# Tagged Questions

For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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### How to find covariance of sample mean and sample standard deviation

I have a question to find the covariance of sample mean and sample standard deviation based on the following: I have tried something on my scratch paper, but for some reason, I cannot upload on here....
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### Linear Regression and finding Correlation Coefficient

In a Simple Linear Regression $y= \alpha + \beta x + \epsilon$, we gather this information: $S_y=20, S_x=5, \widehat{\beta} = 0.2$ how I could find Instance Correlation Coefficient between x and ...
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### Covariance matrix using squared exponential function

I'm writing down the covariance matrix $K$ of a vector X using squared exponential covariance function, and then evaluating the determinant of the matrix $K$. Let's say i add a new point to $X$ , and ...
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### Augmenting a matrix with a highly-incorrelated column

Consider a binary matrix: $$\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 &1 \\ \vdots & \vdots &\vdots \\ 1 & 1 & -1\end{pmatrix}$$ with a random distribution of 1 and -1 ...
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### Given f(x) and two correlated random variables x & y, how do I estimate the correlation of f(x) & f(y)

I have a smooth continuous well-behaved function f(x), where f(x) is positive and mononically increasing with x, and x is positive real continuous variable. Given the mean, variance, and correlation ...
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### Convergence under rank correlation

I have a following setup: Let $c\in{\Bbb R}$, $R^2\in [0,1]$ and $\Psi,\varepsilon_1,\varepsilon_2,\ldots$ independent random variables on a probability space $(\Omega,{\cal A},{\Bbb P})$. Define the ...
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### increment of Brownian motion squared [closed]

$(W_t)_{t \geq 0}$ is Brownian motion, assume t>s, does $E[(W_t-W_s)^2W_s^2]=(t-s)s$ ? In other words, are $(W_t-W_s)^2$ and $W_s^2$ independent?
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### Why is pure sample covariance a bad metric to understand the degree of correlation between two variables?

Covariance helps you understand how variables are linearly related. Would it be possible to have two pairs of variables in a deterministic relationship (i.e. linearly correlated variables) that have ...
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### Comparing two vectors based on order and ranking?

What I want to do is compare the ordering of variables determined by the ranking of each variable. For example: Say, I have a rating system that is made up of 5 different ratings - Excellent Good ...
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### Relation between Correlation and Convolution

We have two functions of time $f(t)$ and $g(t)$, for which convolution and correlation are defined as following: Convolution: $(f(t)\ast g(t))(\tau) = \int_{-\infty}^\infty{f(t)g(\tau-t)dt}$ ...
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### Why is the maximum value of cross-correlation achieved at similar section?

I'm a bit confused and probably need some sleep. When trying to find a short signal inside a long one (or the delay), it's almost a trivial fact that we should look for the maximal valued coefficient ...
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### Multiple variables correlation

There are a number of entities. Each entity has three sets of parameters. Each set of parameters describes entity behaviour in a specific system. The problem is to find mathematical method that would ...
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### Partial Correlation Coefficient

I have the following questions on computing the correlation coefficient. Let us say we have two discrete random variables $X_1$ and $X_2$, where $X_1$ has $n_1$ outcomes and $X_2$ has $n_2$ outcomes....
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### We have an urn with $5$ blue balls and $15$ red balls.

We remove $7$ without replacement. Let $R$ be the number of red balls removed and $B$ the number of blue balls removed. Do you expect $R$ and $B$ to be positively correlated, negatively correlated, or ...
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### The product of a normal and Bernoulli variables, independent from each other

Let $X\sim N(0,1)$ and let $Z$ be a random variable independent of $X$ such that: \Pr(Z=z) = \begin{cases} \frac{1}{2} & \mbox{if $z = -1$ or $z=1$}, \\ \\ 0 & \mbox{...
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### If two functions are even, then X and Y are uncorrelated

I Need some help: Let $Y=h(X)$ be a real square integrable function and X has a density function $f$. Show: If $f$ and $h$ are even functions then $X$ and $Y$ are uncorrelated (but generally not ...
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### correlation coefficient is over 0.7

"correlation coefficient can be over 0.7 then we can say Two factors have some strong relation. Then What is the 'reason' that we can say like that? Explain it." I got that problem and I really dont ...
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### Proof of Correlation Coefficients

Good evening, I have a problem with an exercise: Let $X$ and $Y$ be two real square integrable random variables with var$X>0$, var$Y>0$. The correlation Corr$(X,Y)$ quantifices how far $X$ and ...
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### Inverse Z transform of symmetric function $R_{x}(n) = 3\cdot (0.8)^{|n|}$

On Z-transform table, most of the pairs are only valid for $n≥0$. My question is to find PSD (Z transform) of $$R_{x}(n) = (0.8)^{|n|}$$ Note that $n$ is an integer span from $-\infty$ to $\infty$....
Given $\xi$, $\eta$, $\zeta$ are pairwise uncorrelated, can we say, that $E(\xi\eta\zeta) = E\xi E\eta E\zeta$?