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Describing the distribution of n random variables 
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#1
Apr1307, 02:16 PM

P: 61

Suppose I had n random variables, all of which have the same distribution but different mean and variances. How can I formally describe the distribution of these n random variables.



#2
Apr1307, 03:57 PM

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If they have different means and variances, then they can't have the same distribution.
If you have n random variables all on the same set of outcomes S, then you describe that as a single random variable with outcomes in S^n. (the set of ntuples of elements of S) And knowing the (marginal) distributions of the individual variables isn't enough: they could be dependent on each other in many different ways. 


#3
Apr1507, 06:40 AM

P: 61

So for example, if I had n normally distributed random variables, and each had different mean and variance, how do I describe the distribution of the n random variables. I just need to find out what the overall mean and variance of the n random variables will be?
Would this distribution be known as a joint distribution? Would I be able to use the multivariate normal distribution?? 


#4
Apr1507, 10:31 AM

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Describing the distribution of n random variables



#5
Apr1507, 04:40 PM

P: 61

Thanks for help, Hurkyl.
So, is there any general formula or method for getting the joint distribution of n random variables. For example, if all the random variables were exponential (and I knew all the dependencies of the n random variables), is there a method?? There only seems to be multivariate normal and binomial distributions?? 


#6
Apr1507, 05:30 PM

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Suppose you have two random variables, each of which can take one of three outcomes. Their joint distribution can be described by a 3x3 array of numbers  each entry is simply the probability of that particular joint outcome.
Now, the question you appear to be asking is:
And the answer is no  if you play around with it, you should be able to find many other joint distributions that yield this same diagram. 


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