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Operator splitting • want to solve 0 ∈ F(x) with F maximal monotone • mainidea write F as F = AB, with A and B maximal monotone • called operatorsplitting • solve using methods that require evaluation of resolvents R A = (I λA)−1, R B = (I λB)−1 (or Cayley operators C A = 2R A −I and C B = 2R B −I) • useful when R A and R B can be evaluated more easily than R. J ̓s E s ɂ ރA b g z ȃw A T ł B j N ̃n n ̃W Y N u o B P X R W N Ƀe i t w ~ g ɂ Đݗ A ̃W Y v ~ g Y ɏW ܂ Z b V Ăɂ B ̂ q l ⒇ Ԃ W ܂ ꏊ ɂ Ǝv C Ń~ g Y X ɂ ܂ B. X ԁE ΁E l N 炮 ЂƎ A ̒ ł t F N ₩ ɂɍ炭 c c W E R Ő_ ɍ炭 A Ԃ̏ ƌ Γ Ԃ̉ A c c W ɑ ̕i ͌ A i A D Ƃɂ o ꂽ i ƁA ł͌ 肪 ł i 发 Г Q Ɓj ̑O ܂ł͍ R ɍ炭 ԂƂ č͔ ӏ܂ Ԃ̈ ł A ŋ߂̐A ͋Z p ̐i ɂ A n ʉƒ ̃K f j O ̈ Ƃ Ă 琬 o l ɐ A l G Ƃ ӏ܉ l ̍ Ԃł A D Ƃ A ɂ ̃y W ̋@ Ƃ ĉԂ̔ ߊF Ə ̌ A m A 琬 Z p ̌ } y ̃y W Ƃ v ܂ ̂Ő A h o C X 肢.

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It follows that E(s2)=V(x)−V(¯x)=σ2 − σ2 n = σ2 (n−1)n Therefore, s2 is a biased estimator of the population variance and, for an unbiased estimate, we should use σˆ2 = s2 n n−1 (xi − ¯x)2 n−1 However, s2 is still a consistent estimator, since E(s2) → σ2 as n →∞and also V(s2) → 0 The value of V(s2) depends on the form of the underlying population distribu. ALPHABETICAL INDEX (A B C D E F G H I J L M N O P R S T U V W Y) (Revised 06/05) A Absences Without Pay (Dock. Í Ê ¨ s û É x epg@g gv 4 fþ'g g" v4 fÛg fþfî fÝ3¸g#f÷fÔfïfðfÝf¸fífþ ±fÝfåfø Ýfåg" ¤fçföfÔfïfðfÝg fçfïf¹ epgvg ggy4 fû ?%tf¹ epgvg ggy ° Ü3Æf÷f¸#' % %i (fÛ g d ¦fþ 0fúfùg"1 Âg" wfág fçfïf¹ epgvg ggy Æf÷fÿf¸ 0¿ µ h gwgxgy gfgqg gjh g"0b ÛfÔfïfðfÝg fçfïf¹ 3û.

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BASIC STATISTICS 1 SAMPLES,RANDOMSAMPLING ANDSAMPLESTATISTICS 11 Random Sample The random variables X1,X2,, are called a random sample of size n fromthe populationf(x)if X1,X2,, are mutuallyindependent random variablesand themar ginal probability density function of each Xi is the same function of f(x) Alternatively, X1,X2,, are called independent and identically. F B X G C u h A J x Z ^ i Q T r X Ə j B x ̓ e B n ̏ Q ̂ l ɑ΂ ďA J ̋@ g 傷 鎖 Ƃ s Ă ܂ B ӎu Q ̂ ɁA ` X Ɠ Ă Ƃ ̎d ł B ㋞ r f B O4F @ @ @ @ TEL @FAX. * G " % J G ) Í 1 ± A Â J 8 & J ;.

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