Set Theory:
Set: collection of elements: Dice={1..6]
U=all Elements; (A ̅ )=Complem,ent
set union A U B (AorB)
set intersection: A∩B (AandB)
empty set: ∅
and
Boolean Logic
before experiment, its not known if E takes place. —> true (1) and false (0)
a)
b)
c)
a) Negation, =1-Xe
b) Union, =1-(1-Xa)(1-Xb)
c) Intersection, = XaXb
ggf. Aufgabe Vorlesung 2
Definition of Probability:
Three Axioms / Axiomatic Definition
To each event E, we assign a probability:
p(E)
Axiom I:
Axium II:
Axiom III:
Definition of Probability
Frequentist Definition
If experiment is repeated n times, the event is observred k times:
mit phi>0, for 10 in 10E6.. 10E-5
Def. of Probability:
Classical Def.
p(E) = #outcome of interest/#of possible outcomes= M/N
Union of Non-mutually Exclusive Events
(Stütze= Würfelbeispiel, selber malen!)
in some cases: just first part (erstes Summenzeichen)
Conditional Probability and Indepence
What further?
oben: Schnittmenge = Intersection
in case that A and B independent
Therorem of Total Probability / Bayes Theorem
and:
bayes Theorem:
Bayes’ Theorem
Übersetzungen eintragen!
Last changeda year ago
