11--¡¶Í³¼ÆÑ§¡·Ï°Ìâ

(¶þ)µ¥ÏîÑ¡ÔñÌâ

1£®Æ½¾ùÖ¸±êÊÇָͬÀàÉç»á¾­¼ÃÏÖÏóÔÚÒ»¶¨Ê±¼ä¡¢µØµãºÍÌõ¼þÏÂ( )¡£ ¢Ù¸´ÔÓµÄ×ÜÌåÊýÁ¿µÄ×ܺÍˮƽ ¢Ú¿É±ÈµÄ×ÜÌåÊýÁ¿µÄÏà¶Ôˮƽ

¢Û×ÜÌåÄÚ¸÷µ¥Î»ÊýÁ¿²îÒì³éÏ󻯵Ĵú±íˮƽ ¢Ü×ÜÌåÄÚ¸÷µ¥Î»ÊýÁ¿²îÒì³Ì¶ÈµÄÏà¶Ôˮƽ 2£®ËãÊõƽ¾ùÊýµÄ·Ö×ӺͷÖĸÊÇ( )¡£ ¢ÙÁ½¸öÓÐÁªÏµµÄ¶øÐÔÖʲ»Í¬µÄ×ÜÌå×ÜÁ¿

¢Ú·Ö×ÓÊÇ×ÜÌ嵥λ×ÜÁ¿£¬·ÖĸÊÇ×ÜÌå±êÖ¾×ÜÁ¿

¢Û·Ö×ÓÊÇ×ÜÌå±êÖ¾×ÜÁ¿£¬·ÖĸÊÇÁíÒ»×ÜÌ嵥λ×ÜÁ¿ ¢ÜÊÇͬһ×ÜÌåµÄ±êÖ¾×ÜÁ¿ºÍ×ÜÌ嵥λ×ÜÁ¿ 3. ƽ¾ùÊýÊǶÔ( )¡£

¢Ù×ÜÌ嵥λÊýµÄƽ¾ù ¢Ú±äÁ¿ÖµµÄƽ¾ù ¢Û±êÖ¾µÄƽ¾ù ¢Ü±äÒìµÄƽ¾ù 4. ƽ¾ùÊý·´Ó³ÁË×ÜÌå( )¡£

¢Ù·Ö²¼µÄ¼¯ÖÐÇ÷ÊÆ ¢Ú·Ö²¼µÄÀëÖÐÇ÷ÊÆ ¢Û·Ö²¼µÄ±ä¶¯Ç÷ÊÆ ¢Ü·Ö²¼µÄ¿É±È³Ì¶È 5. ¼ÓȨËãÊõƽ¾ùÊýµÄ´óСÊܸ÷×é( )¡£

¢Ù´ÎÊý(f)µÄÓ°Ïì×î´ó ¢Ú±êÖ¾Öµ(x)µÄÓ°Ïì×î´ó

¢ÛȨÊý(f£¯¡Æf)µÄÓ°Ïì×î´ó ¢Ü±êÖ¾Öµ(x)ºÍ´ÎÊý(f)µÄ¹²Í¬Ó°Ïì

6. ÔÚͬһ±äÁ¿ÊýÁÐÖУ¬µ±±êÖ¾Öµ±È½Ï´óµÄ´ÎÊý¶àʱ£¬¼ÆËã³öÀ´µÄƽ¾ùÊý ( ¢Ù½Ó½ü±ê־ֵСµÄÒ»·½ ¢Ú½Ó½ü±êÖ¾Öµ´óµÄÒ»·½ ¢Û½Ó½ü´ÎÊýÉÙµÄÒ»·½ ¢Ü½Ó½üÄÄ·½ÎÞ·¨ÅжÏ

7. ¸ù¾Ýͬһ·Ö×é×ÊÁϼÆËã¼òµ¥ËãÊõƽ¾ùÊýºÍ¼ÓȨËãÊõƽ¾ùÊýÆä½á¹ûÏàͬ£¬ÊÇÒò( ¢Ù¸÷×éȨÊý²»µÈ ¢Ú¸÷×éȨÊýÏàµÈ ¢Û¸÷×é±äÁ¿ÖµÖ®²îÏàµÈ ¢Ü±äÁ¿Öµ´óÖÂÏàµÈ 8. ¼ÓȨËãÊõƽ¾ùÊý¹«Ê½X??Xf?ÖеÄȨÊý(ƵÊý)ÊÇ( )¡£ f ¢Ùf ¢Ú¡Æf ¢Û

f? ¢Ü¡ÆX f

f9. ¼ÓȨËãÊõƽ¾ùÊý¼ÆË㹫ʽX??Xf?µÄȨÊýÊÇ( )¡£

f ¢ÙXf ¢Ú¡Æf ¢Ûf? ¢ÜX

f10. ¸ù¾Ýƽ¾ùÖ¸±êµÄÈ·¶¨·½·¨ºÍÒÀ¾Ý×ÊÁϲ»Í¬Ö÷ÒªÓÐ5ÖÖ£¬ÆäÖÐ( )¡£ ¢ÙÖÐλÊýºÍËãÊõƽ¾ùÊýÊÇλÖÃÆ½¾ùÊý

