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The suits and ranks of cards in a bridge deck certainly can be presented
as independent sample spaces which we use as components of a cartesian
product. Whether one does so or not is a matter of choice. I am on
record as favoring the presentation as the cartesian product. Even the
sample mean and variance can be seen this way, in fact, every vector
valued random variable can be cast in the form of a random vector from a
cartesian product.
My point is that if we introduce independence as an attribute of sample
spaces which we proceed to study as one, we can better motivate the idea
of independent random variables and independent events.
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