N I Nx

O¶o¶` X?^ØF£o¶o¶ Qî ¡5_#±5 q` X3/Iö T$`_Oìî!þ@¡/s #ô% oä "¤'Ô% _¦ ÄB«L I!.

N i nx. W ¾ Ô D ç ( ì W ¾ ý D È 3 Ø ã À S ¯ ² D ( 3 W Þ Ó î à Ò ß x K ( ì W ¾ Ô D ç ( 3 û ÿ y j I û ÿ D Ñ 8 ~ S ¯ ² º à À 1 Þ È W ¾ r D D Ò ß x K ( À n 2 MRI D W ¾ Ô ç Ø ( 3 h 7 Þ È, W ¾. 1, we see that Y becomes more and more concentrated about „X;. 2 6 ¥ ¾ T n x Qsfofujdt !.

TDÀ P T n x Qsfofujdt !. >/>7 ì _6â Ñ 8 S K r K S Q b Ñ Æ b 8 >/> ¥>&5 >' _ c S6Û &k _ K Z > ~ r M r S \0ñ ÑÒ Å » M ( b U H* b K0 * _ X A r K Z c ú d ?. } u Û S r Ñ b Ã Ó î É Ý b à S ì ( > ì ( è v ?.

H f p q b s l A d j u z / j u p j h b x b / m h / k q !. As n !1 X n converges to X in probability, written X n!p X, if, for every †>0, P(jX n ¡Xj >†)!. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history.

Ô Qsfofujdt !23 26 º !4119!9436!. ¾ À ² Ñ r y Ý w Ó ± u û ì n" d j ( ý @ Ñ Ø x k w Ó 8 & ï Þ Ó î l ± l À ã h % d Ñ r y Ý w Ó 8 & ï Þ Ó î 8ftufso cmpuujoh nfuipe k û Ú ± 1 À 4 1 Ô ( z Ñ 8 x y Þ Ä ý s Ò 8 n 5sjt cvggfs À Ð Õ Þ p$ À ² h 5 ý @ & , ;. For any ¾ 2R Next, suppose that we have an iid sample X1;X2;¢¢¢;X n » N(0;¾2)Then the joint density of X1;X2;¢¢¢;X n is f(x1;x2;¢¢¢;x n j¾)= 1 ¾n(2)n=2 e¡ Pn i=1 x 2 2¾2 I x 1;x2;¢¢¢;x n2R Now writing ·(¾)=¡ 1 2¾2;T(x1;x2;¢¢¢;x n)= i=1 x2 i;ˆ(¾)=nlog¾;.

Ð z W ¾ x y ÿ 8 & ï Þ Ó î Ë ³ W \ 7 } A ý ;. Oct 18, 14 This Pin was discovered by Toshitaka Akihara Discover (and save!) your own Pins on. N NX¡1 i˘0 Z › f (x) dx, ˘ Z › f (x) N2 NX¡1 i˘0 ¾2 Yi ˘ 1 N ¾2 Y, (1) and hence, ¾ £› FN fi⁄ ˘ 1 p N ¾Y, (2) where Yi ˘ f (Xi)/pdf (Xi) and Y represents the evaluation of any specific Yi, eg, Y ˘Y1 This derivation proves our earlier statement that the standard deviation converges with O(p N) Moreover, this expression shows that by reducing the.

ÔüI§xsB´ŸQ› Я— òò £ þ½ ð¯Äû Vñ­µ8—Ovoܹ¡ ƒ ÇôúW‰ÞÜ^Îf»šI¥ Îrp ¥A@ “ñЃ⠻²¹°¹¼³†qµ› ßZîô½OÕD‡M¼‚èF@s Ûž™ü 2moJ‚WŠ}NÆ9Pá‘î >„ ÅyÏÀ_øöÖ ß‹ù=lêÿ t½STº¾šòõ$¸ ÈÊp =¾Zê¿á Ñ¿è/§ àJ i© R ) ‘§LÎÐD6)ÉÂ. } u Û S r 0d >& v6ä >' Ñ p ¸ *ñ ì6ë P1ß º/ !. B õ I Z 8 ' c & ¸ 2 1>& Ç ¡ î ¾>* & ¸%4*ñ B b$Ï6 '>' ;î0 , b Ê g B K ^ 8 Ê ' b S u>* \ Ú(Ô) \ j 9 ì A >&5 Ê >' & ¸%4 c ² \ '¨ ) b A b G#Õ#Ø%4 6 >&3° Ø È#Ø%, >' @ v ~ s C _ à c K I Q K Z > ~>* Ú#Ø \ b j 9 ì \* < } 7H } S 6ë.

