Linked Questions
14 questions linked to/from Covariance and independence?
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Covariance matrices and independency [duplicate]
If we have a diagonal covariance matrix does that guarantee independency?
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57
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7
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Why zero correlation does not necessarily imply independence
If two variables have 0 correlation, why are they not necessarily independent? Are zero correlated variables independent under special circumstances ? If possible, I am looking for an intuitive ...
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Simple examples of uncorrelated but not independent $X$ and $Y$
Any hard-working student is a counterexample to "all students are lazy".
What are some simple counterexamples to "if random variables $X$ and $Y$ are uncorrelated then they are independent"?
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4
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Can somebody illustrate how there can be dependence and zero covariance?
Can somebody illustrate, as Greg does, but in more detail, how random variables can be dependent, but have zero covariance? Greg, a poster here, gives an example using a circle here.
Can somebody ...
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5
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Why are $X \sim U(-1,1)$ and $Y=X^2$ dependent?
Suppose we have two continuous random variables $X \sim U(-1,1)$ and $Y=X^2$. I don't understand why they are dependent.
$$E[X] = 0$$
$$E[Y] = \int_{-1}^{1} x^2 dx = 2/3$$
$$E[XY] = \int_{-1}^{1} x^3 ...
- 143
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2
answers
11k
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Sampling with or without replacement?
I don't know a lot about sampling methods.
I have a large population of size 2,000,000. I used one of those sample size calculators. It says that I need sample size of approximately 10,000.
I am ...
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5
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2
answers
4k
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Independence and orthogonality
I know what it means to say two variables are independent, but can't understand what does it mean to say two variables are orthogonal.Can anyone help me?
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Is there a difference between a causal relationship and a DIRECT causal relationship?
The following site (http://www-ist.massey.ac.nz/dstirlin/CAST/CAST/Hcausal/causal_c2.html) defines a causal relationship as one where one variable 'directly' affects the other, but without the other ...
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1
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Computing covariance matrix from the given variances?
How can I obtain the covariance matrix when all the variances of the variables are known?
This is from the paper
http://www.cs.berkeley.edu/~jordan/papers/CSD-04-1330.pdf
$$V_1 \sim \mathcal{N}(0,...
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1
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1
answer
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Difference between $\mathrm{Poisson}(x_1)$, $\mathrm{Poisson}(x_2)$ and $\mathrm{BPoisson}(x_1, x_2)$
I am trying to find out the difference between treating two random variables as poisson distributions, $\mathrm{Poisson}(x_1)$, $\mathrm{Poisson}(x_2)$, and using a bivariate poisson, $\mathrm{...
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1
answer
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Covariance Zero Equals Independent?
We know that $cov(X,Y)=0$ does not warranty $X$ and $Y$ are independent. But if they are independent, their covariance must be $0$.
My question is: what kind of distribution must $X$ and $Y$ be for ...
1
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0
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682
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Interpretation of (diagonalized) inverse covariance matrix
There are several threads here about covariance matrix and inverse covariance matrix interpretation (here, here or here).
However, I was wondering how to interpret the inverse covariance matrix (or ...
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0
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1
answer
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Independence of random variables and its relation to the expectation
For sochastic processes $X_n$ and $Y_n$ it holds that if they are indenpendant for all $n$ then $$E[X_nY_n] = E[X_n]E[Y_n]$$ But can you go the other way. I mean if $E[X_nY_n] = E[X_n]E[Y_n]$, does ...
2
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1
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What is wrong with this proof/derivation?
Regarding simple linear regression
$y = a + bx + \epsilon$
where
$\epsilon$ is uncorrelated,
E$[\epsilon]=0$,
and
Var$[\epsilon]=\sigma^2$,
the definition of the residual sum of squares is
$...
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