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Can you please help me with this question?

Is the set finite, countably infinite, or uncountable?

a. The set of all real-valued random variables on a finite sample space.

b. The set of all integer-valued random variables defined on the sample space $W$ of positive integers, with $\operatorname{Pr}[w] = 1/(2^w)$

c. The set of all integer-valued random variables on a finite sample space.

d. The set of all possible functions from $\mathbb{Z}_{97}$ to $\mathbb{Z}_{97}$ (modulo 97).

e. $\mathbb{Z}^3 = \{(a,b,c): a,b,c \in \mathbb{Z}\}$ (the set of triples of integers)

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    What do you know? What did you try? Why did this fail?2011-12-02
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    A random variable is just a function. Already if the sample space has $1$ point, there are as many random variables on the sample space as there are real numbers, since the point can be mapped to any real.2011-12-02

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