Ri g h t to Co u n sel (RT C) i s a l aw t hat was passed i n New Y ork Ci t y i n 17 af t er a 3year t enant organi zi ng campai gn T he l aw guarant ees l owi ncome t enant s a ri ght t o an at t orney when f aci ng an evi ct i on i n housi ng. ITg5, Õ/k ¨ n ¾ Í !. ý y £ > ý × ý ñ, ( S h , Q X ¶, S ( k Ô ÿ, Ñ h , Ò b h , È y ñ k Ô, W Ý z ñ k Ô 8 & ï Þ È International Federat.

Rademacher and Gaussian Complexities Lemma 3 Let F be a class of functions that map to ¡1;1Then for every integer n, R n(F) 2 ¡2 r 2 n • D n(F) • R n(F)4 r 2 n If F is closed under negation, the lower bound can be strengthened to. 0 for all †>0 In. Title Šc8705/„¾„ê‡Å‡ÌN›X›» Created Date 11/4/14 PM.

& É Á ¯ é Ü n X s ¾ ¢ ê ­ Æ Ü n X ½ Q wwwwwwwwwwwwwwwwwwwwwwwww & ¾ ¢ ê ­ Æ Ü n X y = O ¨ I wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww & K Ò Á ¿ Ó è Á Õ ¿ Á Õ ´ \ y ¿ Á Õ Z Ñ * z ¿ Á Õ Ê z Z } Ï z Ï Ú & > z Ú & } wwwwwwwwwwwwwwwwww & Ã Þ Ó ç Á ­ · è Ó ë Ø ñ ¾ Ó ¡ é v ð ù ½ Q } D Ï Á ¯ ¶ Z E Ó ç Á ­ · E �. 0 as n !1 Let F n denote the cdf of X n and let F denote the cdf of X X n converges to X in distribution, written X n!d X, if, lim n F n(t)=F(t) at all t for which F is continuous Here is a summary Quadratic Mean E(X n ¡X)2!. = 1 N2 XN i=1 Var(Xi) = 1 N2 ¢NVar(X) = ¾2 X N;.

Title Author Subject n Hc^ÌNHA {b !Ba% ë3 ÝÎ o Keywords n Hc^ÌNHA {b !Ba% ë3 ÝÎ o Created Date n Hc^ÌNHA ½B"n>x © L ¤Äl¤'s_Ø) ÝÇ {ï¦\L. } ç ô>6 º Ø r b>5 º6ë \ K r M ^ > \ b 'Ç x 0'v $ª*ñ ­ å ± î b"g # >/ 4 # Õ í) 5* 4 # Õ Õ ' l g '¼ _ 8 I. I Ý é · p M Í æ Y !.

} u Û S r 0d Ñ b Ã Û Û µ ¡ b à S ì ( > ì ( #Ø Â E ?. ¾ Hw ^ ~N C°^wMx y ¤5 ¨ Pv yN{¡¤5xP ^ PvHw w ³i?. 0 In probability P(jX n ¡Xj >†)!.

Ò ß x 5 ý W ¾ 5 ý Ó ;. \ 25 Ô T ó Í !. ² C ¾ i ¤ ¸ L ¥ ³ ñ Õ é ò L ® q n X y q O l Z u W ` r G s z V X V S ² C ¾ i ¤ ¸ L ¥ ³ ñ Õ é ò L • o Ï y o y v û f ^ s > y ¦ V.

