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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'random variable'
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A couple of things by Koro
Correction id: 1317
Filed on: 2002-12-08 06:19:08
Status: Rejected on 2003-05-22 10:38:56
Type: Erratum
Correction text:
1) A discrete random varible is one with a finite or countable range.
But the definition of continuous ones is erroneous. It is not true that a random variable must be either continuous or discrete.
Continuity of a random variable has nothing to do with its range; it is about the existence of a density function.
A random variable is continuous if it has a density (probability) function;
that is, if there is f_X such that F_X(x) = int_{-\infty}^x f_X(x)dx
This is to say that a random variable is continuous if its (cummulative) distribtion function is absolutely continuous.
2) I agree with the previous post that \mathcal{A} would be a better way to call the sigma-algebra A, as is usually done.
3) The assertion "any function of a random variable is a random variable" is false. Maybe it is refers to the context of the example, in which X is a discrete space (so in that case it's true) but the final sentence appears to be a general fact, and it's not true in general.
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No comment from object owner mathcam.
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