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һ ¼ 
   Ҫ 

1顢ռ¼ 
 1飺صΪ飬ΪE. 
1 ͬظУ 
2 ÿĽжֿԣ֮ǰȷ֪пܽ 
3 ÿǰȷһ. 
2ռ䣺EпܽɵļϳΪEռ䣬ΪÿһܽеԪأΪ㣬Ϊe. 
3¼һпܳҲֵܲ¼Ϊ¼¼ABCȴдĸʾɱΪռĳϣΪ¼ͼ¼бȻ¼Ϊ Ͳ¼Ϊ . 
2¼Ĺϵ 
1ϵȣ¼AصBΪ    . 
2¼¼ABһΪ . 
3¼ ¼ABͬʱΪ  . 
4¼¼(¼)¼ABΪABΪABĲ¼ Ϊ Ķ¼֪ . 
5ԣ  Ϊ¼  . 
6¼㷨1) ɣ   
2) ɣ   
3) ɣ   
4) ż(De Morgan)ɣ  ƹ . 
3Ƶ 
1ƵʵĶ壺¼  ظг Σֵ Ϊ¼  ظгֵƵʣΪ  . 
2ͳƸʣ ʱƵ . ܴʱ Ϊ¼ ͳƸ. 
3ŵʣĻ¼Ϊ޸ÿ¼ĿȣӦŵͣȿܸͣ¼ ĸΪ . 
4θʣ¼ޣĳgĸgĲ(ȡ)ȣλü״޹أӦθͣ ȡһgСһ¼ ĸΪ . 
5ʵĹ壺( )Ϊɲռ䣬¼ ϶һʵֵ 㣺1) Ǹԣ  2) 淶ԣ 3) пɼԣһ ʹ  Ϊ  ϵĸʲȣơʡ 
4ʵĻ 
1¼㣺 0. 
2޿ɼԣ nݵ¼       . 
3ԣ¼B AP(B) P(A) 
P(BA)P(B)P(A).4ԣP( )1P(A)P(A) 1.5ӷʽ¼   ʿƹ㵽n¼ . 
6ɷԣ¼  . 
5˷ʽ 
1ʣ  е¼  Ϊ¼A¼Bʣ 
2˷ʽ  Ϊ¼ABĸʳ˷ʽ. 
6ȫʹʽ뱴Ҷ˹(Bayes)ʽ 
1ȫʹʽ  һ֣  κ¼  Ϊȫʹʽ. 
2Ҷ˹(Bayes)ʽ  һ֣ κ¼  ΪҶ˹ʽʹʽ. 
7¼Ķ  
1¼Ķ Ϊһʿռ䣬¼   ¼AB໥ȼڣ .  
2¼Ķ n¼  еʽ n¼ ໥ 
8Ŭ(Bernoulli) 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
3 ظͳ.γֲ  
 1ֻܽΪŬ飬Ϊ  Ҳɹʧܡ,ɹĸʳ ʾ ɹ. 
2 ظؽnΣõΪnرŬ飬Ϊ  
3 ظؽпжΣõΪرŬ飬Ϊ ֱŬͳΪŬͣ 
4 гɹ εĸǣ  . 

    
1Ȼ¼벻¼ 
 Ȼ¼һ±Ȼ¼¼ָһ±Ȼ¼.ǶԣȷԵ󣬵Ϊоķ㣬ǿ¼. 
2¼뻥¼ 
¼  һ¼һ¼  Ϊ¼¼  ͬʱ  Ϊ¼.ض⣬δػ.ߵĹؼǣռֻ¼ʱ¼ſܻ棬¼.Ϊ¼һ߿Զ¼طһֻһ. 
3¼¼ 
¼    һ¼ķһ¼ķ޹أʱ ¼⣬һ¼ķȻһ¼¼ķӰģ 
ʱ .ͼһֱ 
.ͼ1.1ߵУ 
 ͼ1.1 
 ʾռ¼ĶϵұߵУ ʾռ¼Ļϵ. 
4 ¼  
 ռ ڣ¼ ĸʣ   ռ м¼ ĸ.Ȼ  ǲͬģһ˵  ͬʱʱ аϵȷӹϵʱ .91Żسÿȡһȡ2Σ󣺣1ڶβȡĸʣ2һȡǰ£ڶȡĸ.⣨1ľһ¼ʵ⣬⣨2ľһʵ. 
5ȫʹʽ뱴Ҷ˹(Bayes)ʽ 
¼Ϊĳֽýֲܼ򵥵ؿ¼֮ʱɿȫʹʽڶռлʱһҪע.Ҷ˹ʽ֪׷Ǻԭĸ. 