â ¸ !â â ¢ 2,747 ì ß å k û& H ' w W W S x k K Ñ ¾ Ñàâ ¾ ¿ ½ *â C " c d© " ` ¸ w O V N x Ï f Ñ û ´ 4 Ë 0 Õ½¾Æ e p " ýË £ C Ì w, x Ý â g " Ì < *í ` O d I T d ¨ o ' L ' E < J o Ç Õ½ k K 622,960,000 · ¸ Ç 41,400 Ì M n k KË / Ë Ì Ë ú Ë ÏË ù Ë (ÜË Ð SË Ð %Ë k 0 ` @ _ M ` @ g " É ² r wè x �. And so F is right continuous Thus F is a distribution function If we had n < x instead of n •. W ¾ L K ì W ¾ Ñ K D r 1/2  ¶ x 5 ý ´ Ó P u ¶ 8 W ¾ x w ÿ 8 x Þ Ó Ib Ý, IIa Ý Â IIb Ý D × W ¾ L K ì W ¾ Ñ K D Õ 1/3 Â È ?.

¾ í F· 9/²'¨H H '¨>Þ>á ²6õ H ¨ e ì ¹#Õ1= >Þ G0GoGxG9 ¦ _ >Þ 0Y R e Û >Þ M*ñ N# >0 º Ó Û è7F M*ñ/ ;. ~ ì _ > E 0¿'¼. ¾ °Å °° ?*1/04 7&)( 3(0 2447* &duhhu 3udfwlrqhuv 6hplqdu ° ¨w w% u%u n wuu ¾u w)nuqtrf fsi &ifshji )nuqtrf tk 8hwjjs fsi 2jinf å&snrfynts 6wxghqwv ohduq derxw • lvwru\ ri dqlpdwlrq dqg fxuuhqw lqgxvwu\ wuhqgv • 6wru\whoolqj dqg vfulsw zulwlqj • 9lvxdoldwlrq dqg vwru\ erduglqj • ' dqg ' dqlpdwlrq • 3urgxfwlrq surfhvvhv iru dqlpdwlrq • 0rwlrq judsklfv dqg w.

(17) thus ¾Y = StDev(Y) = ¾X= p N (18) Thus, as N !. 6 ò X ï X F 6 7 ò X ð X ¾ u E 7 6 ó X N L § 5 8 ?. V S M !.

7& & µ á í Ö Á Ç ¦ ¢ ñ ­ è Á ­ n X ¾ l ¾ Ì l 7. I ô X 6 # L ¾ 7 5 ?. N ¢N„X = „X;.

W¤1 ^x ± ~N^{ H H G PvHwMx wyN{Gm ?xPww ~TwM 8 H ^ H U ^ H H Ba yT ^ j~" HxP ¤P¬ H ^x â ¯â Ýg w § Hw. F ¾ u â ¾ u _ ñ X ï X 5 L ¾ / t _ ñ X ð X / u } _ À o X h u } !. Itoigawa City Geopark Promotion Office 1月作成（10,000） Birthplace of Jade and Mt Myōjō’s Great Rock Face Kotakigawa Jade Gorge Bokkachaya Tea House (Restaurant &.

Ô n µ w â !23 27 º !3929!71!. >0 º Ó Û è7F M*ñ °# Û >/ º&Å Û è7F &k &É í ¶ ¸&É ² &k &É í * ¶ ¸ * ° Û ° Û 2 0£ 2 *. N;X z µ 1¡ fi 2 ¶ ¾ p n # Example 2 Suppose X1;¢¢¢; from a normal distribution N(„;.

~ ì P1ß 0¿ b _ Ñ b Ü 8 S 0¿ c  £ M*ñ í *ñ b!. ² O ;. Problem set 5 Expectation 1 (Normal distribution)⁄ Let X be a standard normal random variable, X » N(0;1) a) Calculate the moments EX;EX2;EX3;EX4 Hint use symmetry of the density ’(x) and partial integration b) Calculate the moments EX;EX2;EX3;EX4 of the random variable X » N(0;1) by difierentiating its moment generating function c) Show that for any fi > 1=2.

± T n x n µ w â !23 25 º !3929!71!. 23 27 º !. ,°*G2P*Ì,é" A' oÕ4 Q£5Çd B«L ^ 2 2FYp ÍoÕ*Å ËXë^¾9üoÕ.

This is because the mean of Y is „X and its standard deviation is ¾X= p N, which tends to zero with N If we believe „X = 5, say, then for N large the. ² O Ö û!. I u u q t ;.

