# Questions tagged [independence]

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.

1,022 questions
Filter by
Sorted by
Tagged with
4 views

### Independence of groups within a single predictor variable

Say I have two variables: 'Sale Price' of a house, and 'Overall Quality' which is an ordinal variable with values between 1 and 10 (1=lowest quality, 10=highest quality). I want to perform an F test ...
40 views

### How do you test for independence of a process?

I'm working on a research project for one of my professors. He wants to know whether a variable that takes on different values over a large period of time (say 1,000,000 different values) is i.i.d. ...
23 views

### Does uneven sampling during 3 time periods violate independence for ANOVA?

A continuous variable is measured at 7 AM, 2 PM, and 7PM, over the course of 2.5 months (summer). An animal is being periodically observed, while the site is monitored. The observation periods are for ...
4 views

### Accounting for connectedness during the analysis of nodes in a directed acyclcic graph

I am studying a river network and environmental features measured at different stations along the network. Often, one station is higher up the river than another (or multiple others). I can ...
51 views

### Analyzing the statistical independence of a Bernouli sequence

For my research, I need to check whether a sequence of Bernoulli trails (1 as success and 0 as failure) is a Bernoulli process and are statistically independent. As per the following discussion, and ...
22 views

### Alternative to Multinomial Logistic Regression when observations are not independent?

I am dealing with an experimental design with a categorical IV and DV: In a linguistic experiment, I asked speakers to form as many sentences as they could using a limited number of words. They were ...
52 views

### Given $Z\perp X\mid Y$, is it true in general $Var(Z|h(X,Y))=Var(Z|h(c,Y))?$

Given random variables $X, Y, Z$: If $Z\perp X\mid Y$, then I know that $Var(Z|X,Y)=Var(Z|Y)$ But is it still true in general that $$Var(Z|h(X,Y))=Var(Z|h(c,Y))?$$ here $h$ is a real valued function ...
25 views

### Number of Head-Tail in N independent coin flips

Consider a sequence of independent tosses of a biased coin at times $t = 0, 1, 2, . . .$. On each toss, the probability of a ’head’ is $p$, and the probability of a ’tail’ is $1 − p$. A reward of one ...
23 views

### Is the regressor (sometimes called “independent” variable) actually independent of the response from a probabilistic perspective?

In supervised learning, we refer to the regressors as independent variables and response variables as dependent, but from a probabilistic standpoint, I am having trouble understanding this. To ...
24 views

60 views

### Joint distribution from multivariate Normal distribution

Consider two random variables $\{Y_1, Y_2\}$, which follow a joint multivariate normal distribution: $Y = [Y_1, Y_2]^T,$ \begin{equation} Y_1 \sim \mathcal{N}(\mu_1,\sigma_1),\; Y_2\sim\mathcal{N}(\...
25 views

### What does “A realization of independent copies”? [duplicate]

I read in statistic, "a realization of independent copies" from "Elements of copula modelling with R", and do not understand the meaning. I search and found that it means, the two ...
36 views

### Prove a result on expectation with 2 random variables

Part 1 I wish to show that: $$E(X)=E[(X|Y=y1)*Pr(Y=y1)+(X|Y=y2)*Pr(Y=y2)]$$ where the random variable Y can take 2 possible values. As many comments and answers have suggested, this may be technically ...
6 views

### How to determine the Wald-Wolfowitz Runs Test threshold value for non-normal distributions?

If the underlying distribution is strongly skewed, i.e. Gumbel or Weibel, should the Wald-Wolfowitz Runs Test use that distribution, rather than the Gaussian / Normal distribution, to set the null ...
36 views

### Can I use a chi-square test to determine whether my samples are independent or paired?

I am conducting statistical tests for my current research project. Within the scope of this research project, I have two samples (divided by country clusters). The samples contain approximately 1500 ...
22 views

### Definition indepedence and identically distributed (iid)

Bruce Hansen's book "Econometrics" defines a random sample as follows: "The observations $(y_i,x_i, z_i)$ are a random sample if they are mutually independent and identically ...
49 views

### Test for independence between variables [closed]

I have the weekly prices of two stocks over a period of 20 years. How could I test the independency between those two stocks?
6k views

### Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5

I'm confused about how to reconcile the probability of independent events not having anything to do with prior history, but sequences of events do (seemingly) take into account prior history. This ...
25 views

### difference in CDFs and pdfs of joint distribution of two random variables

We know that the joint probability function of two independent random variables is just the product of their respective pdfs. On the same lines, .can we say that if we multiply the cumulative density ...
46 views

### Under which conditions does $X_1 \perp X_2, X_3$ imply $X_1 \perp X_2 | X_3$?

E.g. let us imagine we have $X_3 := X_1 \text{XOR} X_2$ with both $X_1, X_2$ being sampled from $\{0, 1\}$ with $p=0.5$. Then $X_1 \perp X_2, X_3$ but $X_1 \not \perp X_2 | X_3$. Are there conditions ...
15 views

### Should I use normality or independence test?

I have a datasets with 3 variables and 500 observations. The data is multivariate normal, and the 3 variables are independent. I am doing some 'experiments' with the dataset, where I apply some ...
39 views

### Are these independent random variables?

Let $X, Y, Z$ be pair-wise independent random variables. If $A=XY$ and $B=XZ$, are $A$ and $B$ independent? My thoughts are that they are not independent. For example, if $X$ takes values $-1, 1$ ...
17 views

### Mean field variational inference in high dimensions

Is it expected that independence assumption done in mean field variational inference is going to yield on average better approximations for low-dimensional models compared to high-dimensional ones?
56 views

### uniform distribution, showing that two variables are uncorrelated and not independent

Let (X,Y) have uniform distribution on the four points(0,1),(0,−1),(1,0),(−1,0). How can I show that X and Y are uncorrelated but not independent? Could someone just point me in the right direction ...
69 views

### PCA vs linear Autoencoder: features independence

Principal component analysis is a technique that extract the best orthogonal subspace in which we can project our points with less information loss, maximizing the variance. A linear auto encoder is ...
54 views

### Assume $X,Y$ are two independent random variables. Let $Z=f(X,Y)$. If $Z$ is independent of $X$, $f(X,Y)$ is constant in $X$. Is this true?

Let $X\in \mathbb{R}^n$ and $Y\in \mathbb{R}^m$ be two independent random vectors. Then, say that we have a third real valued random variable $Z=f(X,Y)$, with $f$ being measurable. Say that we know ...
47 views

### How to reason about independence of combinations of events?

Suppose sets $A , B,$ and $D$ are independent. Is it guaranteed that $A \cap B^c \cap D$ is independent from $B^c \cup D^c$? Isn't $B^c$ ($B$ complement, or $B$ not happening) giving me ...
19 views

33 views

### Why do we use the term “uncorrelated” to describe linear dependence/independence?

Terminologically, "uncorrelated" to me means that 2 things have no relationship, not necessarily constrained to linear relationships. However, in statistics, we seem to confine "uncorrelated" to mean ...
For example: An airport screens bags for forbidden items, and an alarm is supposed to be triggered when a forbidden item is detected. Suppose that $5\%$ of bags contain forbidden items. If a bag ...
Consider a random sample of size $n$ from a two-parameter exponential distribution, $X_i \sim$EXP($\theta,\eta$), and let $\eta^*$ and $\theta^*$ be the MLEs. a) Show that $\eta^*$ and $\theta^*$ are ...