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˻λʵϣ̷Ҳ˵人ѧ̷ѧĲʿ
ȫ̷ʿõġʿ˼·ȫȫ
У԰ĿܶΪһ岩ʿϵѧߡĻ
С񡱵Ķ֪֪ǶѡҾ˽һЩ̷ģ
ԱҲһ˽⣬ѱΪѧǡԱ
ˡŬ顱[ȻкۣܶͬǱһŲ죬ֻ
Լ]ĻӦ֪˵ĲʿĿʲôҲӦ
õڿ͹۹淢ʲô¡ϧҵĿڰθҵ
ʱﵽĿģ߶人ѧ̷ѧƺ۶ϰɡ
񡱾ֱԣҪɻʲô

ٴΣѧоرоʷʶرҪעض
оɹķСйѧоȱʷʶǽΪձͨ
磬ڡ񡱿人ѧ̷ѧо޿ȡ˵
Ǹƣûʷʶı֡ûʷʶоȾǲ
עоͷۣҽоĻΪϮ
ƣȫʷʶоŬ
人ѧ̷ѧһǿڸѧѧ۵ۺϡУڴ
оߵĹ۵㣬һֺҪʵо·人ѧԵ
֮йձ̷ѧʢں̶ܴȡǵ̤ʵ
Ͷ̷ɵʶǣоڽǳų⡣
ڹеһо߸Լһ֡ȥ˵Ĺ
㣬Ϊоȥ˼Ժԭ,򡣿Щ
оУһڶǰ˵оûϵͳİգǿƺ
дڲپõ֪ʶһֺܿɱľ档

ԡ˵ΪܿϧǣҶµ
ǺܸߣνĿ͹۹[ʵҸͬ͹۹]о
棬ǻоʷʶἰ½о͹۹ߣ
ܶཫڵĳɹΪо͹۹ķãڵسֵǰ
о޶á

ѧоҪյѧоģ
оЩˣ񡱣ǵЩϵҪ
ôǳϮ˵ĳɹҪôǷ⡣ĳϮǿܣɲе
߶ǳϮġкܶоǰ棬ʵһ
޶ãоô⣬Ҳǲɱġ
ò̬ȣһȥģһЩ⣬Ҳǿ
ġиϵѧ⣬һһ
⣬ٻṩһо·Ͷ

Դ˴˿Ķߡ⣬ͨ롰̷Ҳ񡱱ʾҶ
СȻһԸⱣѧĵĿ
ĻҲӭͨҵĵʼ۷ѧо⡣

Email:dewatong@hotmail.com
ף
죡
ͯ»
200883


(XYS20080803)

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й˺дţ

ʤ
2008-08-01

һΣμ.һȥģ滹д
ˡĵͤΪΪ̫ˣſڵŰݼ˺ܶ࣬Լ
ʶġ̱ۡ߳ߵȴΪʲôϸ겻ϣ
˶÷˴ϼڵ㽭Сôغݡߵ
ǻþСĴпĵͤʫ䡣
ӽ˱㽭ˣдһţȻԼ
š

ܶļŹƾ̨ġ⼸죬䶯Ե֮һǺ
ѧӷ쿼֤ɽкѪͳСһЩ뼶
ý塣ܵʱָǶ׫ӷ쿴ǡηࡰг
ܿͱŭûˡΪ̫ˣҲԶԼǸθ
ӭϴڵĿζԾбըЧ

һšƪ˵˳ݺձı

ձǱȽȨдĳЩ֪СŵĿŶȻήͺ
ࡣһΣ

ɾݴѧʷѧϵӷʾԼڹԪǰ1000ң
ڳ϶ˡļݵĹųˣɾΪܳս
һսԺգʡؾΪ
֮⡣ͨ־ԡΪϡأϣ⣬
Ϊ䣬ʿʳΪϡϼסһأ
ϵﲮ֮Ϊ䣬Ϊϡɴ֤Դں

ݵ䣬ܳӹ⽲ڡҪ˵ͨգ
Ǿ߱רҵ֪ʶѧߺͼҲѱ١һΣ

ձڶһشֽиٱԤƽ׽д
ɹϼԴϵ鼮ɽȴӺǨйĿż
¼ƬҲڼƻ֮С

ξ൱ɿԣװѶߵ

ų̨ںѧѸٲ˳ձͳɾݴѧĽ
ûҵɽҲûҵӷ죬Ѻʵƾݹ
ӵĸûĽи͵ġ󣬿˹
ýĵԶûԭŵĴٶȿ졣

Ϸ󣬿ڱʷĻôѤŪܶϡŹ
ЦʮҲйôһ׶Ρʱ򣬹Ҿ𲽣
򿪹ŵйҪϿɣԷǳණѧ߿֤
XXŴֱ˶꣬ҲƯƺӣͽ
м󡣵죬жйЩˡΪʲô
ΪǿˣԺҵҫ̫ࡣ

ԹתӣΪ˱绤ֻΪ
һԣֻ˵ŵΣԡϸ£人һ
ߵŮѧ¼´ѧ¼ȡţ˺ܶˣʦѧ߼
ɴҵʽҪԡĵνΪ
УνѧҲǴרԤơ

ýҪȵںһ˭Ƽ
飬ͨˣ´μǰжһ
ʵԣٱơ

(XYS20080803)

