Lecture Notes 1-20

Lecture Notes 1-20 - BMW 1-1: An W fig 3. mafia-amafi $5...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: BMW 1-1: An W fig 3. mafia-amafi $5 an mam. A 32: aim 4317 againy 1513:1552; with: Wig 5mm: £9 (335% an mm; 0 w=WogW Qefifiifiw 1.2. Armfiaéé‘figzsm i535. flaw-{agile fifim} wheres} 35 “mph spam g is a {mum 9% yams firm the mph spate, am? $9: $3 a. mm 2 Wm Mammyfimfi 3mm: 11M: fnfimmgaawfiwg mama wt 3 g 35 méthiza fl; gr mm m 9" :4? $2; Miuajj 4.9131325? fififiammm¢ at 2 1 ark-mi? mm mamm‘ The four condition is actually a result of the first three: AU A” = Q A f] A“ ¢ Q5 Pr{A U A“} = Pr{Q} =1 Pr{A U A”} = Pr{A} + Pr{Ac} =1 Pr{A“} = 1- Pr{A} flgfiafiifiim 3.3- L2; he a mama? WE wig: 35a mwfi 35121 .§ mm m3] g: as, mfifimmfiz‘fiflifi’ um $213.35 damn: Rigiij is 335 La $13“; :‘Fiifilgi = - flmfia Li A Esilepilmfifi mwfisximag imam? mafia mm mam 3% mix: 13km mmbum at” m {game E39132 fig a: ham}. a qualifir {mfimmm‘zimmm watts :3 Wfims gmnrfla‘ ma'gsgeflfpkm Quake hm: mpfiami mm the 133m mi mark the 1113;331:152" were {ififmflu The mph spam is fl m“ 5‘33 1:5 E315 33!. $33 “£333.33? gag 43$ £3 £55: afafi 535mg 3mm m There an my figfime muggng aim mafia! 5w asmfiztad wéfix 31mm. film mefifim-‘ia Mir: $21} 7: Mi , wmwflw em Frfin: Iii}-m-W?, mm 1;} 2 @333 fi WEE 22!}m-fiam a mfimj} m mm s: m; a :és- gelazm‘ mag {mm méfias lama Eét‘mflfii at] is: giaw 12323? "3‘ -- a s: at :tieaet'me we is fisheries in the box maturing seam: moses: fiefiae the went a! te be fie set { it; 33% lit; E), in, 6:35, (3;-5a E and the re be {t};- flf; t a}, firfiflelirytefleemorfie, .«f is the event nfhassizsgg a! reset we fieficflee phase, see? 5‘ is: the was! of a hex efanfiiie glam 3‘13? gamete: {are nwhe wfitteu ea , _ _§r§§fl3§_ E‘fi'ggfijifirgljg} “ass Wig“ we; meaIi—Elaéiliiblriafijrfi = #3:??1‘ A key aSpect of using the probability rules is when non-disjoint events are encountered. If A n B at Q , then show that Pr{AU B} = Pr{A} + Pr{B} — Pr{A flB}. Proof: The approach is to separate these areas into disjoint sets (events) and then utilize the property that the probabilities of disjoint events add. 9 ‘ B Since B=(AnB)U(A“nB) Pr{B} = Pr{(A f) 3)} + Pr{(A“ f] 3)} and A=(AflB)U(AflB”) Pr{2"1'}= Pr{(A fl 3)} + Pr{(A f? B”)} Now A U B as disjoints sets is AUB=(AnBC)U(AnB)U(Ac/73) PPM U B} = PIKAH 36)} + PF{(A/7 B)}+ PIKAC f7 3)} Note that Pr{(A” n 3)} = Pr{B} -— Pr{(A f7 3)} and Pr{(A [7 BC)} = PIM} - Pr{(A n 3)} So Pr{(AUB)} = Pr{A}+Pr{B}—Pr{(AflB)}. Q.E.D. Do homework 1.1, 1.2, (pages 36-37 in the textbook) and derive the formula Pr{A U BU C} = Pr{A} + Pr{B}+ Pr{C} — Pr{A {7 B} — Pr{A n C} —Pr{B f} C} + Pr{A n B {7 C} Turn in on Monday 1-25, at the beginning of class! ...
View Full Document

Page1 / 4

Lecture Notes 1-20 - BMW 1-1: An W fig 3. mafia-amafi $5...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online