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SW VandeCarr
Aug28-09, 04:05 PM
P: 2,504
Quote Quote by Elucidus View Post
A "random" variable need not be random.

I roll a 1-sided die and let X be the result. [itex]P(X=1) = 1.[/itex] Not very random. The only thing that is required is that X map S to [itex]\mathbb{R}[/itex].

The term "random variable" was badly chosen since it is neither random nor a variable.

The proper use of a probability is under conditions of uncertainty. A random variable assigns a probability over the closed interval [0,1] to an unknown outcome as an abstract measure based on a given set of assumptions regarding the possibility of that outcome . Once an outcome is known, probability is always measure 1 or 0.

However, strictly speaking, a probability is not a scalar measure of uncertainty. This can be measured by U = 4(p)(1-p) where uncertainty is maximal at p=0.5. (The multiplier '4' simply scales the measure to the interval [0,1].)

People have been arguing about the 'reality' of probabilities for over 200 years, but we're using them more than ever we because we have so much uncertainty. Any process for which their is any uncertainty as to the outcome is random.