network profile
| bio | website | linkedin.com/in/piotrsemenov |
|---|---|---|
| location | Russian Federation, Saint-Petersburg | |
| age | 26 | |
| visits | member for | 5 months |
| seen | 15 hours ago | |
| stats | profile views | 8 |
Researcher and software engineer.
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1d |
comment |
Multivariate normal distribution density function @Babla Sorry for delay. Let $Y_1, Y_2$ have the covariance matrices $A, B$ correspondingly. Let $Cov(Y_1,Y_2)=0$. So the covariance matrix of $2n$-dimensional variable $(Y_1,Y_2)$ is the just $\Sigma=\left(\begin{array} AA & 0 \\ 0 & B \end{array}\right)$. Note that $|\Sigma|=|A||B|$ and $\Sigma^{-1}=\left(\begin{array} AA^{-1} & 0 \\ 0 & B^{-1} \end{array}\right)$. Put this in density function $f_{(Y_1,Y_2)}(x)$ and it decomposes to $f_{Y_1}(x) \cdot f_{Y_2}(x)$. This is the independence of Gaussian variables $Y_1,Y_2$. Hope, it helps. Unfortunately, I cannot update my answer with this text. |
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May 18 |
comment |
Multivariate normal distribution density function @Babla $Y_1$ and $Y_2$ are uncorrelated if and only if $Cov(Y_1, Y_2) = 0$. This means that $Y_1$ and $Y_2$ variates in ways those do not share any statistical data between. From $Cov(Y_1, Y_2) = 0$ you can not reason anything about independence of $Y_1$ and $Y_2$. It must be only the a-priori assumption. |
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May 18 |
awarded | Teacher |
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May 18 |
comment |
$0$-th moment of product of gaussian and sinc function @JFNJr See my answer. Unfortunately, Mathematica was able to evaluate only the first integral. |
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May 18 |
answered | $0$-th moment of product of gaussian and sinc function |
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May 18 |
comment |
Multivariate normal distribution density function @Babla I see. I have rewritten my answer according to your comment. |
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May 18 |
awarded | Editor |
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May 18 |
revised |
Multivariate normal distribution density function I understand the problem of author :) So the proof author wanted is in answer. |
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May 18 |
comment |
Multivariate normal distribution density function @Babla $Cov(\mathbf{c} + B \cdot \mathbf{X}, \mathbf{c} + B \cdot \mathbf{X}) = B \cdot \Sigma \cdot B^\top$, where $\Sigma$ is covariance matrix of random Gaussian vector $\Sigma$. May be I do not understand your problem... |
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May 18 |
comment |
$0$-th moment of product of gaussian and sinc function If you need only the answer, I can calculate it with help of Wolfram Mathematica. |
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May 18 |
answered | Multivariate normal distribution density function |
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Dec 27 |
awarded | Autobiographer |
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Dec 27 |
awarded | Supporter |
