An Introduction to Probability and Statistical Inference, 2nd Edition

Some notation and abbreviations

ℜ real line

ℜ^k, k ≥ 1 k-dimensional Euclidean space

↑, ↓ increasing (nondecreasing) and decreasing (nonincreasing), respectively

S sample space; also, sure (or certain) event

Ø empty set; also, impossible event

A ⊆ B event A is contained in event B (event A implies event B)

A^c complement of event A

A ∪ B union of events A and B

A ∩ B intersection of events A and B

A − B difference of events A and B (in this order)

r.v. random variable

I_A indicator of the set A: I_A(x) = 0 if x ∈ A, I_A(x) = 0 if x ∉ A

(X ∈ B) = X⁻¹(B) inverse image of the set B under X: X⁻¹(B) = {s ∈ S; X(s) ∈ B}

X(S) range of X

P probability function (measure)

P(A) probability of the event A

P_X probability distribution function of X (or just ...