    
1дռ估¼㣺 
1һӣ. 
2ͶһöӲΣ 
1һγ棻2γͬһ棻3һγ. 
31234ĸпظسȡһһ. 
4a,bֻطŵ3ȥһһ. 
ɶռϵĸռ㣺ռָȫԪأ¼ǰȫеӼ. 
:(1) һӣֿܽá1ʾ1㡱㣬.ռΪ ={123456}¼Ϊ{135}. 
2ͶһöӲΣֿܣãʾһγ棬ڶγַ桱һ㣬.ռΪ ={,,,,,,,} ֱʾ¼123¼ ={,,,}¼ ={,,}¼ ={,,,,,}. 
31234ĸпظسȡ ֿ 
ܣ ʾһȡ ڶȡ һ㣬ռΪ ={ } һһ¼Ϊ{1,2,2,1,2,4,4,2}. 
(4)ӷֱΪסҡa,bֻطŵ3ȥоֽ.ãסңʾa׺УbҺСһ㣬.ռΪ ={ףףףңףңңңףңףң}һһ¼Ϊ{ףףףңףңףף}. 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
4 ظͳ.γֲ  
 
2 Ϊ¼ ϵʾи¼ 
1  2    
3¼4һ¼ 
5¼ 6¼ 
7ǡ¼ 8ǡһ¼. 
¼ϵ¼. 
⣺1 2 3  4  5   
6   
7 8 . 

3 ͬط У¼ĸʣ 
1ĳָ иһ 
2 иһ 
3ָĳǡ . 
ǹŵʵһ⣬ŵʵļⶼɹΪһ.ÿ ַŷ  ֲͬķŷ.ĳָ иһ൱  еȫУ루1ȣ2൱ ѡ ӣٷ򣻣3൱ȴ ȡ ĳָĺУٰʣµ  . 
⣺ռΪ . 
1¼ ʣ  
2 ѡ  ѡ¼ĸΪ  
3 ȡ  ѡʣµ еÿһ ַŷ¼ĸΪ . 

4 Χɵһ㣬ڸκĸȣԭ͸õ ļнС ĸ. 
һθ⣬ͨɽϵĶȡݻȣع涨. 
⣺ ʾε ʾ 
ͼ1.2Ӱ ĸΪ 
 . 

5¼  ݣ ¼ĸʣ . 
ʵʽм. 
⣺  ݣ   
   ݣʱ Ӷ  Ӷ . 

6ĳסլ¥ӣ֪һŮһкĸʣһСΪлΪŮǵȿܵģ. 
֪һŮһкĸʣ.ݹʽ  . 
⣺ ={һŮ} ={һк} ={ȫк} ={ȫŮ} 
 ¼ ΪһŮһкΪ   = 
 Ӷ֪һΪŮ£һкĸΪ . 

7ĳ豸쳧õľԪ쳧ṩ.ļ¼µ(1-1). 

1-1 
Ԫ쳧 Ʒ ṩܵķݶ 
1 0.02 0.15 
2 0.01 0.80 
3 0.03 0.05 
ҹĲƷڲֿоȻϵģı־.1ڲֿȡһֻܣǴƷĸ.2ڲֿȡһֻܣ֪ȡǴƷΪ˴ƷԺγ˴ƷҹĸʷֱǶ.Щ. 
¼ȡһֻǴƷɷֽΪ¼ĺֻͣƷһṩġֻƷǶṩġֻƷṩġ¼ݣȫʹʽм.һأֱӼĳһ¼ ĸ Ƚѣ Ƚ׼㣬 ʱɿȫʹʽ .2ΪʣñҶ˹ʽм. 
⣺ ʾȡһֻƷ ʾȡĲƷɵ ҹṩġ.֪ ռ һ֣ = 
 . 
1ȫʹʽ . 
2ɱҶ˹ʽ .ϽֻƷԵڶҹĿ. 

8һտ ̨֪1Сʱ̨ԲҪտĸΪ .1Сʱ̨һ̨Ҫտĸ. 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
5 ظͳ.γֲ  
 ÿ̨ǷҪտ໥ģɸ¼Ķʼӷʽм. 
⣺̨Ҫտ¼໥ģ̨һ̨Ҫտ¼ дɣ ɼӷʽʵã  
 =0.902. 

9ĳ10̨ͬ͵豸ÿ̨豸ĵ綯Ϊ10ǧ.֪ÿ̨豸ÿСʱʵʿ12ӣǵʹ໥.ĳԭ칩粿ֻܸṩ50ǧߵĵ.ʸ10̨豸ĸǶ٣ 
֪Ҫĸʾ󡰸ͬʱ豸5̨һ¼ĸ.Ϊÿ̨豸ʹ໥ģĳһʱ̣豸ֻп벻ԱΪ10رŬ飬öʹʽ. 
⣺ ʾ¼豸 ʾͬʱ豸ɶʹʽã ͬʱ5̨ĸʣ  
ʸ10̨豸ĸΪ0.994. 





  

ڶ ֲ 
   Ҫ 

1 
 ռ䣬ÿһܽ Ψһʵ ֮Ӧ Ϊ ϵΪ .ͨôдĸ ȱʾ. 
2ֲ 
 Ϊ Ϊʵ Ϊ ķֲ. 
ֲȡֵͳƹԣʣ 
1  
2   
3 Ϊ  
4  
5 . 
3ɢʷֲ 
 ֻȡ޸иֵ Ϊɢ. һпֵΪ  ȡ ĸΪ  
 Ϊɢ ĸʺʷֲֲɣ.гɱʽҲΪֲ(2-1) 
2-1 
  
  

  
  

