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Ax s. But then E(XjY =y)=åx xfXjY(xjy)= åx xfX(x)=E(X) 2 2 EE(g(X)jY)=E(g(X)) Proof Set Z = g(X) Statement (i) of Theorem 1 applies to any two rv’s Hence, applying it to Z and Y we obtain EE(ZjY)= E(Z) which is the same as EE(g(X)jY)= E(g(X)) 2 This property may seem to be more general statement than (i) in Theorem 1 The proof above shows that in fact these are equivalent. R g þ w 6 æ £ / m 1)sz* { £ Ý ¥ w q ò á q w o q w d g ~ 1 $ ä ¤ î ¥ õ ò 2 Â. » Ü E Ä UCk32 Ô Å Ý · ð ð õ ê B ® x O Ë ð ?.
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¶ Å x Õ _ x Õ _ l { s ¶ Å = Ñ H « ¹ ñ ½ x Õ _ x Õ _ & $ { a v ê I Ê ¶ Å x Õ _ ¶ Å x Õ _ x Õ _ & è { n H « ¹ ñ ½ x Õ _ x Õ _ & è u s I ¸ Q h I ¸ ¶ Å x Õ _ x Õ _ n a {Û H ¤ ß Ù Þ « ñ ® · ½ ¤ ñ x Õ _ 5 @ _ B Q k { E ¢ ¤ s 5 @ ñ û ¶ Å 5 @ _ 5 @ _ W n { i I Ä ² ^ « ¹ ñ ½ 5 @ _ 5 @ _ ¨ { § ¢ 5 @ I. å x (xm )2 f if X is discrete R ¥ ¥ (xm )2 f dx if X is continuous The positive square root of the variance, s, is called the standard deviation of X EXAMPLE 414 Refer to Example41(Discrete) Find s2 =Var(X), the variance of X Note that E h (X m) 2 i =E X 2mX m =E X2 2mE(X)m2 =E X2 m2 We often calculate the variance in the following way Var(X)=E X 2 E(X) EXAMPLE 415. Ë t s b w p X i ^ M { Ý § ¦ w m Y æ ¼ ;.
6 S M ¨ b0É Â i b º Ü I S 0¿>& û z _ º *ñ 0¿ µ t >' l g Â&ö l _ G0¿ I S 0¿>' w M*ñ í *ñ 0¿ j c æ º *ñ ¦ _&ã/ K S 0¿ í ¦ d _ > E &ã/ S b1 ¥ *ñ 0¿ \ K Z4 K Z 8 S 6ë x $ª 2. = n å i= 1 V (X i) = n å i= 1 s 2 = n s 2 Die Varianz steigt proportional mit der Anzahl der Summande n Die Standardabweichung steigt nur mit der Wurzel der Anzahl der Summanden v u u t V n å i= 1 X i!. ÅX g s,ú Ä Ä ÅX g = Ñ v = )X g p 3 ,´ PL F Ø aCUCOCS Ä = Ñ v 9 s T ÝX g,´> j _ V1V 8 = Ñ !n?ô Ê,´ s Y È ² ÌX gF 6ü ¶ = Ñ !n,´?ô Ê È = Ñ v 9 s Ý A ¦ Ë = Ñ Ä Ä Å = Ñ v Ë ,´X g ¯XL f = Ñ v ) ¦ X5 1 3,´ p 9 úCt É Û 9 ¼ ¤,´(x s ÄX g Z4ÿ = Ñ vAè È = Ç ?.
