I am new in probability theory and still have some difficulties to capture the definition of random variables.
given repeated throws of dice will produce a sequence of random variables. A random variable being defined as a function on a measure space, the previous example could be modeled as being described with the aid of a single random variable: an outcome will be described by the (random) value of the function. But in fact it is not.
given a sample of a population for which the distribution of the height of each individual is to be determined is again thought of as each individual being a random variable and you are not considering a single random variable to describe the process.
It looks like a random variable assumes only one value. Can somebody explain what could my misunderstanding be ? Thanks.