Multivariate distribution : Mean vector?

AI Thread Summary
The discussion centers on understanding the mean vector in the context of a multivariate normal distribution, specifically relating to a given probability density function. The user expresses confusion regarding the theoretical foundations and solutions related to the joint distribution of variables x1 and x2, which are identified as substitutes. The mean vector is identified as (2, -2), but the user seeks further clarification on the mathematical derivation and theoretical implications. The request emphasizes a need for a deeper explanation of the concepts involved. Overall, the thread highlights the complexities of multivariate distributions and the importance of clear mathematical understanding.
aslanbey42
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Hello friends.My English is bad :) .I'll try to explain my trouble.

In question: Q function according to x1 and x2 are substitutes when the joint comes out of solution. Of the solution in theory I do not understand where they come from.Is there another solution or the problem? Where is the theoretical? Can you please explain mathematically?

----Question---

Probabilty density function:

f(x)=\frac{1}{\pi}\left(exp\left(\frac{-1}{2}\left(9x^{2}_{1}+2x^{2}_{2}+8x_{1}x_{2}-20x_{1}-8x_{2}+44\right)\right)\right)

Multivariate normal distibitions

mean vector of the universe?

Answer:

\mu=\left(2,-2\right)

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Thanks
 
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Teory and proof...

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