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S(p,y) = G(p) dGp(1 y p) /¥d Á¦ ¥f¦Þ/¥f f¦ Á  f d /¥d f¦ ¥d¦Þ/¥d d¦ Recall level sets The level set of ris {p–(p) = r} “the set of distributions all mapping to r” 1 cloud 1 sun 1 rain Here We drew the simplex m{clouds,sun,rain} –(p) = “most likely outcome” (mode) A threeoutcome example Level set of the mean all pwith equal expectation Here Y2{ 1,0,1} 1. Ø v ï b % ¨ Ì h u õ â Ù '1$ W ñ ñ þ f O x ¯ È , õ â Ù '1$ V ^ ø ÷ ^ þ ð þ â à % ñ U W v t < I S Ê ;. D Y µ n @ y < Ð < t å 4 t d Ó Ð , > p t Ö.
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í & í ;. ∂x þ ∂ðF f v fÞ ∂y ¼ 0 ð1Þ x Momentum ∂u f ∂t þu f ∂u f ∂x þv f ∂u ∂y ¼ 1 F f ∂p ∂x þν ∂2u f ∂x2 þ ∂2u f ∂y2!. Ý f Þ l ß à, Þ r ¸ x ˘ B Þ l ß ™ r V Ñ ˜ ß 0 — Ñ Ò ‹ 2 ¸ ‘ — • † Ñ.
F Þ ¼ aCardðE M i > L F Þ ¼ a X x2Xjl E ðxÞ À l F ðxÞj Concluding remarksWe determine by means of Rimplicators and contrapositive symmetrical operators of Rimplicators, difference operations for fuzzy sets and symmetric difference operations for fuzzy sets faithful to the. 68 312 T`dpnqsfttfe/qeg!!! !!!. ä õ Ý s Ý ^ { Ä t !.
X and P y X Y !. F x e s ;. ð3Þ where 1 n i is a n ivector of onesWrite Zb i ¼ðZ b i1;y;Z b in i ÞT 3 Estimationprocedure 31 Estimation of nonparametric functions.
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Title HauptkatalogD14Teil2pdf Author edwinr Created Date 11/6/15 PM. Ý s M T ï x ' r ô Ý s æ Y Ý m » W ¢ J þ õ > Ð ù M i ¶ M n Ð y Ü ô ì " y Ü Q W ¹ Ò 0 Û ö !. ì Recalling that L(θSy)∝P(ySθ), let’s šnd our likelihood function L(πSy) ∝πìó ƒ Let’s take the natural logarithm, which is a relatively unimportant step now but will be essential for computational reasons later on ln πìó = ln(πìó) Finding the Maximum of a LikelihoodOptimizing Univariate FunctionsOptimizing Multivariate FunctionsA Full Example 00 02 04 06 08 10.
H þ d È Ó ð q s d " , !. Ø R Y S Ù!. Exp ð r s þ 2 e þ d ð p;.
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C þ ÅL ´ n' n(f þ Å å ¹ · & TÅ â&* u&ð Ì ì À ¾ zDuM naY C·uM % á°Õ¸û~ Ú µ þp &¡ ¿Nô Þ¼Qh Ê Ù · þ á Ú Ì v&*Cò õ u ðոûp &¡ °Õ¸û~ à ô Òi h~ % & % & ¿ Nü Ú õ§N  u ü Ê ·p &¡h, xì\·l3 ÞAÞq0 Ú µ þ Æ Ûæ®XFMM CFJOHæ¯ ¿A{ Þy Ò È ÿ Ù · þeoFÜ ë Û (. Y Þ r n Þ It is easy to see that the conclusions hold from the above inequality Lemma 8 (8). Ú Û ý V j s m i l q k g r u h {} n o y Ü « p q kþ y r s i g l j ª u hHimna Zeusu {m p o þ w r k s m} o l y h q u {j p t n i ¥ g Ý f l j q g k ½ x o.
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F gÞ, Px(F) is a compact subset of X and Py. "f$ {~ e #`# ¬)" d !. I q Ì H º È ¯ » x f < Þ , ñ Ð É ñ ° f ö x = ñ · ö x = ñ þ ² ö Ã f ð þ ½ þ d 5 A ñ x ý ¼ þ > d 5 ý ¶ ð q ¿ · , 6 · ô ü t u ¨ v ¿ 9 È ¸ ý v Ì H , · ô » þ Ì H y h Í I / ¨ º u ¸ þ ¶ " Þ ².
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ð2Þ y Momentum ∂v f ∂t þu f ∂v f ∂x þv f ∂v f ∂y ¼ 1 F f ∂p ∂y þν ∂2v f ∂x2 þ ∂2v f ∂y2!. ï T ß f u ò ½ U ß þ ð 9 s ² È 6 à ß Õ p Y Ü W Ü q b ß þ Ì þ RPH ZZZ DSSO\KRPH FR NU T þ x Ô y q ß S v ß f Ç ° f O v ~ " , !. ¶ H { • Õ j I Õ Õ 9 q ô T , x Õ u Õ j I ô T , • U ³ u õ ³ ² Y MSJ JLI SQJ Y < 9 s.
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D õ n @ ã !. @ ˛ ‹ ˆ − P F % O 5 z H P * F % O 5 Š P fi ” fi P!. Corresponding to the ith cluster, and write mb i for the conditional mean vector of y i ¼ðy i1;y;y in i ÞT given b i Then model (2) can be rewritten in matrix notation as gðmb i Þ¼Z b i ¼ N 1if 1 þ ?þ N pif p þ 1 n i b i;.
F Þ, P y ðF Þ 2 KðY ;. ( ) < p Y B O ú e µ þ ä á K è 108 Î % w / § O Î p 3,537 58% h Î ¢ 1,435 24% Ý @ 6,090 100% ú Î p @ 1 / f § O M ä 4K ¬ / f y c M ô ï a X 3 s ` < n X o ã f Þ p £ ¾ p ã Ò M n X !. 0 u t Æ Â W I X Z A b q X j } ² O ^ y T ç H ë J ú v Ó u t D !.
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