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*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.

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Hurkyl

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If you have

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Would this distribution be known as a joint distribution? Would I be able to use the multivariate normal distribution??

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Hurkyl

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Yes.Would this distribution be known as a joint distribution?

Maybe. Maybe not.Would I be able to use the multivariate normal distribution??

http://en.wikipedia.org/wiki/Multivariate_normal_distribution#A_counterexample

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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??

So, is there any general formula or method for getting the joint distribution of

There only seems to be multivariate normal and binomial distributions??

Last edited:

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Hurkyl

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Let me rephrase your problem in terms of discrete distributions -- maybe it will help you understand what the problem is.Thanks for help, Hurkyl.

So, is there any general formula or method for getting the joint distribution ofnrandom variables. For example, if all the random variables were exponential

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.

Code:

```
0.05 0.20 0.10 | 0.35
0.15 0.05 0.05 | 0.25
0.10 0.15 0.15 | 0.40
-----------------+-----
0.30 0.40 0.30 | 1.00
```

Now, the question you appear to be asking is:

Code:

```
* * * | 0.35
* * * | 0.25
* * * | 0.40
-----------------+-----
0.30 0.40 0.30 | 1.00
```

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.

What do you mean by "dependency?" If you weren't asking the question you're asking, I would have assumed that parenthetical meant you(and I knew all the dependencies of thenrandom variables), is there a method??

There only seems to be multivariate normal and binomial distributions??

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