 . 
ɢķֲУ 
10-1ֲΪ ʺ  
2ֲΪ ʺ 
  
3ɷֲΪ ʺ 
  
ɶ  һ  һ̶ķǸ  . 
 ܴ Сʱֲòɷֲƴ棬 
  . 
4ηֲΪ ʺ 
  Ϊ . 
 ܴ Сʱ .] 
5ηֲΪ ʺ 
 . 
4ʷֲ 
 ķֲ ڷǸ ʹһʵ   Ϊ.  
Ϊ ĸܶȺ. 
ܶȺʣ 
1  2  
3  4  
5   . 
ķֲУ 
1ȷֲΪ ܶΪ 
 .ӦķֲΪ  
2ֲָΪ ܶΪ 
 .ӦķֲΪ  
3ֲ̬Ϊ ܶΪ 
 ӦķֲΪ  
 ʱ ʱ ӱ׼ֲ̬.ʱֱ  ʾ ܶȺͷֲ .ʣ . 
һֲ̬ ķֲ ׼ֲ̬ķֲ йϵ . 
5ķֲ 
1ɢķֲ 
 ΪɢֲΪ(2-2) 
2-2 
  
   

  
   

 ΪɢֲΪ(2-3) 


2-3 
  
   

  
   


 ֵͬʱҪϲΪһӦĸ. 
2ķֲ 
 ΪɢܶΪ  ĸַܶ. 
1  ȡֵ  ʱ ܶΪ 
 . 
  ķ. 
2ֲ ķֲ 
 Ȼ . 

    
1ͨ 
Ƕռ ϣÿһܽ Ψһʵ ֮Ӧ.Ӷ֪ͨȡֵǰһģȡֵͳƹԸģԣͨĶһ䣬Ķռ. 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
6 ظͳ.γֲ  
 2ֲ  
ֻһϰ.е鼮ֲ 鼮ֲ Ϊ. ڼ ʱ ĸǷ. ʶûʲô𣻶ɢ ʱ ֵͲͬʱҪע . 

    
1кǷǷֲ.Ƿֲжķֲ. 
1 2  
3  
ɸݷֲĶ弰ʽж. 
⣺1  ϵ.ͬʱ . ķֲ. ͼο֪ǽߣ ɢķֲ 
2  ϵ½ ķֲ.ֻҪ е Ϊ  㵥 ʱ ķֲ.  Ȼ ķֲ 
3  ϵ ķֲ.   ɵʲܶȺ ʹ .ͬʱ ͼҲǽߣ ȷҲɢķֲ. 

2װдСȵ10ŷֱΪ0129.ȡ1۲ǡС555.Զһֲɺͷֲ. 
ȡ1ĺ롱Ĳͬȡֵͬ.ݺǡС555ɶȡֵ.һķֲֲĶ壬ֲֲ. 
:ֱ ʾֽС555ʱռΪ  Ϊ  ȡÿֵĸΪ  
   ķֲΪ(2-4) 
 2-4 
  
 0 1 2  
  
  




 ʱ  
 ʱ  
 ʱ  
 ʱ  
ɴ÷ֲΪ . 

31СʱڽĳͼݵĶӲɷֲ.֪1Сʱ˽ͼݵĸΪ0.01.1Сʱ2߽ͼݵĸ. 
1Сʱڽͼݵһ  . ʾ1Сʱ˽ͼݣ ʾ1Сʱ2˽ͼ.ͨ һ . 
⣺ Ϊ1Сʱڽͼݵ ʱ ֪  .Ϊ . 

4 ܶȺΪ  
1 2 3 ķֲ. 
ܶȺ ó ܶȺ ϻ֣ ֲĶ ķֲ. 
⣺1 ã  2  
 3 ʱ ǲ¼  ʱ  
 ʱ ԣ ķֲΪ . 

5˿ĳдڵȴʱ ԷּƣֲָܶΪ ĳ˿ڴڵȴ10ӣ뿪.һҪ5Σ ʾһδȵ뿪ڵĴд ķֲɣ . 
Ȼ ΪȡֵΪ012345 . ֲɵĶ壬 ķֲɣ . 
⣺ ȡֵΪ012345 .ã 
  ķֲΪ 

 (2-5): 

2-5 
  
0 1 2 3  5 
  
   

ԣ . 
6ĳλƸ2500ˣԳɼӸ߷ֵͷ¼ã10000˱豨ߵĳɼ ֪90359ˣ601151ˣʱ¼ͷΪ٣ 
֪ɼ ֪ ֵԣĹؼ ٽһֲ̬׼. 
⣺⣺   
 ׼ֲ̬ã 1 
ͬ  
 ͨ׼ֲ̬ã 2 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
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7 ظͳ.γֲ  
 ɣ12ʽã   
֪¼Ϊ 豻¼ͷΪ  
  
 ׼ֲ̬ã ã  
ʣ¼ͷΪ79. 

7 ķֲΪ(2-6): 
2-6 
  
1 2 3 4 5 6 
  
  

 ķֲ. 
 ɢ Ҳɢ. ȡֵͬʱ ЩȡȵֱֵϲӦĸ.Ӷõ ķֲ. 
⣺  ĶӦϵ±2-7 
2-7 
  
1 2 3 4 5 6 
  
0 -1 0 1 0 -1 
  
  

ϱ֪ ȡֵֻ-101ֿܣ 
  
  
 ԣ ķֲΪ(2-8) 

 2-8 
  
-1 0 1 
  
  


8 ֲ̬  ĸܶ. 
 ں  ϵӣҿɵʿɰʽ ĸܶ. 
 ⣺ ֪  ȡֵΪ . ʱ  ʱз Ӷ ɴ˵ ĸܶΪ . 

