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Intro

Contents

What is Probability and Stats?

Probability basics

NameSymbolDescription
Sample spaceSa list of possible outcomes (make sure they are unique values)
A specific eventA, B, C,...a subcollection of outcomes in S
Simple eventA, B, C,...an event that contains one outcome that cannot be broken down any further
Compound eventSan event that contains more than one outcome
Complementary eventA', Acan event that contains all outcomes not in the original event (A′ contains all outcomes not in A)
Union of 2 events (A or B)A ∪ Ban event that contains all outcomes in A, B, or both (make sure not to double-count outcomes)
Intersection of 2 events (A and B)A ∩ Ban event that contains only the outcomes in both A and B
The probability of AP(A)the chance of event A has occured: P(A) = number of outcomes in A / number of equally-likely outcomes in S
A belongs to BA ∈ B
Null setEmpty set
Universal setΩ, Sa set that contains all the elements or objects of other sets, including its own elements
Atom, singletonω, s
Proper subsetA ⊂ B if set B contains at least one element that is not present in set B
SubsetA ⊆ B if all elements of A are also elements of B

Random Experiments and Outcome Space