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֪ʶǻۺ͵ӵļֵ



֪ʶըϢʱں嫵֪ʶﲶõϢ
ϢˣҪϢûϢٵ⡣֪ʶ
ǻȻϵ֪ͬʶǻ۵Ļʯǻֻ֪ʶһ̶
֪֡ʶʵлõʶ;ܺͣǻǱжϡ
֪ʶʱԣȶǻ۾ǰհԣ֪ʶ
ԵġеġԵģ֪ʶȴԵģ֪ӵ
֪ʶ츣ࡣ֪֪ӵ֪ʶĻ֪ʶ۵
һ̶ȣлĽתΪܱ
ת֪ʶ֪ʶԶܴ¡ֻ֪ʶãȱ
ֻϢ⣻Ӽ⣬ǻ۵㡣õĵӻʹéٿ
¡ڿѧʷҵճеӲʤö١ٹѯ
˾ӹ˾Ϊλ˳ı߻Ļ

ڿѧоУогֵġ쳣󣬱ȥ˼ֱ
ʾյסµķͲڡ쳣֮Сûʹ㵽
˿ѧõſڣδýȥĿõĻԻ͡һµķֻ
˵вٿѧ˴ǰʾֻһ֮ң
ȴƤˣԭǣ۲Ԥϵ󡣿
жķ־100꣬ĵоɷʱѿг
̼͵ĲΪʶʧ˷ֶĻᡣ
100Ժظĵʵ飬Կĵνʽ˷룬Ӷ
˿еĶ壻ڷX-ǰѧҶַ߹ܸ
Ƭͼģ壬ȴûϸ˼ԭΪ
Ƭ⣬ӽֽ¨ټЩƬоֵƬй
X-£ŵ

ֵǧӺܶࡣڿеøǲԶһƪè
۵Զ£˹ٴѧѧҴά˹
è״ԶʹΧƳ̫תƵǳ
Ϊܡ˹һϵѧרңרҺƹʦ
˼ɸУѧʦ˶ʵһ룬
쵼оСʵʩһ롣ӿܻʹԭΪҪ
25ͻʮԪ۲⵽̫Χ̫ϵתƵ
Ǽƻ޺ͼ˾ѡ

ҵϵĵӣʹ˾߳1952ǰĵȶǺɫģձ
֥˾ܶࡣ˾³ʯ˭ܹù˾߳
·Ͱѹ˾10%ĹɷݸʱһְԱѵȵĺɫΪɫ
˾飬ڶƳһϵвɫȣ·áӴһ
Ĺȥֻкɫȵʷ

Թ룬Ժþڡ·Ժ2000
811¡ʿֹ˾⳥ȫר˶Ӫ˾2.4Ԫ
гʷ뽨ʦ³ӪһС˾2080ĩ
С˾ʿṫ˾˽˶԰Ĺ룬ʿ1989ܾ
ļƻǣ4 ȴ1Ԫڷ˽˶԰1997
ɿšǣС˾·Ժϵʿᣬָصʿթ͵
ҵܡṩʵ˵ʡΥĬԼΥܹϵҪ14Ԫ
ѡԭʦƣ޽˶԰88ͬС˾ƻ
ݷԺ6 ͬթָأʿС˾
⳥2.4޵Ĳþðͥճԭʦ˵þ
ȫС˾Ҳܹ塣ģ㲻
˵Ĺ룬ʿᶼˡ

Ҫ֪һ¡ǷǡСĴ
ߣ츣֪ࣻвһΨͼĶͻᡣ
ͬʱäĿݡһҶĿ̩ɽӹȨǵʱҪʢٺ
˹缶μҡ˹̹ͻĿѧʦԼŵͰ
ļ޽ͬʱӦϣպīĶħ޴֪
¹ɴĸġĺĿѧҡҪΪ
Ĳ³ŵʽӢۣҪԭ¶ڽ̷̵ͥ٤ʽѧ
ȻӦѧɡѧɣٻţټǿѧ
ǰͻʯǿѧٵֺͱ־