¾2) where „ is known and ¾ is unknown Find a 1¡fi confldence intervals for ¾2 Solution We use ¾c2 = 1 n Pn i=1(Xi ¡„) 2 to estimate ¾2, and we deflne the pivot to be h = n¾c2 ¾2 It was shown that h follows chisquare distribution with n degrees of freedom Let ´2 n(fi=2) and. } b H æ _ _ ~ Õ b S u>0 4 6ë b¬ ï µ \ /1*& 1 / W Z r 8 ~ r K S @ /1* Y, * c > ~ r O Ò v > \ ( b ó ² Ì \ K Z , A)F A6õ \ \4 \ ~ ^ @ } ¤ Ñ ± b75 F _ v ~) r 8 ~ r M ó _6õ M > e 8 O ß Ö Ý Í î �. Q Ó ¾ æ r !!.

¡fi1 n¡fi 6= ;, we can flnd nfi 2N such that Unfi isolates a point of ¡fi(F) By construction U n fi does not isolate a point of ¡ fl (F) for any fl. N = p n X„ n ¡„ ¾ ¡!D N(0;1) To see this is the same, just multiply the numerator and denominator by n in the flrst form to get the statement about Sn The common way that this is used is that Sn approx» N ¡ n„;n¾2 ¢ or X„ n approx» N µ „;. And h(x1;x2;¢¢¢;x n)= 1 (2)n=2 I x 1;x2;¢¢¢;x n2R;.

U ^¾ u F n N ~ _ X j 02 ~8 6 1349 F 8 6 G U ^¾ u i I j Ө @ a¾ ~ Щҧ u @ ɡA ݥL O @ ¾ ~ ɭ C n O A¾ ~ ɭ i I j i A U L F Ѧۨ u թM H աA L ФF ¾ ~ H A ̫ A¾ ~ ɭ. A H¦ T n x!. ¾ À _ ­ ° >Ù>Þ >Ù >Ù >Ù f½ >Ù >Ù >Ù f½ >Ù % &>Ù >Ù >Ù >Ù f½ >Ù >Ù >Ù eg % (>ã>Ü e©h g0gyg^gvg{gg>Ìe h g2g g>gy>Ìe h g^g gug1g >Ìh h g_g >Ìegh gjgÌeuh gngdgygjgÌeth gvgxgegygjgÌ x Ðh g8g g^g g_g b gggag0fÜgmg2fþ fÿ>Ý>ä$ gig gyfÛg fþg9g4g gvg^gqg=fûfö8p )g"& >þ?.

0 0 h f p j u p j h b x b / d p n 0 F n b j m !. ¾ v µ v U P o Z ( u P U o Z µ v µ v Á m µ v P ~' Z P µ Z ¾Z Z º Ì µ P µ v P. $ ¾ s¾ È s È s È ¾ ê Ý s¾ ± ª»¤ ª «ÈsÈ ±« « 9 × j±¾¢ ÈÝ R I G H T T O C O U N S E L W ORK S T O S TOP EVIC TIO NS!.

HW7 Junyi Dong 1 Theorem 3 Under the assumptions in Theorem 2, the MLE µˆ of µ satisfies that p n(µˆ ¡µo) converge in distribution to n(0,¾2), where ¾2 ˘¡ 1 E @ 2 @. ¤ ª ì F ã ò w Å ì w E ¶ U ­ B Å ì w l ® b P X C e P X C y P X i ¤ Ê j 1 D ¤ J n Ì w i Æ ° _ É Í C g Æ ° ­ B _ h g Æ ° V X e _ h g Æ ° ë @ _ h C @ ´ ç i05 N j ª ñ ¥ µ ½ g Æ ° ¯ S  « _ iConcentric Sphere Family Environment Rowntree É æ Á Ä1901 N É ñ ¥ ³ ê ½ g Æ ° ­ B _ h Í C V ¥ E. Once again we can represent the joint.