9֪  ĸܶ. 
 ݷֲĶ壬 ķֲȻ󵼣ɵõ ĸܶ. 
⣺  ǲ¼  
   
  Ӷ ĸܶΪ . 

  

 άֲ 
   Ҫ 

1άϷֲ 
  Ϊǵ飨 Ϊά. 
裨 Ϊάʵ  ƶԪ 
 Ϊ Ϸֲ. 
Ϸֲ»ʣ 
1 Ǳ  ķǼ 
2  
  
3   Ҳ 
4   
 . 
ʽʾ  ڵĸΪ . 
2άɢϷֲ 
ά пȡֵ޶Իжԣ Ϊάɢ. 
 Ϊάɢ,пȡֵΪ  3.1Ϊ Ϸֲ. 
3.1 
  
  
   

  
  
  
    
   
       
   
      
Ϸֲɾʣ1 2 . 
3άܶȺ 
һǸ ,ʹöά ķֲ ʵ   Ƕά Ϊ ܶȺܶȺ. 
ܶȺʣ 
1һʵ   
2  
3ƽ ϣ ȡֵĸ 
  
4   . 
4άıԵֲ 
 Ϊά 
  ֱΪ  ͹ ıԵֲ. 
  Ϊɢ ֱΪ  ͹ ıԵֲ. 
 Ϊ 
 ֱΪ  ͹ ıԵܶȺ. 
5άֲ 
1ɢֲ 
 ΪάɢϷֲɺͱԵֲɷֱΪ 
  ̶ ʱ 
 Ϊ  ֲ.ͬ  
2ֲ 
 ΪάܶȺͱԵܶȺֱΪ . ʱ  㴦  £ ܶȺΪ . 
ͬ . 
6Ķ 
  ֱ ϷֲԵֲ.κʵ    ໥. 
 Ϊάɢ  ໥ĳҪ . 
 Ϊά  ໥ĳҪǶκʵ  . 
7ķֲ 
ά ϸܶȺΪ   ĺ ķֲΪ . 
1 ķֲ 
 ΪɢϷֲΪ  ĸʺΪ 
  . 
 ΪܶȺΪ  ĸʺΪ 
 . 
 2 ķֲ 
 ΪܶȺΪ  ĸʺΪ 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
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8 ظͳ.γֲ  
  . 

    
1¼ ʾ¼  Ļ¼Ϊʲô һ  
ͬ¼ ໥ʱ һ 
 ˷ԭ .ֻ¼  ໥ʱ 
 Ϊ . 
2ά ϷֲԵֲֲ֮ʲôĹϵ 
ɱԵֲֲĶ빫ʽ֪ϷֲΨһȷԵֲҲΨһȷֲ.֮ԵֲֲΨһȷϷֲ. ֪һֲӦıԵֲΨһȷϷֲ. 
ǣ ໥  .˵ ʱԵֲҲΨһȷϷֲӶֲҲΨһȷϷֲ. 
3໥ĸ¼໥ǷͬΪʲô 
 ໥ָɶά  һȡֵһȡֵӰ죬 .¼Ķԣָһ¼ķһ¼Ӱ죬 .߿˵һ. 
ǣɶά  ͬһ ռϵһά Ҳһ ռ¼.ˣѡ  ¼ôߵһ£ӶԵĶ弸ͬ. 

    
1һ2Ʒ3ƷзŻصĳȡ޷Żصĳȡ. ΪһγȡôƷ ΪڶγȡȡôƷ.Էֱֳȡ£1 Ϸֲɣ 
 2ά ıԵֲɣ 
 3  Ƿ໥. 
ά ıԵֲ, .ɶά ıԵֲɵĶ壬 Ϸֲɱиеĸӣù ıԵֲɣϷֲɱиеĸӣù ıԵֲ.  Ƿ໥ɶάɢ  ໥ĳҪ֤. 
⣺ 0-1ֱֲ 
  
1зŻسʱϷֲΪ 
  
 гɱ3-1ʾ. 
ڲŻسʱϷֲΪ 
  
 гɱ3-2ʾ. 




3-1 3-2 
  
  
0 1     
  
0 1 
 0 
 1 9/25 6/25 
6/25 4/25 0 
1 3/10 3/10 
3/10 1/10 
2зŻسʱԱ3-1Сӣù  ıԵֲΪ3-33-4.ڲŻسʱԱ3-2Сӣù  ıԵֲΪ3-53-6. 
 3-3 3-4 
  
0 1   
0 1 
  
3/5 2/5   
3/5 2/5 
 3-5 3-6 
  
0 1   
0 1 
  
3/5 2/5   
3/5 2/5 
 3зŻسʱΪ   ໥ڲŻسʱΪ   ໥. 

2 ܶȺΪ  
1 2 3  Ƿ໥. 
ܶȺ  ȷ ɱԵܶȺĶ壺 ֵ .  Ƿ໥⣬öά  ໥ĳҪ֤. 
: 1Ϊ   
2Ϊ  
 ʱ  Ϊʱ  ͬ  
3  
 ˣ  ໥. 

