Rolf Turner wrote:
>
> Sports scores are random variables. You don't know a priori what the
> scores are
> going to be, do you? (Well, if you do, you must be able to make a
> *lot* of money
> betting on games!) After the game is over they aren't random any
> more; they're
> just numbers. But that applies to any random variable. A random
> variable is
> random only until it is observed, then POOF! it turns into a number.
>
may i respectfully disagree?
to call for a reference, [1] says (p. 26, def. 1.4.1):
a random variable is a function from sample space S into the real
numbers.
and it's a pretty standard definition.
do you really turn a *function* into a *number* by *observing the
function*? in the example above, you have a sample space, which
consists of possible outcomes of a class of sports events. you have a
random variable -- a function that maps from the number of goals into,
well, the number of goals.
after a sports event, the function is no less random, and no more a
number. you have observed an event, you have computed one realization
of the function (here's your number, which happens to be an integer) --
but the random variable does not turn to anything.
vQ
[1] Casella, Berger. Statistical Inference, 1st 1990
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