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yt uncertain under decisions Making wing: follo the elieve bI ose Supp 04 . 0 =). . . | time on there me gets 25 A( P 70 . 0 =). . . | time on there me gets 90 A( P 95 . 0 =). . . | time on there me gets 120 A( P 9999 . 0 =). . . | time on there me gets 1440 A( P ose? cho to action Which etc. cuisine, rt o airp vs. flight missing r fo references p my on ends Dep references p infer and resent rep to used is ry theo y Utilit ry theo y robabilit p + ry theo y utilit = ry theo Decision 6 13 Chapter
z/T=9/1+9/I+9/L=()d+()d+(T)d=(匝>Io1p)d:3 (m)divem=(V)d 7 Jo asqns Aue s!quana uy 9/T=(9)d=(9)d=()d=(8)d=(亿)d=(I)d83 I=(m)d"区 I>(m)d>0 1's 7m Kana Joj (m)d quawuBisse ue yilm aeds aldwes e s!japow Aullqeqod o aeds Auqeqoud y quana olwone/puom ajqissod/quiod aldwes e s!m aip e jo sllo ajqissod g a aeds ajdwes ay1-7 ias e yim uigag sorseq Ku!l!qeqoId
basics y Probabilit space sample —the Ω set a with Begin die. a of rolls ossible p 6 e.g., event atomic / rld ow ossible p/ oint p sample a is Ω ∈ ω space sample a is del mo y robabilit p r o space y robabilit p A s.t. Ω ∈ ω every r fo ) ω( P assignment an with 1 ≤) ω( P ≤0 1 =) ω( Pω Σ . 6/1 = (6) P = (5) P = (4) P = (3) P = (2) P = (1) P e.g., Ω of subset any is A event An ) ω( P} A∈ω{ Σ =) A( P 2/1 =6/1 +6/1 +6/1 = (3) P + (2) P + (1) P = 4) < roll die ( P E.g., 7 13 Chapter
8 EI adeyD z/1=9/1+9/1+9/T=(9)d+()d+(t)d=(an.4=ppO)d83 (m)d=(xi=(=X)d :X'A'Kue joy uolinq!asip qeqoud e saonpu!d 3n.4=()ppO83 sueajoog jo sjea ay8a 'aue awos on squiod ajdwes woyy uonouny e s!ajqeuen wopue y solqeriea wopuey
ariables v Random the e.g., range, some to oints p sample from function a is riable va random A oleans Bo r o reals . ue tr = (1) dd O e.g., : X r.v. any r fo distribution y robabilit p a induces P x =) ω( X: ω{ Σ =)i x = X( P }i ) ω( P 2/1 =6/1 +6/1 +6/1 = (5) P + (3) P + (1) P =) ue tr = dd O( P e.g., 8 13 Chapter
(9VD)dI+(9-VD)d+(9VDL)d=(9∧D)d← (9VD)∧(9VD)∧(9VoL)≡(9∧D)83 an s!1!yplyM u!squana olwole jo uonounfsip uollsodold q-VD0‘3s2Df=a3n4=/:83 epow o jeuo!!sodod =quod aldwes 'sa]qeuen ueajoog y!M sajqeuen ayn jo sague ayn jo nonpod ueisaue)ayn s!aoeds ajdwes ay "a'!'sa qeuen wopuel jo nas e go sanjen ayn Kq paugap ae squod aldwes ay 'suone!dde Iu!uaO an.!g=(m)g pue an.!n=(m)aayM squiod =gVD quana asof=(m)y auaym squiod ajdwes jo 1as DL quana an.1g=(m)y aaym squiod aldwes jo nas D quana :g pue K sajqeuen wopuel ueajoog uanl an s!uonisodoud ayl ajaym (squlod aldwes jo as)quana ay se uonsodod e o yu!yL suorqsodoId
ositions Prop oints) p sample of (set event the as osition rop p a of Think true is osition rop p the where : B and A riables va random olean Bo Given ue tr =) ω( A where oints p sample of set =a event se al f =) ω( A where oints p sample of set =a¬ event ue tr =) ω( B and ue tr =) ω( A where oints p =b ∧a event defined re a oints p sample the applications, AI in Often the i.e., riables, va random of set a of values the yb riables va the of ranges the of duct ro p rtesian Ca the is space sample del mo logic ositional rop p = oint p sample riables, va olean Bo With . b ¬ ∧ar o, se al f = B, ue tr = A e.g., true is it which in events atomic of disjunction = osition Prop )b ∧a( ∨)b ¬ ∧a( ∨)b ∧a¬( ≡)b ∨a( e.g., )b ∧a( P +)b ¬ ∧a( P +)b ∧a¬( P =)b ∨a( P ⇒ 9 13 Chapter
OI I odeo 'awooino jo ssalpuea Kauow aso]on se os naq on paouoj aq ueo swoixe asay aejoIA ey san!l!qeqod o1 3u!poooe siaq oym qua3e ue :(IE6I)au!ap anJL (9VD)d-(9)d+(D)d=(9∧D)d83 s31lμqeqo1d panejal aney isnw squana paneja Klleiol ulejao 1eyn Kjdw!suolluyap ay 乙K4 l!qeqo.Id∂sn AuM
y? probabilit use y Wh related have must events related logically certain that imply definitions The robabilities p )b ∧a( P −)b( P +) a( P =)b ∨a( P E.g., >A B True B A violate that robabilities p to rding acco ets b who agent an (1931): Finetti de outcome. of rdless rega money lose to as so et b to rced fo eb can axioms these 10 13 Chapter