Multivariate distribution : Mean vector?

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SUMMARY

The discussion centers on the mathematical understanding of the mean vector in multivariate normal distributions, specifically addressing the probability density function given by f(x) = (1/π) * exp(-1/2 * (9x₁² + 2x₂² + 8x₁x₂ - 20x₁ - 8x₂ + 44)). The mean vector is definitively identified as μ = (2, -2). The user seeks clarification on the theoretical derivation of the Q function in relation to the joint distribution and its implications.

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  • Understanding of multivariate normal distributions
  • Familiarity with probability density functions
  • Knowledge of mathematical notation and vector representation
  • Basic skills in statistical theory
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  • Study the derivation of the mean vector in multivariate normal distributions
  • Learn about the properties of joint probability distributions
  • Explore the concept of the Q function in statistical analysis
  • Investigate applications of multivariate distributions in real-world scenarios
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Statisticians, data scientists, and students studying multivariate statistics who seek to deepen their understanding of mean vectors and joint distributions.

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---

probability density function:

[tex]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)[/tex]

Multivariate normal distibitions

mean vector of the universe?

Answer:

[tex]\mu=\left(2,-2\right)[/tex]

--------------


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