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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When does the law of large numbers hold for RVs from a distribution with infinite variance?

Under what conditions does the law of large numbers hold (or fail, if that is easier to describe) for independent identically distributed random variables drawn from a distribution with a finite mean ...
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11 views

How to estimate dependency or in-dependency between variables [on hold]

Is it possible to estimate "the rate/degree (or something similar)" if there is dependency between 4 different types of variables that are categorical. If the 5th variable is a outcome variable(the ...
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2answers
66 views

How to interpret Fisher Test?

How do I interpret the odds ratio for this fisher test output in R? ...below is my matrix that I input into fisher.test in R: ...and below this is the output of the test in R:
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7 views

Independence of errors in fixed effects regression

I am trying to run a fixed effects regression and am currently testing assumptions. This probably is rather a "beginner question", but how do I test the assumption of independence of errors for ...
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2answers
62 views

Independence of observations violated

I discovered a (probably) major flaw in my research design. I am examining investors and their investment performance. Or in other words, I want to investigate if some investors are better than ...
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274 views

With categorical data, can there be clusters without the variables being related?

When trying to explain cluster analyses, it is common for people to misunderstand the process as being related to whether the variables are correlated. One way to get people past that confusion is a ...
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1answer
43 views

Null distribution of fisher's exact test; where the nullity is used?

For 2x2 contingency table, we can test independence of row and column variables by using Fisher's exact test where we assume all marginals are fixed. ...
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25 views

Notion of “the same” distribution in definitions of “iid” and “exchangable”

Schervish's (1995) Theory of Statistics defines exchangeability like this (p. 7): A finite set $X_1, …, X_n$ of random quantities is said to be exchangeable if every permutation of $(X_1, …, X_n)$ ...
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9 views

Use inclusion-exclusion to find explicit formula for $P(A_k)$ w/o using PGF

Probability with Martingales This was answered here using bounds and here using PGF. I would like to try inclusion-exclusion. Let $H_1, H_2, ...$ be independent events with $P(H_k) = p$ where $...
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1answer
25 views

Independent Events in Probability and Two dimensional random variable

I am trying to solve this problem, and get an answer I am not sure about. "On his way to work, Mr. Smith passes 3 traffic lights. The probability of green light is 0.6 in each traffic light, ...
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54 views

Level of Mutual Information Among Bootstrap Samples vs. Delete-50% Jackknife Samples

Q: I wondered if anyone could offer a mathematical proof or similar, that, on average, delete-50% jackknife samples are not inherently more “independent,” in terms of information content, than ...
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Multiple regression with (partially) non-independent predictors?

Question 1: Let’s say I want to predict SAT scores, and I have a hypothesis that IQ is a better predictor of SAT scores than weight is. What is the method that would allow me to reject the null ...
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22 views

Probability distribution arising from the combination of a normal variable and an other random variable

Let $X\backsim N(0,5^2)$ and Y be an independent random variable taking the values +1 and -1 with equal probability.Find the distribution of $S=XY+\frac{X}{Y}, T=XY-\frac{X}{Y}$ I have solved the ...
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23 views

What is the joint probability of this two handicap events related with Champions League today's Final?

A gambling company has these two handicap events related with today's Real Madrid versus Atlético de Madrid match: Real Madrid -1: 5.00 Atlético de Madrid +3: 1.04 Are these events dependent or ...
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1answer
193 views

Looking for proof of conditional dependence, when the conditioning variables are linearly related

Suppose we have three random variables, $X$, $Y_1$, and $e$ (for error). Variable $e$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture ...
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12 views

Significance across Categories of Quantitiative Data

I have a quantitative independent variable that has been grouped into categories (A-G). Example: Age of people by decades (20s, 30s, 40s, etc.) I want to determine if the difference between the ...
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1answer
34 views

Are the distances of the kNN i.i.d?

Imagine the set of i.i.d observations $D = \{x_i\}_{i=1}^N \subset X^n$. Let the distance function $d \colon X^n \times X^n \rightarrow \mathbb{R}$ be used to find the $k$ nearest neighbors to the ...
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Splitting an i.i.d. sample in two by criterion - what survives of independence and population representation?

Assume that I have available a $k$-dimensional i.i.d. sample of size $n$, collected in the $n \times k$ matrix $\mathbf X$. Each column represents a series of realizations from a random variable. ...
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1answer
46 views

Skewness for a sum of independent weighted bernoulli random variables with different probabilities of success

Suppose $Z_i$ are independent Bernoulli random variables with differing probabilities $P_i$. Also suppose weights $W_i$ are positive and constant. Let's define the random variable $S$ which is the ...
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22 views

Independence test for three categorical variable

I want to know if my use of the $\chi^2$ test of independence is valid. I have three binary categorical variables, $X,Y,Z$, and I want to test the following hypothesis. If you are in the group $X = 1$...
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1answer
32 views

Understanding statistical independence of events using a relative frequency interpretation

This is what I've read in my textbook: "If $n_A$ and $n_B$ are the number of times the independent events $A$ and $B$ have occurred, then we expect that the ratio $\frac{n_{AB}}{n_A}$ (num. of times ...
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1answer
41 views

Independence and homoskedasticity

Does $E(u|x)=0$ imply homoscedasticity? If yes, why? Also, does $E(u|x)=0$ mean that $u$ and $x$ are fully independent? If answers to both these question are no: Does full independence of $u$ and $...
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Probabilities concerning incoming calls at a call center and a question of independence

I work at a call center in a department where we receive two grades of calls: A and B. 15% of our calls are grade A, and 85% are grade B. Only two people work in my specific department, me and my co-...
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17 views

Combining independent observables for the same quantity, how to check independence

Let's assume we have a set of observations $\{x_i\}$ of a physical quantity $x$. We have a model $x=X(y)$, where $y$ is a free parameter. Let's assume that we have two distinct observables, $f(x)$ and ...
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1answer
38 views

Chain rule for Bayesian Networks

Suppose we have a simple Bayesian Network as follows: $X_1$ --> $X_3$ <-- $X_2$. Using the chain rule of Bayesian Networks, we can say the following: $$ f(x_1,x_2,x_3) = f(x_1) f(x_2) f(x_3 | x_1,...
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1answer
28 views

Testing the independence of a time series

I’d like to test whether my time series of consecutive payments is independent or not and thought that since this is a pretty common condition in statistics it should be easy. Well, turns out is isn’t ...
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109 views

Independence of reward and future state in stochastic process?

Consider a Markov decision process in which we transition from state $s_t \rightarrow s_{t+1}$ by taking action $a_t$, and then apply an update to a single entry from a table of $Q$-values based on a ...
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20 views

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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3 views

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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90 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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79 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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33 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
110 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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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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140 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 $$ f(x)=2x\ \ \ 0<x<1$$...
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1answer
48 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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7 views

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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131 views

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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49 views

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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1answer
37 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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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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24 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 que ...
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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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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, X_{10}\...
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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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24 views

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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4answers
162 views

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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46 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 ...