G: Joint Distribution of Random Variables

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Discussion Overview

The discussion revolves around the concept of joint distribution of random variables, exploring whether any two or more random variables can be jointly distributed, and under what conditions they may not be. The scope includes theoretical aspects of probability distributions and their relationships.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants propose that joint distribution functions can always be defined, particularly noting that for independent random variables, the joint distribution is the product of the individual distributions.
  • One participant questions whether a bivariate normal distribution is always defined for two normal random variables, seeking clarification on the existence of joint distributions when random variables have different distributions.
  • A later reply affirms that a joint distribution can be found even when random variables have different distributions.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which joint distributions exist, with some affirming that they can always be defined while others question the implications of independence and differing distributions.

Contextual Notes

Unresolved aspects include the specific conditions under which joint distributions may not be defined and the implications of independence on joint distributions.

sauravrt
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Are any two (or n) random variables always jointly distributed in some sense?
When will two RV's be non jointly distributed?

Saurav
 
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Joint distribution functions can always be defined. In case of independent random variables, the joint distribution is simply the product of the individual distributions.
 
mathman, thanks for the reply.
So if there are two normal random variables, the a bivariate normal distribution is always defined between them?

If I have random variables, each with different distribution, even so it is possible to find a joint distribution between them?

Saurav
 
sauravrt said:
mathman, thanks for the reply.
So if there are two normal random variables, the a bivariate normal distribution is always defined between them?

If I have random variables, each with different distribution, even so it is possible to find a joint distribution between them?

Saurav

Yes, to both questions.
 

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