# 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.

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### What does the minimum of a random variable mean?

Let $X_1, X_2, X_3, \cdots,X_n$ be independent and identically distributred (iid) random variables. Then, how would you know/calculate what $min(X_1, X_2, X_3, \cdots,X_n)$ is?
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### What does it mean when we say the estimators need to be independent when using Ensemble Methods in Machine Learning?

In collective learning (ensemble methods) we need the estimators to be Independent/ uncorrelated from one another. Do I understand correctly, that this means we need to draw the data samples without ...
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### How to force hidden code in autoencoder to produce independent code units?

I am trying to construct an undercomplete autoencoder with number of hidden neurons in middle layer (bottleneck) much lower than number of input (and output) neurons. However, I would like to create ...
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### Use both historical prices and fundamentals data for predicting portfolio profit?

Get highly accurate probability distribution for the future price of portfolio using all the data available. Each stock has two historical data - daily prices (scalar time series updated daily) and ...
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### Robust sum of non-independent random variables

What approach could be used to sum non-independent variables? I have probability distributions of stock prices and want to calculate the probability distribution of the portfolio price (sum of some ...
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### Independence assumption of one-way ANOVA

Let's say that I am interested in how exam test score varies with a person's height. To do this, I take a sample from a school, and then I split this sample into two categories, (1) shorter than 165cm ...
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### Range of probability for non-independent events

Suppose the probability of rain on day 1 is $p_1$ and probability of rain on day 2 is $p_2$. Then the probability of rain for the entire two-day period is $1-(1-p_1)(1-p_2)$, under the assumption that ...
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### Does a martingale difference sequence (mds) imply strong mixing?

I read this from an econometrics paper (Dufour and Pelletier, 2014) " The typical hypothesis which is imposed in the time series literature is that the $u_t$'s are either independent and identically ...
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### Why aren't all Normal and Rademacher variables independent?

In Wikipedia page: https://en.wikipedia.org/wiki/Normally_distributed_and_uncorrelated_does_not_imply_independent, we find a classical counter-example showing that two normally distributed and ...
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### Finding probability of $U$ independent of joint pmf $f_(X,Y)(x,y)$ - meaning?

Given two random variables, $X$ and $Y$, with a joint pmf: $f_{(X,Y)}(x,y) =$ \begin{array}{ll} 0.3 ,\text{if} \space (x,y) = (3,0) \space \text{or} \space (0,6) \\ 0.2, \text{if} \space (...
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### How to understand the normality assumption of the errors?

We know one of the Gauss-Markov conditions is $\mathrm{Cor}[e_i, e_j]=0$ for $i \neq j.$ Also, we assume the errors are normally distributed, i.e., $e_i \sim \mathcal{N}(0, \sigma^2).$ My teacher ...
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### Testing independence of n binary variables

I have 6 binary (dummy) variables corresponding to different possible states that could apply to the subjects, and each subject has two of the six possible states, ie the sum of all of their dummy ...
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### Correlation between two linear sums of several products of random variables

I would like to understand the correlation between two linear sums of several products of random variables. Well, it is quite difficult to describe the exact question I have. Basically I want to ...
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### Characteristic function of $X+X^2$ if $X$ is a standard Gaussian random variable

Can anyone please tell me how I can find the characteristic function of the random variable given by the sum $X+X^2$ where $X$ is a standard Gaussian random variable? Many thanks!
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### Are the random variables XY and X^2 independent if X and Y are zero - mean Gaussian independent random variables?

Assume that X and Y are random variables which are normally distributed as N(0,s_X^2) and N(0,s_Y^2), respectively. Furthermore, assume that X and Y are independent. Could anyone please tell me if ...
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### In Simple Linear Regression $\hat \beta_1$ and $\bar Y$ are independent [duplicate]

I want to show that, in simple linear regression $\hat\beta_1$ and $\bar Y$ are independent. My attempt: I have calculated the $\mathcal Cov(\hat \beta_1,\bar Y)$ and it turns out to be $0$.I also ...
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### Where is the bomb: How to estimate the probability, given row and column totals?

This question is inspired by a mini-game from Pokemon Soulsilver: Imagine there are 15 bombs hidden on this 5x6 area (EDIT: maximum 1 bomb/cell): Now, how would you estimate the probability to find ...
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### joint distribution of a random matrix and its column size variable

Suppose $C_k$ is a random matrix contains columns of measurement vectors that are random variables: $$C_k=[c_k^1,...,c_k^{m_k^c}]$$ $m^c_k$ is the number of columns as well as a random variable. All ...
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### What defines a correct / incorrect model in Bayesian inference when it comes to independence

This might be a very broad question but I'm wondering whether we can say a model of Bayesian inference is "correct" or not about assuming independence. For example, suppose there are $N$ coins each ...
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### Does the conditional density $f(X|X+Y<a)$ equal to $f(X)$ when $X,Y$ are independent continuous random variables with $Y$ having full support?

I wonder if the following equation holds when continuous random variables $X,Y$ are independent from each other and random variable $Y$ has full support on $\mathbb{R}$. \begin{align} f(X)=f(X|X+Y<...
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### Probability of multiple parasites given the presence of one parasite

I am trying to simulate parasitic plants that infect trees. I would like to test wether the presence of one parasite makes it more likely that the tree has more than one parasite. The number of trees ...
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### Independence of Mean and Variance of Discrete Uniform Distributions

In the comments below a post of mine, Glen_b and I were discussing how discrete distributions necessarily have dependent mean and variance. For a normal distribution it makes sense. If I tell you \$\...
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### Violation of Independence of Observations - Logistic Regression

Apologies if this seems a basic question but I can't find enough detailed information about what exactly constitutes a violation of independent observations. The regression I'm wanting to run is ...