notes_set_2_math_a

# notes_set_2_math_a - ECE594I notes, M. Rodwell, copyrighted...

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Unformatted text preview: ECE594I notes, M. Rodwell, copyrighted ECE594I Notes set 2: Math Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 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 * . &quot; or &quot; : 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 * . &quot; and &quot; : 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...
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## notes_set_2_math_a - ECE594I notes, M. Rodwell, copyrighted...

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