# Definition of the population of a discrete random variable

Consider the classical example of a random variable obtained by rolling two (fair) dice - the sum can take values between 2 and 12, where 2 and 12 have a probability of 1/36 and, for example, 7 has a probability of 6/36 to be drawn.

What is now precisely the (whole) population in this example - all 36 possible experimental outcomes or only the set of values from 2 to 12?

• Because "population" seems to be a vague term with many meanings, could you explain what your definition of it is? – whuber Mar 10 '17 at 15:51

## 1 Answer

It depends on the question(s) you want to answer. If it's only about the sum, then the population is 2,...,12. If you have a question about the two dice, then the population is (1,1),...,(6,6).

• This answer might technically stand up, but I fear it could lead many novices to create incorrect models. It also does not match the more advanced distinction between a sample space (aka "population") and a random variable. – whuber Mar 10 '17 at 14:35
• What I had in mind is, for example, a Normal random variable. The population (as opposed to a sample) is considered as all the realizations of the random variable, while the sample space may be the actual human population on which the measurement (say height) is taken. So I see the term "population" to be related to "sample out of the population" and not necessarily to the sample space. In the dice example, if your sample is rolling two dice every time, then your population will be all rolls of two dice. – Zahava Kor Mar 11 '17 at 1:07
• I'm not having much luck finding definitions in textbooks or on the Web that agree with that characterization of a population. Wikipedia's description is typical: "In statistics, a population is a set of similar items or events which is of interest for some question or experiment ... [It] can be a group of actually existing objects or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker)." – whuber Mar 11 '17 at 19:09