# Is the sample space of two jointly random variables of the form A x B where A is the sample space of one random variable and B is ...?

... the sample space of the other?

And if it is, is A x B and B x A considered the same thing with respect to their joint probability distribution? Now I'm not asking if A x B is different from B x A, which they are if we are just talking about sets in general.

Saying, e.g, "the probability of picking a King of Ace and rolling a 3 in fair dice" is really no different than saying "The probability of rolling a 3 in a fair dice and picking a King of Ace". So this suggests that either A x B or B x A works as a sample space. We just need to pick one.

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- nbsaleLv 63 years agoFavorite Answer
Yes, the sample space could be A X B or B X A. Those are just sets of ordered pairs. There's nothing that requires A or B to "go first" in the ordered pair.

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