G: Joint Distribution of Random Variables

AI Thread Summary
Any two random variables can be jointly distributed, with joint distribution functions always definable. For independent random variables, their joint distribution is the product of their individual distributions. A bivariate normal distribution exists for two normal random variables. Even if random variables have different distributions, a joint distribution can still be established. Thus, joint distributions are versatile and applicable across various scenarios.
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.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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