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circular permutation: CHAPTER ONE : 4 main formulas : ( n - 1 ) ! or in ! Symbols : n( AnB ) = n ( A)th ( B )- n(AUB ) choosing : Subset : C h (AUB ) = h ( A ) + h (B) - n (AVB) n (Ac )= n( v )- n (A ) select 'K' from set of n' Union " or ": U n ( A ) = n ( AnB ) T h (An Bc) intersect " and": n (x ) = K ! ( n - K ) ! complement " not " : Ac DE MORGANS LAWS : (AnB) = ACUBC secting or x ] = 1 - Pr [ xx x] Pr [ x > x] = Pr [ x > > ] + Pr (x=x] = 1-pr(x>x]y Pr [Bin, p) = K] = (n ) PK (I-pin-k E( X) /M = x . pr LX=x] VIX ) = EL( x - M)?] or = ELxz] - E[x]2 5 = VV(x) ECB(nip))= mp V(B(n,p)]= np(1-p) o (Bin, P ) ) = Inp ( 1 -p ) If X and Y= ax+b are random variables: X , y , and w= ax- by + c are random variables : E [ YJ = Ecak+ b] = GELKJ+b only if they're E L W J = E [ q x + b 4 + c ] = q E [ k] + bELyJ + C VEYJ = Vlax +b] = a= VCX) independent If X and y are independent variables! O [ Y J = 0 ( ax + 6 ) = lalo (x ) (EDY] = ELATELY] E ( X ] = E [ XJ + E LY] CHAPTER V [ X + 4 ] = V ( x J + V ( V ] FOUR : (V lax+ by] = az V(x) + b= VLy) Pr [z