3ά ܶȺΪ 
  ķֲ . 
ܶȺĶԿֲ  ڵйأɷֱ. 
⣺ ʱ   
  ʱ  
  
  
  ʱ 
  
  ʱ 
  
  ʱ 
  
  

4 ܶȺΪ   ֲܶ. 
ͨ ܶȺͱԵܶȺ  ֲܶ. 
⣺ ʱ  
  

5 ܶȺΪ  . 
ñԵܶȺٸʵĶ. 
⣺Ϊ 
  
  
  
 . 

6  ໥  ĸܶȺ . 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
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9 ظͳ.γֲ  
 ɰֲĶ ٽһøܶȺ ڼ۴λʱҪָ. 
 ⣺ ֽ ʱŲΪ0  ȡֵ㣨ͼ3-1. 
 ʱ  
 ʱ  
 ʱ 
  
  
ͼ 3-1  ʱ  
  




  

  
   Ҫ 

1ѧ 
ɢ ķֲΪ  ƼĺΪ ѧ. 
 ܶȺΪ  ƴ˻ֵ Ϊ ѧ. 
ѧʣ 
1 ǳ  
2 ǳ  
3   
   
  
4 ໥  
 ໥  
 . 
2ѧ 
ɢ ķֲΪ  ĺ ѧΪ ʽм. 
 ܶȺΪ  ĺ ѧΪ ʽл־. 
3ķ 
 һ Ϊ ķ. Ϊ ı׼. 
㷽Ҳùʽ . 
ʣ 
1 ǳ  
2 ǳ  
3 ໥  
 ໥  
  
4 ĳҪǣڳ ʹ . 
4ֲֳѧ뷽 
1  
2  
3  
4  
5  
6  
7  
8 . 
5 
  Ϊ  ԭ. 
 ڣ Ϊ  ľ. 
 Ƕά Ϊ  ׻ԭأ Ϊ  ׻ľ. 
5ά 
(1) ѧ  
 ɢ  . 
  
  .ֶǾ. 
 2 ķ  
 ɢ  . 
   .ֶǾ. 
6Эϵ 
 ЭΪ .1+1׻ľأм㹫ʽ . 
 ϵΪ . 
ϵʣ 
1  
2 ڳ ʹ =1  Ը1أ 
3   .֮һ. 

    
1ڸʲô壿 
֪һķֲͳƹ.һķֲǲ׵ģҲûҪ.ȽϼҲоҪڸкܶӦãͬʱҲ̻ĳЩҪʵ. 
磬ѧӳȡֵƽֵΪеƽȡƽʱ䡢ƽɼɱȣӳȡֵĲ̶ȣƫ̬ϵ̬ϵӳȡֵĶԳԺͼ.ˣڲͬϿ첻ͬԼ򵥶ʵؽٵʵ. 
2ѧΪʲôҪ͹־ 
ȣѧһֵΣѧӳȡֵƽֵ.ˣԼ͹˵ֵ֤ĴڣҶԼ˵Ĵ޹أӶֵ.ɢӶͬ.Ҫ͹־Ϊ˱֤ѧĴ. 
3ϵ ӳ  ֮ʲôϵ 
ϵ   Эͱ׼ģӳ  ֮س̶. ʱ  1أ ʱ  أ ʱַΪǿ. 
4  ໥ͲһʲôĹϵ 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
10 ظͳ.γֲ  
 1  ໥  .Ϊ    Ӷ 
   . 
2  أ  һ.磺 
 Ϊ   
 ֪  .  
 , ,֪  . 
3  أ  һ.ɷ֤˵. 
4  أ  һ.Ϊ   
  ʱ Ӷ  . 
 ǣҲ Ӷάֲ̬ʱ    ǵȼ۵. 

    
1 ķֲΪ   . 
ֱӰɢͷĶм. 
: ͬ  
 . 

2 ĸܶȺΪ  
1 2 3 . 
ѧĶ弰Эϵļ㹫ʽ ıԵܶȺ ȻڷֱѧЭϵ. 
⣺1  
  
  
2  
   
3  
  
 . 

3¼ ڵ гֵĸΪ  ʾ ζ ֵĴ  . 
ķֲʽ. 
⣺ ǣ . 
   
   
ڸ ໥ .ʽ  

4   ໥ 
  ϵ. Ϊĳ. 
ַ1ĸʷֲʽ2ֱĹʽ㣻3йض. 
 ⣺  
  
  
 . 

5 ໥  
 . .֤ 
1 2 . 
ĳЩʼһļɽ֤ 
֤1  
  
2  
 . 
  

 ɺļ޶ 
   Ҫ 

1бѩ򲻵ʽ 
 ѧ   вʽ  . 
2 
1бѩ: ໥Уѧ ͷ ڣ   
 . 
2Ŭ:  ظ¼ Ĵ ¼ һзĸʣ  . 
Ŭ˵ ܴʱ Ƶ  ĸʣ֤Ƶʵȶ. 
3ļ޶ 
1ֲͬļ޶: ǶֲͬУ޵ѧͷ  .ʵ  ķֲ  . 
2ŵ: ǲֲͬ໥Ƿֱѧͷ , . , ʹõ ʱ ,  ķֲ   
 . 
 ܴʱ, . 
3Ī˹: ӲΪ Ķֲ  . 

