2, \ldots, ...
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16 views

What's the difference between correlation and dependence? [duplicate]

Are the statements $$\text{Corr}(X,Y) = 0$$ and $$P(X \cap Y) = P(X)P(Y)$$ Apologies, I am pretty sure I am screwing up notation here. The first statement makes $X,Y$ random variables. But the ...
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If distance correlation $DCOR(X,Y) = 0.5$ then are X and Y dependent or independent?

If distance correlation $DCOR(X,Y) = 0.5$ then are $X$ and $Y$ statistically dependent or independent? What about when $DCOR(X,Y) > 0$, are they statistically dependent for sure even when it's less ...
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Does leaving out an important predictor in a mixed linear model violate the independence assumption?

I have data from an experiment with 3 groups, measured at 4 time points, where each subject performed a task where 2 factors are manipulated: valence (3 levels) and predictability (2 levels). I know ...
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1answer
44 views

Can rank variables be iid?

I'm curious about the responses to some questions I've found on this site -- but I can't post comments yet, so I am starting a new question. At least two people have asked about regression to predict ...
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Power of permutation test for testing whether X,Y are independent- Homework question

I'm trying to solve my homework question in the attached Image:I'm stuck on 1.(c). Two directions I had in mind were: the central limit theorem, and the Poisson estimation for a large number of ...
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Independence of categorical variable from a continous one

I have test scores for some people (say, 10 tests for each of 1000 persons, R data frame with 1k rows and 11 columns: person name and test results) and I want to ...
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1answer
20 views

Prove independence of variance estimator and mean estimator in normal distribution [closed]

How to prove that $S^2$ and $\bar{X}$ are independent given that $X_i \sim$ normal$(\mu, \sigma^2)$.
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29 views

Understanding Process Behind Calculation of Loss (cat model)

I currently studying event loss table (ELT) produced by RMS (Risk Management Solution) as the output of cat model. This table can be used to generate distribution of loss. Some important points ...
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1answer
44 views

An entropy and mutual information problem

Let's suppose we have 4 random variables X,Y,Z and T and that the following equations hold about the entropy: $$H(T|X)=H(T)$$ $$H(T|X,Y)=0$$ $$H(T|Y)=H(T)$$ $$H(Y|Z)=0$$ $$H(T|Z)=0$$ I want to prove ...
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1answer
56 views

Is being the first-born independent of age?

If one were to assert that, in a large population, the fact of a person or an animal being the first-born in the family was independent of their age, then what assumptions (if any) would one have to ...
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10 views

Not sure how to analyse this experiment. everything seems dependent

a student conducted an experiment and I wonder if you can help me to evaluate the right statistical model. He took soil samples with one plant (soil core has 20 cm in diameter) from different ...
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22 views

Methodology to generate conditionally independent data correct?

I am trying to generate samples from continuous distributions that are conditionally independent. More specifically, I would like to generate samples from the following joint distribution $f(x,y,z)$ ...
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violation of independence assumption for comparison of means

I have a binary dependent variable (following a pattern by my subjects or not). I want to test the relationship between a characteristic of subjects (i.e., personal innovativeness) - categorized into ...
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218 views

Real life examples of difference between independence and correlation

It is well known that independence of random variables implies zero correlation but zero correlation need not imply independence. I came across plenty of mathematical examples demonstrating ...
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Implications of independence of several random variables

Consider 4 real-valued random variables $X,Y,Z,V$ defined on the same probability space $(\Omega, \mathcal{F}, \mathbb{P})$. Assume that $X$ is independent of $Y,Z,V$, i.e. the probability ...
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dependent and independent risk factor

when a certain association appears only when we adjusted for certain potential confounders. In this case, can we say that this association is independent of this confounder. in my case, I'm studying ...
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13 views

Conditional independence and product of variables

I am reading a paper and the paper states the following: "Suppose that e1 and e2 have the standard model error properties of being mean zero and have conditionally independence of each other, so e1 ...
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100 views

ANOVA - Independence condition for paired data

Hi I'm reading the book "OpenIntro Statistics" about ANOVA and in section 5.5.4 when explaining the conditions for applying ANOVA under the voice 'Independence' it states: Independence. [...] For ...
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Why do we use the chi-squared test to test independence of 2 categorical variables?

I sometimes use the chi-squared test to test the independence of categorical variables. I know how to do the test but don't know the underlying concepts and details. So, I was wondering about the ...
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Why does linear regression need mean independence?

If random variables $X$ and $U$ are independent, then they are mean independent by a rule of conditional expectation 'Pulling out independent factors'. If random variables $X$ and $U$ are mean ...
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How to test independence of two markov switching processes using likelihood ratio test

I would like to test for independence of two first order markov switching processes with two states each. I have read this can be done using the LR test (I know that this will be simulation based ...
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34 views

Factorial ANCOVA: Independence of the covariate and treatment effects

I would like to test whether the assumptions of a 2x3 ANCOVA are met. How do I exactly test the assumption "independence of the covariate and treatment effects" in this case? I proceeded as follows: ...
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1answer
45 views

Point-Biserial Correlation (r) for non homogeneous independent samples

I am performing an independent t-test, in which the independent variable is the "group" which has two values A and B representing an approach the participants used, and the dependent variable is a ...
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53 views

ANOVA - Assumption of Independence

I am also a little bit confused about the assumption of independence. I have the following situation: one continuous dependent variable (radiant power of a medical device) a few independent ...
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63 views

Is Independent jeffreys prior different from independent reference prior?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derived the Jeffreys prior for $\theta_1$ and $\theta_2$ independently (so for, e.g. $\pi(\theta_1)$, setting in the ...
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1answer
69 views

Independence of variables

Q:Two variables X and Y have same mean and variance.If U=X+Y and V=X-Y then, are U and V independent and correlated? I found that U and V are uncorrelated. But don't know how to check for ...
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Estimate point in metric variable where probability of success of a conditionally Bernoulli distributed variable changes (independent observations)

There is a metric variable X and a conditionally Bernoully distributed variable Y, where the probability of success of Y changes at a threshold x of variable X. The obervations are independent. I want ...
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Can longitudinal studies ever be treated as having independent observations?

This may be a dumb questions, but for sake of statistical analyses I'm wondering if the data of a longitudinal study can ever pass the assumption of having independent observations? For example, I am ...
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Practicality of sparse inverse covariance matrix assumptions

For a set of $p$ datapoints in $m$ dimensional space, if the features are packed in a $p\times m$ matrix $X$, then $C = XX^T$ is the covariance matrix and $K = C^{-1}$ is the inverse covariance ...
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Non Linear Endogeneity

Consider the following Linear Regression Model.$$y_{it}=x_{it}\beta+\upsilon_{it}$$ where x is a scalar and $$cov(x_{it},\upsilon_{it})=0$$ It is know, however, that $cov(.)$ is a measure of ...