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.

learn more… | top users | synonyms

0
votes
1answer
16 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 ...
0
votes
0answers
20 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 ...
1
vote
1answer
31 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). $E$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture variable $Y_2$ ...
0
votes
0answers
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 ...
1
vote
1answer
33 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 ...
0
votes
0answers
6 views

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. ...
2
votes
1answer
37 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 ...
0
votes
0answers
18 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
vote
1answer
31 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 ...
0
votes
1answer
40 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 ...
1
vote
2answers
22 views

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 ...
0
votes
0answers
16 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 ...
1
vote
1answer
36 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 | ...
1
vote
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 ...
0
votes
2answers
108 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 ...
1
vote
0answers
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 ...
0
votes
0answers
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 ...
1
vote
0answers
88 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 ...
0
votes
2answers
75 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 ?
1
vote
0answers
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 = ...
2
votes
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 ...
3
votes
1answer
109 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 ...
2
votes
0answers
16 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 ...
6
votes
2answers
135 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\ \ \ ...
1
vote
1answer
46 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 ...
0
votes
0answers
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 ...
5
votes
2answers
123 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 ...
3
votes
0answers
46 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 ...
0
votes
1answer
29 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 ...
2
votes
2answers
53 views

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 ...
0
votes
0answers
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 ...
0
votes
0answers
12 views

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 ...
1
vote
1answer
33 views

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 ...
4
votes
0answers
24 views

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, ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
6
votes
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 ...
2
votes
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 ...
2
votes
0answers
26 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
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$(\mu, \sigma^2)$.
0
votes
0answers
30 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 ...
0
votes
1answer
46 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 ...
3
votes
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 ...
0
votes
0answers
11 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 ...
0
votes
0answers
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 $f(x,y,z)$ ...
0
votes
0answers
14 views

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 ...
8
votes
2answers
225 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 ...
1
vote
1answer
32 views

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 ...
0
votes
0answers
38 views

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 ...