This preview shows pages 1–12. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE594I notes, M. Rodwell, copyrighted ECE594I Notes set 2: Math Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu 8058933244, 8058933262 fax ECE594I notes, M. Rodwell, copyrighted Topics ce. independen theorem, Bayes y, probabilit l conditiona y, probabilit Sets, functions on distributi and density , variables random trials, Bernoulli cases. limiting as Poisson and Gaussian ons. distributi Binomial tions. Transforma ECE594I notes, M. Rodwell, copyrighted Set Definitions { } s # real all of set e.g. objects... of collection a Set = = R { } deck a in cards of set = C { } uppercase sets lowercase, elements : notation = a, b, c, d A { } t fi it t b l 1,2,3,4 : set Finite = A { } { } 3 and 1 between s # real : set infinite y uncountabl ... 8, 6, 4, 2, 0, : set infinite Countably = = C B ECE594I notes, M. Rodwell, copyrighted Set Definitions : Subsets B A . of elements also are of elements all if of subset a is B A B A : subsets Strict B A ot e hich ements as ditional d , of elements also are of elements all If of subset strict a is B A B A . in not are which elements has ly additional if and A B ECE594I notes, M. Rodwell, copyrighted Set operations, logic operations . set universal of subsets both , and Sets S B A * * ets f *Union * . " or " : gy terminolo logic Boolean . or either within elements all of set : Sets of Union B A C B A B A B A C + = = gy g * * Sets of ion *Intersect * . " and " : gy terminolo logic Boolean . or both within elements all of set : AB C B A B A B A C = = ECE594I notes, M. Rodwell, copyrighted Other set operations ts f ifference ) operations logic hence (and operations set other define also can We etc., sets of s complement sets of difference these, knows student that the asssume will ...but we , necessary. as out figure can or ECE594I notes, M. Rodwell, copyrighted Exclusive Sets { } set), empty (the if * exclusive * are sets Two ce. independen l statistica for point Key = B A elements. common no have they i.e. exclusive. mutually be to said are and events the y, probabilit In B A ECE594I notes, M. Rodwell, copyrighted Probability . * outcomes * possible of set a are there for which *, experiment * an is y probabilit of idea the Key to y. probabilit numerical a has outcome possible Each happens). always (something one is outcomes * distinct * all of ies probabilit the of sum The ECE594I notes, M. Rodwell, copyrighted Examples of probability in oss { } { } , tails heads, : coin a Toss = = T H S 1 ) ( ) ( ) ( 2 / 1 ) ( ) ( = + = = = T P H P S P T P H P { } { } , received photon no received, photon : polarizer a through photon a Shoot = = N R S { } { } 1 ) ( ) ( ) ( 2 / 1 ) ( ) ( , p , p = + = = = N P R P S P N P R P ECE594I notes, M. Rodwell, copyrighted Events outcomes. possible of set a is event An outcomes. possible are , , , 4 3 2 1 x x x x events. are and 4 2 2 1 x x B x x A = = ECE594I notes, M. Rodwell, copyrighted Rules ( Axioms ) of Probability 1. and between y...
View Full
Document
 Fall '10
 MADHOW

Click to edit the document details