# Tagged Questions

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

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### Correlation of two random variables

A random sample of $100$ variables is given. Each of them is independent and identically distributed with $N(0,1)$. What is the correlation between sum of $98$ variables and sum of $100$ variables?
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### $(Y_i - \hat{Y}_i)(\hat{Y}_i - \bar{Y}_i) = 0$

$(Y_i - \hat{Y}_i)(\hat{Y}_i - \bar{Y}) = 0$ in the image below (third and fourth line of the proof!). Why?
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### Min/Max variance of 3 correlated variables

You have 3 different random variables (assets) all with exactly the same variance. What is the maximum and minimum variance of the 3 variables (assets) combined? Proposed ...
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### testing correlation coefficient in a bivariate normal distribution

How can I show that $\dfrac{\hat{\rho } \sqrt{N-2}}{\sqrt{1-\hat{\rho}^2}}$ has a t-student distribution with $N-2$ degrees of freedom. I think I have to write it as a quotient of a normal $(0,1)$ ...
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### Proof that correlation coefficient squared equals the coefficient of determination

Hi I as the title says I'm looking at the proof that $r^2$ = $R^2$ in the case of simple linear regression, but I don't understand one part. There are different versions of the proof, but in most of ...
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### Probability at least one, using correlation

I have a problem using the correlation in combination with the "at least one" probability. I have $P(A)=57\%$, and $P(B)=74\%$, and I calculated their correlation coefficient and it is $0.1557$. To ...
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### How to find the percent variation in Y is explained by X?

I know that the r^2 value for the data is 0.9832. Is there a way to use that value to find the percent variation in Y is explained by X? Or do I need to use the data given to me?
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### Uncorrelated and X given $Y = 0$

Is the following true or false? Suppose that $X$ and $Y$ are two discrete random variables defined on the same probability space. If $E[X] = E[Y] = 0$ and $E[X | Y=y] = 0$ for all $y\in Y$, then $X$ ...
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### Decorrelating variables using Cholesky decomposition

I am looking for a method to decorrelate several variables, so that their covariance matrix is diagonal, while keeping the original mean for each of them. I found this old article which seemed pretty ...
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### Is the sum of all cross-correlation samples representative of target existence likelihood?

Answers to this question take the peak in the cross correlation as the measure to the likelihood of the trigger signal exist in the received signal - this is pretty much text book. My question is ...
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### What is the correlation of two normal distributions with equal mean and known relation between variance

If I take the sample mean of a scaled $\chi$ distribution of $N$ samples, the distributions of these means should lead to a normal distribution $\mathcal{N}(\mu,\sigma)$. This procedure is repeated $M$...
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### Properties between Pearson correlation of two function and the correlations of their derivatives

For two functions, $f(t)$ and $g(t)$, I can calculate the Pearson correlation $Corr$. Does the correlation, $CorrD$, between the derivative functions, $f'(t)$ and $g'(t)$, has some properties with ...
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### The relationship between diagonal entries and eigenvalues of a diagonalizable matrix

Let $\mathbf{C}$ be an $n\times n$ Hermitian matrix. Let $\dagger$ indicate a matrix conjugate-transpose. Let $\mathbf{V}\mathbf{D}\mathbf{V}^\dagger$ be the eigendecomposition of $\mathbf{C}$, where ...
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### similarity between two ranked sequence

How can I measure similarity/distance between two sequences of ranked numbers/letters. The two sequences are of different length, and only have some elements in common? For example, if I have three ...