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jetoso
jetoso is offline
#5
Mar19-06, 07:13 PM
P: 74
Good, so X and |X| are random variables. Let me put it in this way:
1. If X is a random variable, then |X| is also a random variable too.
2. If |X| is a random variable, then X is a random variable too.

First case, we say that X and |X| are two different random variables. But I do not see any condition for |X| to be a random variable given that X is a random variable, so I think this statement is not true at all.

Second, since we can not map back a real number to the sample space, say using |X|, then the fact that |X| is a random variable does not imply that X is a random variable too, so this statement is false.

What do you think?