Summary of Statistical notation for LC Probability and Statistics PDF

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Summary

Dr Henning Sulzbach. Content for the 2017/18 LC Probability and Statistics module. This document contains the notation used throughout the module, including information on sets, Venn diagrams and De Morgan's Laws/...

Description

Notations For a set Ω and subsets A, B ⊆ Ω: • A ∪ B := {ω ∈ Ω : ω ∈ A or ω ∈ B},

(union)

• A ∩ B := {ω ∈ Ω : ω ∈ A and ω ∈ B}, c

• A := {ω ∈ Ω : ω ∈ / A},

(intersection)

(complementary set)

• A \ B := A ∩ Bc = {ω ∈ Ω : ω ∈ A and ω ∈ / B},

(set difference)

• A and B are disjoint if A ∩ B = ∅. The corresponding Venn diagrams: Ω

Ω A

A

B

B

A∩B

A∪B Ω

Ω A

B

A A\B

Ac For a finite or infinite family A1 , A2 , . . . of subsets of Ω: S • i Ai := {ω ∈ Ω : ω ∈ Ai for some i}, T • i Ai := {ω ∈ Ω : ω ∈ Ai for all i},

De Morgan’s laws: for a finite of infinite family A1 , A2 , . . . of subsets of Ω: !c !c \ [ [ \ c Ai , Aci . = = Ai Ai i

i

i

i

i...