In mathematical terms, given a random variable X with distribution F, a random sample of length n =1,2,3,... is a set of n independent, identically distributed (iid) random variables with distribution F. [1] A sample concretely represents n experiments in which we measure the same quantity. For example, if X represents the height of an individual and we measure n individuals, Xi will be the height of the i-th individual. Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these variables (which are the values that these random variables take). In other words, Xi is a function representing the measurement at the i-th experiment and xi = Xi(ω) is the value we actually get when making the measurement.