# Questions tagged [covariance]

Questions about covariance, a measure of (linear) association between two random variables.

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### Joint distribution and covariance of Poisson process and waiting time

Hi I am having a trouble solving for this problem where I have to find 1) Joint distribution of $W_{1}$, $W_{r}$ for $r\geq2$. 2) $\operatorname{Cov}(W_{1},W_{r})$ for $r\geq2$. [Notation ...
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### Covariance of squared terms

Let (X,Y) both follow weibull distribution and cov(X,Y)=c. Determine the cov(X^2,Y^2). I can't make it out. Any help is appreciated.
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### Calculate covariance of 2 random variables when only given variance and cov

So I've been given the following exercise: Let $X$ and $Y$ be two random variables. Let $Var(X) = 2$ and $Cov(X, Y) = 1$. Compute $Cov(5X, 2X + 3Y)$. How do I do this when I don't have the second ...
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### find the correlation coefficient of two random variables after the same function transformation

we have two random variables: U1 and U2 follow uniform distribution between 0 and 1: U1 ~ U(0,1), U2 ~ U(0,1) and correlation: corr(U1,U2) = ρ covariance : cov(U1,U2) = corr(U1,U2)/12 Then we do ...
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### Covariance matrix problem

We consider 2 independent throws of the dice. We note the faces of the dice with $0,1$ and with $X,Y$ the random variables corresponding to the first and second throw. What is the covariance matrix ...
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### Does this property of covariance require independence between random variables?

Lemma 5.3.6 in this page states that: $$\textrm{cov}(X+Y,Z)=\textrm{cov}(X,Z)+\textrm{cov}(Y,Z)$$ Does this property require that X, Y and Z must be pairwise independent?
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### Covariance function of a Gaussian Process, sin and cos

Let $X(t) = \varepsilon_1 \cos(t)+ \varepsilon_2 \sin(t)$ where $\varepsilon_1, \varepsilon_2 ∼ N(0, 1)$ iid. Find the covariance function $C_X(s, t)$. I know that E(X) = 0 so Cov(X(s),X(t)) = E(X(s)...
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### How to deal with underflow issues in high-dimensional entropy calculation?

I was not sure if the question makes sense here or should better be placed in a computational/CS forum, but I hope you can give me some insights. I am working in image processing and use the ...
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### Computing Covariance of Sums of i.i.d. Random Variables

Problem: Suppose that $X_1,X_2,\dots$ are i.i.d. random variables with $E[X_1]=1$ and $E[X_1^2]=5$. Let $S_n=X_1+\cdots+X_n$. Compute $\text{Cov}(S_a,S_b)$ for $1\leq a<b.$ Attempt: By the ...
### What does $cov(x_1,x_2) >> 0, cov(y_1, y_2) >> 0$ and $cov(x_1+y_1, x_2+y_2) = 0$ tell us about $x_1, x_2, y_1, y_2$?
I was posed this problem where we know: $$cov(x_1,x_2) >> 0 \\ cov(y_1, y_2) >> 0 \\ cov(x_1+y_1, x_2+y_2) = 0 \\$$ What does this tell us about the structure of $x_1, x_2, y_1, y_2$? ...