# [R] Inference for R Spam

Wacek Kusnierczyk Waclaw.Marcin.Kusnierczyk at idi.ntnu.no
Thu Mar 5 08:48:51 CET 2009

```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

```