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Defineafunctionk(x,y) h(x)/h(y) = 1, whichisboundedandnonzero for any x ∈Xand y ∈X Note that x and y such that n i=1 x i = n i=1 y i are equivalent because function k(x,y) satisfies the requirement of likelihood ratio partition Therefore, T(x) n i=1 x i is a sufficient statistic Problem 5 Let X1,X2,,X m and Y1,Y2,,Y n be two independent sam ples from N(µ,σ2)andN(µ,τ2.

Asswy u y. Y >a Ñ #!. BASIC STATISTICS 5 VarX= σ2 X = EX 2 − (EX)2 = EX2 − µ2 X (22) ⇒ EX2 = σ2 X − µ 2 X 24 Unbiased Statistics We say that a statistic T(X)is an unbiased statistic for the parameter θ of theunderlying probabilitydistributionifET(X)=θGiventhisdefinition,X¯ isanunbiasedstatistic for µ,and S2 is an unbiased statisticfor σ2 in a random sample 3. ?§« ¬ ¯ ° m~n o qis t v q w9x { F B)GªH\(C D E;) VONE me} G t k @ B #9#{ '(C y%;.

Problem 334 Solution We can find the expected value of X by direct integration of the given PDF. P § È µ Ø G M N ¾ µ î ,q G ô $Ò 5 7o Ó î ,q ,q / ` £ ¾ =Â8p Ì Ç ¾7 V § ` £ ¾ î ,q 9?. Suppose Y 1 and Y 2 have joint pdf f(y 1,y 2) = e−y 1, 0 < y 2 ≤ y 1 < ∞ (a) Consider U = Y 1−Y 2Use auxiliary transformation V = Y 1 to get y 1 = v and y 2 = v−u Note u > 0 as y 1 > y 2Furthermore, 0 < y 2 < y 1 inplies 0 < v − u < v or 0 < u < v Jacobian is J = det " dy 1 du dy 1.

Problem Solution To show that Y(t) is widesense stationary we must show that it meets the two requirements of Definition 1015, namely that its expected value and autocorelation function must be independent of t Since Y(t) = A X(t), the mean of Y(t) is. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history. Ë > ¯ $¤ ì Î ë î , ( F " >U >W >Y N Í Ì õ » É > H % ¼ ³ Ñ 9 Ã 2$ Î /9 *y Ë Í î >!T 1 V 1 Ñ n "ø õ *¬ ` ¼ î E = > # µ)¿ ç > À Ñ 9 0 * Í Ì Î Ç § É ½ º Â >\ ô 1 9 õ í ® Î H % ¼ Î ¥ >S É Ý Â Ä Ñ Ó Ñ ç í ® ç õ Ñ ® Ò E Ã ò >S É ° Â >\ H % ¼ Ë y § Ç Ç å.

G y R29 å12 D5 Ô yReceived Dec 5, 17 ⃝c 18 The Society of Materials Science, Japan ∗ Y q » y ý Á G ¶ y ­ ­ ¶ æ ß y ý Á ¢. Problem3 SupposethatX andY areindependentrandomvariables,eachuniformlydistributedontheinterval(0,1)LetV =X−Y andletW =XY FindthedistributionfunctionofV. G(x;y)=xy 1 Find g –f 2 Find f –g 3 Determine if g–f is onetoone, onto or a onetoone correspondence and in the latter case, flnd its inverse 4 Same question for f –g Solution 1 (g –f)(x)=g(f(x)) = g(x;2x)=x2x=3x 2 (f –g)(x;y)=f(g(x;y)) = f(xy)=(xy;2x2y) 3 g–f is a onetoone correspondence, and its inverse.

J ê Ó ê Þ í ­ s b q y È = W r O } u ² é y c T v z » Ç é W È d ¾ } U Ð O = z ¿ Á y È = } 6'*V v Æ Â = s 6'*V Ê Ñ ¶ Ë · ® r ç » Ç é y ( C C W M s ¾ } 9 Æ Â 6'*V v Ê p \ k \ r u Z s § _ L y t @ v ë d ÿ j u Æ Â y. 3 Motivating examples X sep/re Banach space and functionals J " X !R 1 = R f1g De nition (Weak/strong convergence and Mosco convergence) Weak convergence J". / Ñ ¾ i ã = y ( i ç Ï ê { HE Õ è ¯ µ å ñ « Ä ­ ¿ á / ( i ´$17 C G µ { 266 E Õ ë ¶ ¥ ­ Æ ( i { { ­ µ å ñ W W r X O { õ ¢ Ö ¢ y ¢ ¸ { Õ ç Á Æ Ó § Þ y E ( i { Õ ë ¶ ¥ ­ Æ y s Ï ( i þ ¥ O U.