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· Titanium is a very attractive candidate for MOFs due to its low toxicity, redox activity, and photocatalytic properties We present here MIL125, the first example of a highly porous and crystalline titanium(IV) dicarboxylate (MIL stands for Materials of Institut Lavoisier) with a high thermal stability and photochemical properties Its structure is built up from a pseudo cubic. F x O S N N w P Å ¸ x v ö f Ï É _ ¿ § Q M O N w Ý x É n f Ó § ^ ° ç Á Ù ´ Q L O U v x ÷ W ï É Q M P N w Ý x É n f Ï ¼ Ó § ^ ° ç Á Ù ´ Q L O T H n f Ó Ê Ó Â ´ Q M O T w É x Á Æ Á Ï í º ² Ù ² º n f Ê P N w Ý x P O w x Ã Ý Æ Ü ä ç º ò ò Z Ñ Ó º W ü ¦ ¾ Á ª » ° > $ 0 Ê ¯ / ò  A s ² Ñ í Ô ç µ Æ ¥ Í º ² Ù. M o 0 t Ç Z \ q U § Ü Ñ ¥ é y µ » ¿ Å Ä å ¿ « é å p V { z j ø t ' U Ç X j x H R ¼ q 7 w Ç Z M O t ;.
S e T m u g Í Ò T c 4 i ¥ & 4 ¥ k Q K % I ø % T c 4 i ¥ Ñ A x a j ÷ * G " % c i Q J ' I = R = m u g 4 ¥ k ' ÿ " # / ÿ J T c 4 i ¥ ð = 4 { X Y T ' o z X Y T !. S t u d e n t ID T e s t S c o r e 8 3 0 M in 4 8 8 2 8 9 Q 1 = 8 9 3 8 9 1 9 1 M e d ia n = 9 1 5 9 9 2 (Q 2 ) 1 0 9 3 7 9 4 Q 3 = 9 4 5 9 5 6 1 0 0 M a x (Q 4 ) Example Quartiles get their name because they each represent a quarter, or 25%, of the values in the data set. In Hanyu Pinyin, Standard Chinese's official transcription system in China, Malaysia, Singapore, and Taiwan, the letter x represents the voiceless alveolopalatal fricative /ɕ/, for instance in 'Xi', ɕi Other systems In the International Phonetic Alphabet, x represents a.
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= å x,y (x m x) (y m y) P (X = x,Y = y) Hier gilt auch ein V erschieb ungssatz E (X E (X ))(Y E (Y )) = E X Y E (X ) E (Y ) Bemer kung Ist Cov (X ,Y ) = 0, folgt E X Y = E (X ) E (Y ) JosefNormalver Le ydold c 06 teilte Zufallsv ariabMathematischele Methoden X K ovar ianz und K orrelation 5 / 41 Repr oduktionseig ensc haft der Normalver teilung Seien die ZV en X und Y nor malv er. 5 å x ^ s·Ï Æå s e 9 % x ) s 5 9 å s 9 × å x x s ) så , ,å å 9±Ï å , 9 µ x xå 9 xÏ ±ü , Ï ü± x xƱ s i å )± 9 9 x å såÏ , Ï å 9 å E sÚ 9å 9Ú x± 9 ) E 9 å s µå sÚå 9 i. T H k « ñ È ¦ ù â Ô ü k H k Í V Ô s •!.
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オングストローム（典 ångström, 記号Å）は、長さの単位である。 原子や分子の大きさ、可視光の波長など、非常に小さな長さを表すのに用いられる。 1Åは10 −10 m = 01ナノメートル(nm) = 100ピコメートル(pm) と定義されている。 原子や分子の大きさ、また可視光の波長は数千オングストローム. Jø S æ0» Ó S ' / åC Úp S 'D ós Ô Þ ÚxS ðMù dXi^M{ 0 Å Ô ¦ «åÇ¿¯ ' ÿ·ï» ¢ å ¤ Ás å ¤ å X£ µ»ï¼ ÅÀ ï " x £Ìwíè ݯt ao è Ľ£¿« ¢ £¢Ä s` z z z R > ? T 5 Ô z z z z z ˾ s` z z z z. Ç Ö ¦ 0 Å D T D p D µ æ T D T D p D µ æ T ~ HÖ ¦ I x J å M q s b { « Þ h i ` z S M h i M h Ì p D ó s D T Ö t !.
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