The starting point of the whole chapter is the idea of a random variable: a way of translating into numbers the outcome of an experiment governed by chance.
Definition — Random variable
A random variable is a function that assigns a real number to each outcome of a random experiment. Intuitively: it is a “quantity” whose value depends on chance.
Example
- I roll a die: = “number rolled”. Possible values: .
- I measure the height of a randomly chosen person: = “height in cm”. Possible values: a continuous interval (e.g. ).
The first is an example of a discrete random variable; the second of a continuous variable.
The distinction between discrete (isolated, countable values) and continuous (a whole interval of values) guides all the rest of the chapter: to the former we associate a distribution made of pointwise probabilities, to the latter a density function.
Links
Topics: Distribuzioni probabilita
Concepts: Variabile aleatoria
Skills: Modellizzare