ì º @ ~ _ iKAWAMURA, Atsuhiro j ¤ ú Ô F P V j O O U V T Q N V U ú » Ý 3,500,000 ~ ½ B impact on the safety and reliability of combustion equipment, but is also a factor that prevents its use as a material cycle Previous studies had shown that clinker formation may be suppressed by mixed firing with the smallsized Biocoke of the same size as wood pellets In this study, the. Þ Ó î r 8 ý ä Ý xftufso cmpu ³ À Þ Ó î ñ Ô Õ d ª ( × #$" lju 1jfsdf 3pdlgpse * 64" 8 Þ È Þ. But if n is the smallest integer x < n then if y < n also we see again that (x;y does not contain an integer So P xx F(y) = F(x);.

í M ² M N } í ¾ S ì ( > ì ( S ?. ¾ q ` ï x à b Ì Ï J @ @ @ ´ f @ @ @ Y w I v Æ w ` ï v Æ Ì Ö A É Â ¢ Ä Ì T v É v í ê é B ê w ¹ ¿ ¾ q ` ï v à b Ì Ï J V ` w ^ âè L n A ´ å T Ú Z e A Ï È s T s B § { L A l V ¤ m Ç ñ Ý B ¹ ¿ ¾ q m ` A ä ¹ e ³ ¼ m ï @ ¹ ¿ ¾ q A ü Ù V ¦ A Ý ¢ V s A Î W ^ } Ð e ã m i V j A ú é B Ü ½ w ` ï. î ì î ì X ì õ X ì ô î ì î ì X í ì X ì ñ ò X í ñ ó X ô ó ï & í õ ð ' E Ç X ^ Ì À l } o l À o u v l } o Ì } o P o } l < u P o o } o i v u P v o ~.

¾ m%4 ú $ª0£#ì>& >' _ ö Y C$ª*ñ ­ å ± î b z m x µ $Î y M \ \ v _ %4 Æ b7 @ 8 £$ª*ñ I O S u b0£#ì \ K r M >1 0£#ì b 6ë ç ô>0 º Ø ?. ¾2 n ¶ Central Limit Theorem 14 Example Insurance claims Suppose that an insurance company has 10,000 policy holders The expected. ¾ , B\ù\µ\Î\· \ð\é C « ¾ © Ç\è\ö\ ¯ ³) ² «\µ\ó ¾ = ó \Ñ Ç\Ò\Á\Ð £ ÿ\Á\ « ¾\Õ Sd?\ü.

$ Ð A p O ;. (16) and ¾2 Y = Var(Y) = Var ˆ 1 N XN i=1 Xi!. W ¾ x y ÿ a 8 * & Þ È Ò ~ 3 a Ý Á ¨ Ó h ì ® Þ Ó î ~ "4$64 ì 4*D x ) < (00 11 02 2 é Ñ W ¾ Á ¨ Ó h 3 & ï Þ Ó W 5752 z º TBS À D ç Within Normal Limit (WNL) ý Ó ñ É 7 × 1680 z (292%), Benign Cellular Change (BCC) 38 z(666%), Atypical Squamous Cells of Undetermined Significance.

T ó Í ó , !. 0 E o É » > > ¾ 4 b Æ > > > > > > > y U P V > O N X Q N Í O O X R S { > > >Ì H7 @ H9H H g* iG G\G GVFþ âFñ3¸G FÿFÔFóFåFÔ& FFéG F¹>Ì H H 0 'ÅFû7 FçFöFÿ5 '¹G GEGqG GeGhG GEGyG"#ÝFÔFêF¸GhG FÒG FÔFÿ S º'¹G"#ÝFÔG FãFøF¹>Ì > Ì f É b Æ É v ¦ ä R b í ø ² ² Å ° º » ² P b í Ö w Í x b í Ö w Ö Í Ö x  ´ æ ® à > Ù º ø ² º * í í. N ¾ ¾¡3 i=1 (Xi ¡„)2 = 0 Solving these equations will give us the MLE for „ and ¾ „^ = X and ^¾ = v u u t1 n i=1 (Xi ¡X)2 This time the MLE is the same as the result of method of moment From these examples, we can see that the maximum likelihood result may or may not be the same as the result of method of moment Example 4 The Pareto distribution has been used in.

Title Microsoft PowerPoint æ °å 㠳㠭ã 㠦㠤㠫㠹æ æ æ ¡å¤§å æ å¾ ã ®æ °ã ã 観å ã «é ¢ã ã 㠢㠳㠱㠼ã èª¿æ »å ±å æ ¸pptx.