Expectations of Joint Distribution.

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SUMMARY

The discussion centers on calculating the expected value E[XY] for dependent variables X and Y within a joint distribution framework. The key formula presented is E(XY) = ∫(xy * joint density) dA, which emphasizes the integral of the product of the variables and their joint density function. Understanding the relationship between joint distributions and conditional distributions is crucial for grasping the underlying logic of this calculation. Participants seek clarity on the conceptual basis rather than just the mathematical formula.

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  • Understanding of joint distributions in probability theory
  • Familiarity with conditional distributions
  • Knowledge of integration techniques in calculus
  • Basic concepts of expected value in statistics
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  • Study the properties of joint probability distributions
  • Learn about conditional expectation and its applications
  • Explore integration methods for calculating expected values
  • Review examples of dependent random variables in joint distributions
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Students and professionals in statistics, data science, and quantitative research who are working with joint distributions and need to understand the computation of expected values for dependent variables.

sid9221
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How would you work out E[XY] where X,Y are dependent variables in a Joint Distribution.

I know there is a relationship with the conditional distributions but I can't understand the logic behind it, hence am hoping someone here can give me directions to work out this expectation.(I don't just want a formulae, I want the idea behind it)
 
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If you have the joint distribution, then E(XY) = integral of (xy multiplied by the joint density).
 

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