
B
Probability Distributions
B.1 General Features
A probability distribution is a function that assigns a probability to e ach mea-
surable subset of a set of events. It is associated with a random variable, here
denoted as X.
A discrete probability distribution can assume only a finite or countably
infinite number of values U, such as
{A, B, C, D} or {[0, 5], (5, 7], (8, 10]} or n ∈ N, (B.1)
and is characterised by a probability function Pr(·) that satisfies
X
u∈U
Pr(X = u) = 1 and Pr(X = u) ∈ [0, 1] for all u. (B.2)
A continuous probability distribution must assume an infinite number of values
U, typically R or an interval of real numbers, and is characterised ...