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¹̩ҩȻƷרͬ

ʦã
 
 
   ҽϿһԳ"¹̩ҩ"Ĺ˾Ȼڰٶƹ
ǵĲƷ"ŵά̩"ܰȡ쳣 

  ǵҳhttp://www.txlzlw.cn/index1.asp   ðٶ"ͬ"ؼ
ʣǵҳͷһС
 
   ֪йͬ2001꿪ʼѾڼ룬
˾ȻǵĲƷרͬƭ֮⣬Ȼͬ
ȺǵҳϻűѧҩϢоĺйԤ
԰ƹĵı
 
   ǳϣʦܳʱע
 
   ݰǿ

ӰվݿҽƭȨۼҩ

(XYS20080803)

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صİ

ߣС

һ

Ѿȫͣʮˡ

ʵϣµ׿ʼûа취ˡ

ԭѾ˲ˡй͸ٹ·ĽͨѾ
ǳҪĸ͵ҺԭϣһҲ˲ԭϿǰ
ʮңѾϴˡʱһһԭϣ
˾쵼ʮż

ȻļСȥӦӦ

УһˣСγҲ飬飬
һûա

һҡͷ˵ˡ˺ܾãص̾һưˣͣ
£ͻöˡ˾ˣ۾ˡ

ԭϽƷҲ˲ȥˡٹԶĿͻǰһ
··乫˾ߡ·Ѿշ״·˹˾90%϶
ȷżˣҹֵĻ˳Ѿ塣ʵѾ޷ⷢ
ˡ

ʮչ˾ʽż٣ǲɢ44ˣ칫4ˣż١ż
ڼ޹ʣԱн

·ݹ˾Ӫҵ361Ԫ·Ϊ17Ԫ



ǰ죬ʵеģͬСǮһ𵽳ȥ޴

˾ڱ⣬߲˶ԶǳƬũ¡Ϊ
棬͸ũҲˡũϰҪϡҳԾǣ
ˣﻹĹϡ

ϹĹߡժõ϶ѻɽ

СڡСǮԹϳԹϡ

ϹǮһ

ûء̵ģûгѽҶˡ
ˣӺˡ80Ķϣȫõˡ3Ԫ࣬ȫ
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캢ϻƴǱһһǮһߵᡣ
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ϹӲһʮ߰˽ĴϣմĴĨһ֪
ǺˮỹǱ顣



죬źӻĸҡ

ѣ㡣

ɣͶԵ㡣һء״Ҳûйѽ

裬ǰһǮ𣿡

˼е˵ˣܻǡĲ3ǮһСѣ
תȦûһһʮǮ

裬ǵݽ𻹹Ұֻóҩ

Тһ𣿲ԡܹǧǮֳҩԼ
СһǧǰͰҲܹưһ㣬ˡ

裬û£ʱġ˲Ǹ㲹㡣
̫̫2000ǮʱѾõġ

ҾͲˡ˰ɣܲ

(XYS20080803)

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"˻ᣬܲӰǵ"и

ߣиҪ

2008˻᱾һйü£Ҳȫ绪˶
ԺĴ֮¡Ϊ˰˻ĳɹһЩǿ涨Ϊ
˻İȫҲ⡣һ£ǲ
ưڱĳݽһǵó֤ʱݵĹ
Աȴ˵Ҳڴ˽ޡԭ˵й涨л
͹Ļպ̿˲ڴ˽ޡǿ˵ʲôֻл񹲺
ĵ֤ĻղСģ˵й˻һ
ϵ꣬ΪԼһйˣûм
ңҵʱĺԼǸ˸öѽʵǣ
˽ޱͰ˻кι

ֻ˵ĳЩƶĳЩ涨ʱܲԶӣ
Ĺ涨˼ҿйѽ

(XYS20080803)

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뱴Ǹ

ߣ¿ķ굶

joysongXYS20080731У򳵸⣬һ
ˣǰУ԰ͬѧһ۹ˡΪ˰
Լķд˷MatlabͼˣҪ
ͬѧеĴ󣬵ʱֵĺܡҾͰǰĲַݴ
ǲοƪıʽƣͼʡˡ

herculesXYS20080802жӵɵġӾȵ˼
ѧ澰еı飬źûˡ
ͬر㲻ĵһǲ
߷ձǺ㲢ûµѡᣬĹؼͬ
˵ķǳѾ1/3Ӯĸѡĳǣһտǣ
1/3ĸʲûиı䡣

ٸ˵Ӱɣ100000ŲƱ1ţͷĸΪ
1/100000ߵȻ֪н˭ҳ֮ΪΪƭ
Ƕͷģֱ99999ûͷĲ˵֮⣬
99998˶ûͷͷĸѾ1/21/100000ϲ
!ʣĻ

Ǹѧʽ⣬ΪʽЧУΪʽ
˼֣㲻Է˼룬Ƕ㷨Ҳһ⡣


ԭ⣺

ڽһϷĿָŹѡһźһγ
źֱһͷɽĿĵȻҪõȽֵǮĽγ
ȴܿźʵһѡѡһ
ź֪źʲôˣһŸ㿴ң
Ȼһͷɽ˸㣬㻹һѡĻᡣô
㿼һ£Ǽֵһεѡ񲻱䣬Ǹıһεѡ񣬸пܵ
γ 

