"
PHILOSOPHIES OF PROBABILITY
Jon Williamson, in
Philosophy of Mathematics, 2009
2 VARIABLES
"The most basic framework for probability involves defining
a probability function relative to a finite set
V of variables, each of which takes finitely many possible values. I shall write
v@V to indicate that
N is an assignment of values to
V.
A probability function on V is a function
P that maps each assignment
v@V to a non-negative real number and which satisfies
additivity:
∑𝜐@𝑉𝑃(𝜐)=1.
This restriction forces each probability
P(
v) to lie in the unit interval [0,1]."
https://www.sciencedirect.com/topics/mathematics/probability-function#:~:text=A probability function on V,interval [0,1].
"probability density function (PDF), in statistics,
a function whose integral is calculated to find probabilities associated with a continuous random variable (see continuity; probability theory). Its graph is a curve above the horizontal axis that defines a total area, between itself and the axis, of 1.21 Jun 2024"
https://www.britannica.com/science/density-function