C » ` h ¯ Ø Ì Ñ Z t o Í h } ¼ g " w G O Fig 1 t Ô b } ^ t { c ® V s ` w h t ¼ g " † j Ø !. Y = 1 100 ∑100 i=1 Yi, the sample mean 2 average the Yi’s for guys whose Xis are between 0210 3 average the Yi’s for guys whose Cis are 3?. Y = 0311X (2) (b) From the graph, we can see that the regression passes through the center of the major part of the data, but does not capture all the features of the data (c) Plug x = 30 into (2), and the result is the point estimation of mean GPA with ACT score being 30.

Now we defineP Y i = 1{ith set of twins is MM} and X i = 1{ith set of twins is FF} Clearly n 1 = n i=1 Y i and n 2 = P n i=1 X i, and also Y iX i = 0 since a given set of twins cannot be both two males and two females Using these definitions, we have Cov(n 1,n 2) = En 1n 2−En. P b m T Ò å ¿ « µ Ö ³ ß ç w \ \ U Ù ï Ä!. F e ` > ~ä «»¢ï e º y t Ê yyyyyyyyyy ' Ì H ( H ( H ( H ( H ( $ èú j©Ã.

EC02 Spring 06 HW5 Solutions February 21, 06 5 What are EY and VarY ?. 60 CHAPTER 3 MULTIPLE REGRESSION Theorem 31 The LSE βbof β is given by βb= (XTX)−1XTY if XTX is nonsingularIfXTX is singular there is no unique LSE of β Proof Let β0 be any solution of XTXβ = XTY Then, XTXβ 0 = X TY and S(β)− S(β0 = Y TY −2βTXTY βT XTXβ − Y TY 2βT 0 X TY − βT 0 X TXβ 0 = −2βTXTXβ 0 β TXTXβ 2βT 0 X TXβ 0 − β T. Is Y(t) = A X(t) a wide sense stationary process?.

Y I(µÒ ȵ Ò I¡Ì IÅyÈÒ Iº I´yµè I ¡® È µ. > µ ì ð W E l Ç u o u u t v Ç U o ð U î ì í ô í W ï ð D Title math0c18s Author asalehigolsefidy Created Date 4/13/18 AM. Title 年度第2四半期連結経営指標推移 Author 株式会社リコー Created Date 11/4/ PM.

Observation's Z Y value is given by predicted Z Y = • Z X Notice the regression towards mean ρ is always less than 1 in absolute value, and so will make the predicted Z Y closer to 0 (or equivalently make Y closer to to µ Y) than the Z X was to 0 (or X was to µ X) Inferences re based on sample of n (x,y. ï è µ ï(SUS316L) ;. C è µ Q ¨ s ã y N S V ¥ u z k 4 4 q u a B j u a Ä C B C e u a k q V B \ 4 q C PP¼ PP e 4 { q V D è Ë /)&62 x 2 ) 3 3 3 3 3 3 3 3 3 3 3 3.

V § V § ` ü Æ G ô G ô. &'3 ¢ ñ × · ½ è ³ ¿ # È ¼ y M &'3 y ¹ ­ ½ ê Û Æ z ¤ Ö r Æ u § Å ½ s q f Á J v d ^ s ê & v `. Y Z x dx What is the extremal if the b oundary condition at x is c hanged to y Find the extremals J y Z b a x dx F Z x x y y dx Find the externals a F y y y k k constan t b y Euler s equation F y y c so y ky c y ky c dy ky c dx idx Using the fact that Z du p u a ln j u p a w e get Z dy.

N Ç *> Ç *> Ç *> ¾0b M È ¾0b M È Ø G M ` ü Æ ` ü Æ ` ü Æ ó Ì1 ` ü Æ 4Ç% ;. Title キャンセル・プロテクション キャンセル内容報告書 兼 特別措置手当金請求書 Created Date 4/7/ PM. ^ y ) ß z F Ö Î s Q y 9 ÿ @ Ç ) v p X ` T b q O d } à ´ ¿ ¥ ñ H ¤ ¥ r z ° ¿ ¥ ñ H O ± ð ¬ d F õ S W M d } ^ z D ¦ & u ÿ s u = ½ ¢ â r ¸ v ú è d ^ s W Ë b Z u n j Ö û ½ ¢ â v e ¿ ¥ ñ ù ¥ ` j y v ê è O x d y.

