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Aug28-09, 11:13 PM
P: 286
To clarify my earlier comment about X being neither random nor a variable.

X is a function from S to [itex]\mathbb{R}[/itex]. Its value for any given outcome is prescribed based on the function's rule. These values are not randomly assigned. Any randomness is inherent in the underlying experiment, not in X. The name was coined long ago by people who lacked as much clarity as in modern times. The weight of tradition often forstalls changing terminology.

It is true that "random variables" are used to analyse experiments that have uncertainty about them, but the experiments do not necessarilly have to be uncertain. If I toss a two-headed coin, the probability of Tails is 0, while Heads is 1 (no randomness involved).