    
1ʲô 
1.  ˵θ  ܴʱ¼ ĸʽӽ1.ΪǸʣԲųС¼ .ǲȷйһ˵. 
2ڸк壿 
ɸܴʱƵʺƽֵȶ.Ͽ϶ƽֵֵƵʴʵĺԣ֤˸һЩĺԣΪͳƶṩ.˵ǸҪĻ. 
3ļ޶кʵ壿 
ֲ̬ǵļ޷ֲֲ̬.ļ޶ʲô£ԭֲ̬һЩܺͷֲطֲ̬.Ϊֲ̬ṩ. 
4ļ޶кͬ 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
11 ظͳ.γֲ  
  ͬ㣺ͨо⣬оУĶǸеĻ⣬ڸҪ.ͬ㣺о ʱʻƽֵļޣļ޶оܺ͵ķֲļ. 

    
1ÿĳ¼ ĸΪ0.8бѩ򲻵ʽƣ Ҫ󣬲ʹ ظ¼ Ƶ0.790.81֮ĸΪ0.95 
бѩ򲻵ʽйƣסʽ. 
:  ʾ ظ¼ ֵĴ  ֵƵΪ  
  
  
  .ɼ 
32000ظпʹ¼ Ƶ0.790.81֮ĸΪ0.95. 

2֤·  
 θ  . 
֤ бѩ򲻵ʽ  
 ʱ,  
Сڵ1·. 

3һ鹲100ӡˢ.ŰʱÿűŴĸΪ0.0001УʱÿŰ󱻸ĸΪ0.9УԺ󲻶15ĸ. 
⹹һֲͬУ޵ѧͷȻһ׼Ӧļ޶ý. 
⣺  ǶֲͬУ .  ΪУԺ.ļ޶¡ 
  
 . 
  

 ͳƵĻ 
   Ҫ 

1 
ͳУоȫΪ壻ÿԪسΪ. 
гȡһָ壬ΪһиĸΪ. 
ӷֲΪ  سȡ໥ ͬķֲ Ϊ õΪ .һξĳȡ¼  һ۲ֵҲʾЩ. 
2ͳ 
  һ򲻺δ֪ Ϊͳ.ͳҲһͳ 
1ֵ  
2  
3׼  
4 ԭ  
5 ľ . 
2ֲ 
  һ۲ֵǰС˳Ϊ 
 Ϊ˳ͳ. 
 Ϊֲֲ. 
3һЩͳķֲ 
1 ֲ 
   һͳ ɶΪ  ֲ . 
2 ֲ 
   ໥ ɶΪ  ֲ . ֲֳΪѧֲ. 
3 ֲ 
   ໥ ɶΪ  ֲ . 
4̬ͳķֲ 
   һ 
1ֵ ֲ̬ 
   
2  
3ͳ . 
   һ  һ໥. 
1ͳ  
2 ʱͳ  
  
3ͳ  
4ͳ . 

    
1ΪʲôҪͳΪʲôͳвܺδ֪ 
ͳĿΪ˽ֵΪһڽͳƶϺоʽϢʹ֮׽ʾʵ. 
ͳԺδ֪޷۲ֵδ֪Ĺֵʧȥͳδ֪. 
2ʲôɶȣ 
 νɶȣָͨκԼɱ䶯ıĸ.ͳУɶǶĶͣΪͳԵ.Ϊһ Ķ ָԳƾ ȣĴСӳ ɱ䶯ԼĶ.˵ɶȣǶ͵. 

    
1 1 ȫȣ2 
 .ʣ ǷΪ 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
12 ظͳ.γֲ  
 ໥ֲͬǼɴ˽֤. 
:1   ȫȣ ֲͬ Ǽ. 
2 ô ͬķֲ֪ Ƿ໥ һǼ. 
2  ȡļ Ϊֵ Ϊľأ Ϊͳ 
1 2 3 ʲôֲ 
֪ͳķֲз. 
⣺1   
   
2   
  
3 ã  ֲĶã . 

3ӲΪ ֲֲָܶΪ  
  . 
ֲָ֪ǵʽм. 
⣺  
  
  
 . 

4  ȡļ Ϊֵ. ȡʱУ 
1 2 . 
⣺1Ҫʹ  
 ȡ . 
 2ļ޶Ҫʹ  
  
 ȡ . 
  

  
   Ҫ 

1ĵƼ 
 һƲֵΪĵ. 
1 
 һ ۲ֵƲ ֵͳ Ϊ Ϊֵ. 
(2)عƷ 
ΪӦعķ.˼ǣ δ֪ǰ عӦǰ أȻδ֪صĺϵĹ. 
3ȻƷ 
 ܶȺΪ  Ϊδ֪ ȡ  Ϊһ۲ֵ ܶȺΪȻ ȡ  Ȼ ļֵ Ϊδ֪ ļȻ.˼ǣ֪ ʷֲʱ ι۲⣬õһѡȡ ֵ Ϊδ֪ ֵĹ. 
4ӱ׼ 
1ƫ. ڣ ֵ  ƫ.Ϊƫ. 
2Ч.  Ϊ ƫ ƹ  Ч. 
3һԣԣ. Ϊ Ĺ  йأΪ    Ϊ һ¹. 
2 
 ķֲ кδ֪   ʹڸ  䣨 Ϊ ŶΪ ˫. 
    Ϊ ŶΪ ĵ. 
1ֵ̬뷽䣨7-1 
7-1 
ƵĲ   
  ͳ ŶΪ  

