G: Joint Distribution of Random Variables

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SUMMARY

Joint distribution functions can always be defined for any two or more random variables (RVs). In the case of independent random variables, their joint distribution is the product of their individual distributions. Specifically, for two normal random variables, a bivariate normal distribution is always defined. Even when random variables have different distributions, it is still possible to establish a joint distribution between them.

PREREQUISITES
  • Understanding of joint distribution functions
  • Knowledge of independent random variables
  • Familiarity with bivariate normal distribution
  • Basic concepts of probability theory
NEXT STEPS
  • Study the properties of joint distribution functions
  • Learn about independent random variables and their implications
  • Explore bivariate normal distribution in detail
  • Investigate joint distributions of random variables with different distributions
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Statisticians, data scientists, and anyone involved in probability theory or statistical modeling who seeks to understand the relationships between multiple random variables.

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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