This discusses lots of different interpretations of “random”. The general sense seems to be that a random process is unpredictable in detail, but has some predictable properties such that the process can be modelled mathematically by a random variable (or sequence of random variables).
Here, the notion of “modelling by a random variable” means that if we take the actual outcome and apply statistical tests to check whether the outcome is drawn from the distribution defined by the random variable, then the actual outcome passes those tests. This doesn’t mean of course that it is in an objective sense a random process with that distribution, but it does mean that the model “fits”.
Maybe take a look at the Wikipedia entry http://en.wikipedia.org/wiki/Randomness
This discusses lots of different interpretations of “random”. The general sense seems to be that a random process is unpredictable in detail, but has some predictable properties such that the process can be modelled mathematically by a random variable (or sequence of random variables).
Here, the notion of “modelling by a random variable” means that if we take the actual outcome and apply statistical tests to check whether the outcome is drawn from the distribution defined by the random variable, then the actual outcome passes those tests. This doesn’t mean of course that it is in an objective sense a random process with that distribution, but it does mean that the model “fits”.
Hope that helps...