Y "A" — (íi˙ RM4TA3p)I Ìœflš yEj˙˙ï@œflšf> “ª˝˛I (Æâ) z« t y ð‰q 400V œflšf> 10% ÞüłiE 400 (400 x 10%) = 360V “ª˝˛łiE 400 (400 x 10% ) = 380V 2 Zelio Control RM4 ‰ RM4T (›) t < t 0 volt 15/18 25/28 15/16 25/26 UL1 L2 L3 105 x " è µ < U " è µ < U Ý >. Ó è · ½ ¢ é NJ F Ö ¤ V ¥ F Ö ¤ Ö ¥ d 5 5 5 56))LQDO ² p à  p 7) 7) í 4( í ¾ í5 3¶ 0Y ^ ;µ p ¸ < X í 4( í ¾ í % ¸ d S { ² p )Y5 p 7) ¾ í í 2z ¿2!. Show that Y = X2 has an exponential distribution with mean = 2 Solution Note that the function y= x2 is strictly increasing and hence invertible on the e ective domain with x>0 , and its inverse is given by x= h(y) = p y Then h0(y) = 1 2 p y By the method of transformation, we get the pdf of Y.

< y E s s v Ñ ¶ Ë · v U \ § ß y ö v y r M } è n j ^ s W I X O } ² O < y E y r z Î W o V e ^ y þ ü r y § è y ö Ö b q O } v Ó § ê · Æ z$ è · Æ ) Â < y E W h ¸ r d ç y V s v u n q O }. M h } ¼ g " ;. Title 19年度通期連結経営指標推移 Author 株式会社リコー Created Date 5/8/ PM.

Same as in 1, because height certainly do not depend on the number of cats Intuitive description of regression (height) Y = variable of interest = response variable = dependent variable. È µ å Á Ò ñ ® µ Ä ¡ Î ª Å ñ z F y Õ z Æ 8 v y E « S  b q U b j W Õ z Æ 8 v y t U ~ h P y u  C g y t # \ ç F Ö v  d ^ s s O j b b j y r U f O j b d } u U  v O b q z U n 9 U ~ J  ½ y ü ¸ y ® / 9 ô. Then we may write ‚ = k2 where k>0 Then y00 = ¡k2y has.

È ® µ È ® ( 6 ¯ å ¼ 6 ¯ å ¼ ª\ ´ \ 3 Ù ô ¼ #\ ¿ È ® µ ½ å ¼ À 5 Ï ­ Ã ~ ÿ ö ¹ Ð ¼ ¿ ­/ ­ Ã Æ ß 6 ­ å ¼ ù\ 3 Ù ô ¼ À\ ª\ ´ \ ö ¹ ­ y0wj 6 ® å ¼ #\ ¿ È ® (È ® Â À\ 6 ­ å ¼ 6 ¯ å ¼ ±\ ¿ È ® µ ª\ ´ \ È ® Â 6 ® å ¼ 6 ¯. , ¨ON(j( 'K ¨(B 9( D E;) men orqG Cs t v w "Q ;OW(P( D. µ Þ « Ø Ã í å { ` h ÿ X v µ Þ « w Ì ï Â JrÒ å ¿ « µ Ö ³ ß ç ¾ V m W z ý Ú ³ ï ù ^ d h µ » ç.

2 8 Y 1 P roctor S D , M am o JC L Intim al retention of cholesterol derived from apolipoprotein B 100 and apolipoprotein B 48containing lipoproteins in carotid. Y$ è¯ µ ^$ è~´ > ey _ & ú~^ ú H~ × ?. Ú E u r è y Õ ç ¢ Î µ Û è µ v p X } O d } r è z ³ Ñ · v U n ` s y " 2 f ¼ ¤ ´ ô v H d Ö û v r è W b j z.

U n 9 ¦ ´ Ï ½ ² É y / Ä O U v o O q µ Ï ½ ² É r z c ¾ / Ä b q O d } U # \ v u n j Î < r Ï ½ ² É Title repair_request Author MAKI NAGAMOTO Created Date 1/14/21 PM. Y = a e^(b x) where a and b are constants The curve that we use to fit data sets is in this form so it is important to understand what happens when a and b are changed Recall that any number or variable when raised to the 0 power is 1 In this case if b or x is 0 then, e^0 = 1 So at the yintercept or x = 0, the function becomes y = a * 1 or. Õ ç ¢ Î µ Û è µ Ú E ( v } Q ^ s ( è y 9 Q C Æ ô r M s ß ß b q U > y s U z Ú E y } O v d Õ ç ¢ Î µ Û è µ ¸ î ½ W Õ ç ¢ Î µ Û è µ u ~ v z Ú E y / ¤ v d Q q Ê Q « U ~ r à y ª ¢ Ç ç ¢ ñ u q b U n ` y z Ú E y.

> µ î ð W W } o Ç v } u o v P t v Ç U E } À u î õ U î ì í ó í W ï ò WD Title math0a17f Author asalehigolsefidy Created Date 11/29/17 747 PM. Y$ è¯ µ ^$ è~´ > ey _ & ú~^ ú H~ × ?.