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I'm reading a definition in DeGroot's book that begins with the statement:

"Let X be a bounded discrete random variable whose p.f. is f."

Then he goes on to define the expectation of X.

However, I cannot find a definition of what is meant by a "bounded" discrete random variable anywhere in the book (after an hour of looking). I do know what a discrete random variable is, but what does the word "bounded" mean in this case?

Thanks.

David
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1 Answers1

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Bounded, in this case, means what it means in pretty much every mathematical context - there's a maximum and minimum that the variable never exceeds. If you think about the normal random variable, Z, technically Z could be anything, it's just that as you get farther and farther away from zero, the probability diminishes exponentially.

So, $P(Z > z)$ is never actually equal to zero for any finite z. [EDIT] This means that Z is unbounded.

In a bounded random variable, X, there's some value m and some value M such that:

$P(x < m) = 0$ and $P(x>M) = 0$

Duncan
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  • And this means that the normal random variable Z is unbounded? – David Jun 03 '14 at 16:08
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    That's correct. Z is unbounded. Edited my answer to make that clear. Z is also different because it's not discrete, but you already mentioned that you know what a discrete RV is. – Duncan Jun 03 '14 at 16:33