  
 ֪   
  

 δ֪   
  

  
 δ֪ 
  
  

 ֪ 
  
  

2ֵ̬뷽ȵ䣨7-2 
7-2 
ƵĲ   ŶΪ  

  
 ֪ 
  

 δ֪ 
  

  
 δ֪ 
  

 ֪ 
  


    
1˵ΪʲôҪƣ 
ֵò һֵ˽ ĴСһĲοֵûиֵľȷ̶ȺͿų̶ȣʹ岻.ͨһͳ 䣨 ʹδ֪ ĸʲС趨ĳ . ֵԽ  ֵĸԽ󣬼ֵõ䣨 δ֪ Ŀų̶Խ󣬶 ĳԽСַӳ ľȷ̶Խ.Ʋṩ һƷΧ˹ƷΧľȷų̶ȣֲ˵ƵĲ㣬й㷺Ӧ. 
2Ŷ 壿 
Ŷ ַʽ. 
һ䣨 ԣ ʾ䣨 аδ֪ĸʲС趨ֵ . 
ƶԣ ʾ·õȫУ ֵ䲻 . 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
13 ظͳ.γֲ  
 3оɿ֮ìܣ 
  ĳȳΪȣ Ϊ Ŀɿ̶.Խ̣ȷ̶Խߣ Խ󣬿ɿ̶Խ.̶ʱ߲ܼ.ˣָԭǣչ˿ɿ̶ȣɿ ʱ߾.ֻܽ. 

    
1 ӼηֲֲΪ  Ϊδ֪ . Ϊ һ ľع뼫Ȼ. 
ݾع뼫ȻƷֱӽй. 
:1Ϊ  ľعΪ  
2ȻΪ  
 ȡ  
 󵼣  
ã ļȻΪ . 

2 ǲ ƫƣ ֤  ƫ. 
 ֤ƫԣֱӰ壺 ֤. 
֤  ⣩ 
 Եó  
ˣ  ƫ. 

3ĳĸ˿.俹ǿ  δ֪ȡ9˿ǿȣλkgΪ 
578582574568596572570584578 
巽  ŶΪ0.99. 
ڲ δ֪ȡͳ Ӷ  ŶΪ ֱΪ 
  . 
⣺   
  
Է ŶΪ0.99Ϊ 
 26.96440.48 
 ŶΪ0.99Ϊ 
 5.1920.99. 

4̬壬 .ֱ  ȡΪ   .̬巽 ŶΪ0.98. 
 δ֪ȡͳ  ŶΪ Ϊ . 
⣺ ã ԣ ŶΪ0.98Ϊ0.21524.5714.  

ڰ  
   Ҫ 

1Ļ 
1 
ķֲĳּ裬ȻṩϢݸ۵ԭԼܡǡܾжϣһͳƶͳΪ. 
ݵԭǣС¼һǲ÷. 
2 
ڸƶʱԣľ.ԭ Ϊʱܾ жϣΪһ󣻵ԭ ʱ жϣΪڶ. 
ƷһĸʲһС Ϊˮƽ. 
3Ļ 
1ԭ  
2ݼ󣬹ʵͳ 
3ڼ £ͳӵĸʷֲ 
4ѡˮƽ ȷٽֵ 
5ֵͳĹ۲ֵɴܻܾ Ľ. 
2̬ļ 
 . 
1ھֵ ļ飨8-1 
2ڷ ļ飨8-2 
8-1 
  
  
ͳ ܾ 
 鷨 ֪ 
  
  
  
  

 鷨 δ֪ 
  
  
  
  

8-1 
  
  
ͳ ܾ 
 鷨 ֪ 
  
  
  
  

 鷨 δ֪ 
  
  
  
  

3̬ļ 
 Ϊ  Ϊ . 
1ֵ̬ļ飨8-3 
2̬巽ļ飨8-4 


8-3 
  
  
ͳ ܾ 
 鷨( ֪)   
  
  
  

 鷨 δ֪) 
  
  
  
  

8-4 
  
  
ͳ ܾ 
 鷨 ֪)   
  
  
  

 鷨 δ֪)   
  
  
  


    
1ʲôԼ飿˼ʲôʲôȱݣ 
ԼָֻһǷļ.ԭǣֻҪ󷸵һĸʲ趨 . 
˼ǣС¼һһ㲻Ӧ÷ʵƶԭǷ. 
ȱǣֻһ裬Լ鷽ĺûͬһڶԼ鷨. 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
14 ظͳ.γֲ  
 2ʵһУԭ뱸λǷȣӦѡԭ뱸裿 
ǿƷһĸʣԼ鷢ԭ𱣻ã׾ܾԭ裬ԭ뱸ĵλǲȵģΪˣЩصġʷġȡΪԭ裬Щ²ġܵġԤڵȡΪ. 
3ļ֮ʲôϵ 
ӦĲļϵһĳȷڴ˲ļĽ. ֪ 
 Ϊһ.ڸŶ  Ϊ . ˮƽΪ ľܾΪ Ϊ .ϽԿŶ   ļˮƽΪ ĽӦģеһȷһ. 

    
1ݳϷֽǿȷֲ̬.¯ֵǿȷֱΪ48.549.053.549.556.052.5ܷΪǿȵľֵΪ52.0  
Ϊ δ֪£ . 
:   
ȡͳ  
 ɶ  ֲٽֵ  
ͳ Ĺ۲ֵ  
 Խܼ ΪֽǿȵľֵΪ52.0. 

