Can a Probability distribution be "random" A quick question. I know many models probability models exist (normal, uniform, etc.). Wikipedia has a nice article listing them all (almost). My question is simple, you have a population defined by a set of numbers, but when you look at these numbers, you can't seem to figure out what is their probability distribution, it's not normal, it's not uniform, etc. Of course the population has its own probability distribution but if it doesn't fit any of the known models, how you would qualify this distribution in mathematics. What would be the correct wording? Is saying the probability distribution is random, or stochastic correct?
Thank you. 
 A: The question is not altogether clear, but I'm going to guess what is intended, and maybe I'll get it wrong.  Let's say the proportion of voters who will vote "yes" in next week's referendum is $R$.  You take a random sample of 200 voters.  How many of those will vote "yes" is a random variable.  The conditional distribution of that random variable, given $R$, is a binomial distribution with parameters $200$ and $R$.
However (and this is an example of what I guessing you might mean by a population being "random") it may be that uncertainty about the value of $R$ can itself be expressed by a probability distribution.  Suppose someone decides to express that uncertainty by saying that the probability that $R$ is in some set $A\subseteq [0,1]$ is $\displaystyle\int_A 6r(1-r)\,dr$.  (It's easy to check that if $A=[0,1]$ then that integral is  $1$.)  That is sometimes expressed by saying that $R$ is treated as a random variable.  In that way, one would be speaking of some attribute of a population being "random".
Some purists, perhaps most notably Edwin Jaynes, object to the use of the word "random" for that sort of thing, saying that one is assigning a probability distribution not to a "variable" that is "random" but to a quantity that is uncertain.  The idea is that you can throw away your list of 200 voters' names and draw another list at random, but you cannot do the same with the whole population, so that should not be called "random".
This is the Bayesianism-versus-frequentism issue.  One may say that $60\%$ of the voters will vote "yes", but if one cannot say that in $60\%$ of all instances, there was life on Mars a billion years ago, then a frequentist will refuse to assign any probability to that statement.  Bayesianism, on the other hand, holds that all uncertainties about the truth of propositions can be modeled via the usual mathematics of probability.  Many Bayesians will say that when one assigns a probability distribution to something like the mass of the dwarf planet Pluto, one makes that a "random variable", but that is terminology that Jaynes objected to.