㳡־ǳĿ󣬾ȫѧľٹۣѧ
ĽҲ˽νʢǰݡŦԼʱҲ
鱨ֵİ칫ںͲ˹ɻʻԱӪۣʡ
ѧԺѧǺī˹Ī˹ʵҵļԱǽй 
ڣشһ⡣


1ʷ

źΪ򣬵1ѡţΪĸʾ
Ϊ1/3˿ɷΪȸŵ3

1ѡ  ˿        3ź      

1   1/3ʣ          ó
2 1/3ʣ           ó 
3 1/3ʣ           ó 

ϵɿֻе1ѡˣҲǲܵó
Ϊ1/31ѡˣѡʱ2/3ĸʣʱ˽һ
ֻ3һǳ˵һµóĸ2/3Ҫȥѡ
1ѡһҪѡɣ

2϶Ϊ1/2Ĵԭ

Щ϶óĸ1/2Ǵģԭ£

1ѡ֮ǰ˾ͽĳŴ򿪣򻻵óĸʵȷ
1/2ǣڵ1ָһţź1/3Ŀǳ2/3Ŀ
ֻܱ1/3Ŀܴ2ѡ1򿪣2/3Ŀ
ûѡؽʣµŴ򿪡

Ǹ͵⡣

3n1

Ϊ˸˵Ⲣõһͨʽԭġ21չɡn
1䡣£

3.1 ó1δn1ѡ򣬴Ϊn/(n+1)
£óĸΪ(n/(n+1))*(1/(n-1))...(ʽ1)

3.2 ַΪ

3.2.1 һ1ѡ2λȻ򣬴˸Ϊ1/(n+1)

3.2.2 1ѡ򣬴Ϊn/(n+1)ڴ£
ĸΪ(n/(n+1))*((n-2)/(n-1))

3.3.3 ϲĸΪ1/(n+1)+ 
(n/(n+1))*((n-2)/(n-1))(ʽ2)

3.3  ó뻻ĸ(n/(n+1))*(1/(n-1))+ 1/(n+1)+ 
(n/(n+1))*((n-2)/(n-1))Ϊ1˵û©

3.4 صԭ⣬n=2뵽ʽ1УûóĸΪ2/3n=2
ʽ2УûĸΪ1/3

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԰֡ѰֵĵǸͶ԰ֵĴ𸴣ԼһڸʵĹ

С

Ǽǰдƪδ˿ҵ
⡣·һΡ¼Եʹ뵽һ֮йص
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ǰЩ˿Ͼͽ۶λ˿̱ԡ¿ķ
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᳤ʱ䷴ĥԼǰ˿дĶһλͬ¾
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ʱ̱ʾĲԼǳܱ˲֪
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֣˾ʹϡд¿ķ굶ѰϵǸһΪԼİ
λ½⡣

ڶƪ԰¿ķ굶йظĻظ

ոշǸţͿ¿ķ굶ѵġСšۡѰйظ
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Ҳ

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Сʱʡ

óֵĴһΣ

ģСָΪһȷ㷨ǣĳһСʱĽʣ
нĸʡСʱʡ㷨Ǵģֻ
սΪ1ʱܳнĸʡСʱʣõ
սСʱϸʣСʱʡñʽʾΪP(
)P(Сʱ|ս)=P(ս.Сʱ)

ҵĻشǣսСʱĸʾСʱʡȻСʱ
꣬սǶġСʱ첻߼

ǰдĶգ83գ˰ֵĴδ𸴣
ʾϣΪֹԸҲͬС½һCollins
£ĻһաдʷĿ£ǿԲο
David Freedman<Statistics>뱾κ룬йͳ
Ƴ,1997ꡣ

1964618ɼһٰһӺһŮӱ١
쵱ָĿߵṩϢΪÿһһᣬɫ
1/10ӵĺ1/10˲ͬ1/1000ȵȡ
ˣõһǧ֮һռ쵱ֵ˵һκ
һ˾бĻ᣻ûһԾЩ潫
ġݴʱ߷ԺƷһþ֮
һǲֶ֧Լݡ෴ЩȻǲġ
ӵĺӡ͡˲ͬ塱Ǵġ

һлԵķǣʳ˷ͬһظ
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