2̨ӹͬһֱȡ69䳤ȣ ȷֲ̬ʣǷΪ̨ӹȵķ죨  
Ϊ δ֪£ . 
:   
ѡͳ Ϊ  
  
 ʽ Ϊ̨ӹȵķ. 
  

ھ ͻع 
   Ҫ 

1 
1 
ͨݴǷһɿӰ죬Ӷȷ϶ָӰҪһأνЧӦЧͳƷ. 
أӣΪԿƵʵΪػ. 
ˮƽػӵĲͬȼĲͬ״̬ΪصĲͬˮƽ. 
飺ֻһػڱ仯ɿֲ䣬ķΪ. 
飺вֹһػڱ仯Ϊ.ֻжڱ仯ͽ˫. 
2ķ 
 jͬˮƽ ܵ ˮƽ¾ظi( ).ÿһˮƽΪһ ÿˮƽܵmΪȡ Ϊm .طһ㷽£ 
1H0  
2з9-1   
3ѡȡFͳ 
 Fͳֵ 
4Ըļˮƽ FֲҵFͳٽֵֵ 
5Ƚϵóۣ 
 ֵ ٽֵ ܾH0ˮƽӰӰ죻 
 ֵ ٽֵ H0ˮƽӰ첻ûӰ. 
ط9-2. 
 9-1 
 ˮƽ 

   
  
   

   

 1 x11 x12    x1j    x1r 
 2 x12 x22    x2j    X2r 
            
i xi1 xi2    xij    xir 
              

 m xm1 xm2    xmj    xmr 
  
  
  
   
   
  

  
  
  
   
   
  

  
  
  
   
   
  


2ع 
1 
عݽر֮عϵѧģͣӦͳƶϵһ㷨򣬶عϵЧͳƷ. 
һԪԻعģΪ  УabΪعϵ. 
2С˷ 
9-2 
 
Դ ƽ  ɶ Fͳֵ Fٽֵ 
ֵ 
   
  
  
  
  
   
  
  

ܱ 
 
 
  
 ߣMr_Mas2008-12-14 03:40 ظ˷    
 
--------------------------------------------------------------------------------
 
15 ظͳ.γֲ  
    
  
  
  


Իع鷽̿ɱʾΪ С˷ûعϵĹֵ 
   
   
3Լ 
ع鷽 ǷЧxy֮عϵǷֻҪعϵ Ƿ.ֻֿ  
  
1ʾ x޹ yxûعϵܷ1ͱʾ 
2жֿܣʾyx֮عϵ. 
 鷨Լ. 鷨Իع鷽ЧԵһ㲽Ϊ 
1裺   
2ѡͳ  ֵ 
3ڸ £ϵõٽֵ  
4Ƚϵóۣ 
  ܾ ع鷽Ч 
   ع鷽Чز. 
ʵӦУ ʱòжع鷽Ч. 

    
1۵Ƿǻع 
ʵָ  Ӱ죬Ӱ.ַΪԵĺ.ԵһСԣֻʵĲͬ磺ӵƷ֡ͺšӹĹաϵƷʵȵ.أһΧȡֵ磺˵ߡأ¶ȣƷĺϸʵȵ.ǵʱڷķΧǵʱڻعķΧ. 

    
1ĳƹ˾    4Ƴ.˾ܾΪ߾ƵչŻش4Ƴȡ3ƿƣָͬһƷԱȹ涨ɫ㡢ζ׼ֽ֣ԭʼ9-3ʾ. 
9-3 
  
   

 1  5 8 7 11 
 2  6 9 8 10 
 3  6 8 6 12 
ʣͬƳԾƵӰ죨  
⣺1H0  
 2з9-4ʾ. 
 ñһУ еݼ 
9-4  
 ˮƽ 

   
  
  
  

 1  5 8 7 11 
 2  6 9 8 10 
 3  6 8 6 12   

  
17 25 21 33  =96 

  
289 625 441 1089  =2444 

  
97 209 149 365  =820 

  
  
(3)ѡFͳFֵٽֵ 
  
  
ֲ鸽5  
4Ƚϵó 
Ϊ ܾH0ʾͬƳԾƵӰ. ΪˮƽӰرʵԭʼݿɼ رߣֱѿж죬˵ĽǷʵģҲ֤˷Ŀѧ. 

2ĳִƷڹгqλ۸pλԪ/.гϤqp֮һ9-5ʾ. 
9-5 
۸ pi 2 4 4 4.5 3 4.2 3.5 2.5 3.3 3 
 qi 6 2 2 1 4 1.5 2.8 5.1 3.4 4.2 
ƷԤΪp=4.6Ԫ/ҪϽqpĻع鷽̣ǷԤгϽΪ󣿣  
⣺ݣС˷  ֵ. 
  
  
  ֵõҪqԼ۸pĻع鷽Ϊ 
 . 
qpĻع鷽̽飺 
1   
 2ѡͳ ûعĽ  
Ϊ   
  
  
3鸽7õ  
4 
 ܾ qpĻع鷽Ч. 
˵ع鷽 ЧԤ. 
p=4.6ʱгϽԸƷΪ10.136-2.044.6=0.752.  
 

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