STAT 241 - Lecture 18
Today (October 15 2025)
Recall: Building foundations for Probability
Modelling
Axioms of Probability:
Given a random experiment and sample space S, a
real-valued function P, defined on subsets of S
(events), is a probability function if:
Axiom 1: For any event A, P(A)
Axiom 2: P(S)=1
Axiom 3: If
Random Variable (r.v.), a function that assigns a
real number to each element of S, i.e. the
domain of the function is S and the range is a
subset of the real numbers.
Mathematical expressions involving r.v.’s
correspond to events (subsets of S)
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