26

)¡£ )¡£

¢ÚÖÚÊýºÍµ÷ºÍƽ¾ùÊýÊÇλÖÃÆ½¾ùÊý

¢ÛËãÊõƽ¾ùÊýºÍ¼¸ºÎƽ¾ùÊýÊÇλÖÃÆ½¾ùÊý ¢ÜÖÐλÊýºÍÖÚÊýÊÇλÖÃÆ½¾ùÊý

11. ¸ù¾Ýµ¥Ïòʽ·Ö×éÊýÁмÆËã¼ÓȨËãÊõƽ¾ùÊýºÍÖ±½ÓÀûÓøÃÊýÁеÄδ·Ö×é×ÊÁϼÆËã¼òµ¥ËãÊõƽ¾ùÊýÊÇ( )¡£

¢ÙÒ»Ö嵀 ¢Ú²»Ò»ÖµÄ

¢ÛijЩÇé¿öÏÂÒ»Ö ¢Ü¶àÊýÇé¿öϲ»Ò»ÖÂ

12. µ±Ö»ÓÐ×ÜÌå±êÖ¾×ÜÁ¿ºÍ¸÷±êÖ¾Öµ£¬¶øÈ±ÉÙ×ÜÌ嵥λ×ÊÁÏʱ£¬¼ÆËãÆ½¾ùÊýÓ¦²ÉÓÃ( )¡£

¢Ù¼ÓȨËãÊõƽ¾ùÊý¹«Ê½ ¢Ú¼òµ¥ËãÊõƽ¾ùÊý¹«Ê½ ¢Ûµ÷ºÍƽ¾ùÊý¹«Ê½ ¢Ü¼¸ºÎƽ¾ùÊý¹«Ê½ 13£®ÖÚÊý¾ÍÊÇËùÑо¿µÄ±äÁ¿ÊýÁÐÖÐ( )¡£

¢Ù¾ßÓÐ×î¶à´ÎÊýµÄ±äÁ¿Öµ ¢Ú¾ßÓÐ×îÉÙ´ÎÊýµÄ±äÁ¿Öµ ¢Û¾ßÓÐÖеȴÎÊýµÄ±äÁ¿Öµ ¢Ü¾ßÓÐÆ½¾ù´ÎÊýµÄ±äÁ¿Öµ 14£®Ä³ÄêijÊлúе¹¤Òµ¹«Ë¾ËùÊôÈý¸öÆóÒµ¼Æ»®¹æ¶¨µÄ²úÖµ·Ö±ðΪ400ÍòÔª¡¢600ÍòÔª¡¢500ÍòÔª¡£Ö´Ðнá¹û£¬¼Æ»®Íê³É³Ì¶È·Ö±ðΪ108£¥¡¢106£¥¡¢108£¥£¬Ôò¸Ã¹«Ë¾Èý¸öÆóҵƽ¾ù¼Æ»®Íê³É³Ì¶ÈΪ( )¡£ ¢Ù3108%?106%?108%?107.33% ¢Ú¢Û

106%?1?108%?2?107.33%

1?2400?600?500 ?107.33@0600500??10868%¢Ü

108%?400?106%?600?108%?500?107.20%

400?600?50015£®ÒÑ֪ij¹«Ë¾ËùÊôÆóÒµµÄ×ʽðÀûÈóÂʺÍÕ¼ÓÃ×ʽð¶î£¬¼ÆËã¸Ã¹«Ë¾µÄƽ¾ù×ʽðÀûÈóÂÊÓ¦²ÉÓÃ( )¡£

¢Ù¼òµ¥ËãÊõƽ¾ùÊý ¢Ú¼ÓȨËãÊõƽ¾ùÊý ¢Û¼ÓȨµ÷ºÍƽ¾ùÊý ¢Ü¼¸ºÎƽ¾ùÊý 16£®±êÖ¾±äÒìÖ¸±ê˵Ã÷±äÁ¿µÄ( )¡£ ¢Ù±ä¶¯Ç÷ÊÆ ¢Ú¼¯ÖÐÇ÷ÊÆ ¢ÛÀëÖÐÇ÷ÊÆ ¢ÜÒ»°ãÇ÷ÊÆ

17£®±ê×¼²îÖ¸±êÊýֵԽС£¬Ôò·´Ó³±äÁ¿Öµ( )¡£

¢ÙÔ½·ÖÉ¢£¬Æ½¾ùÊý´ú±íÐÔÔ½µÍ ¢ÚÔ½¼¯ÖУ¬Æ½¾ùÊý´ú±íÉúÔ½¸ß ¢ÛÔ½·ÖÉ¢£¬Æ½¾ùÊý´ú±íÐÔÔ½¸ß ¢ÜÔ½¼¯ÖУ¬Æ½¾ùÊý´ú±íÐÔÔ½µÍ 18. ÏÂÁбêÖ¾±äÒìÖ¸±êÖÐÒ×Êܼ«¶ËÖµÓ°ÏìµÄÊÇ( )¡£

27

¢ÙÈ«¾à ¢Úƽ¾ù²î ¢Û±ê×¼²î ¢Ü±ê×¼²îϵÊý 19£®±êÖ¾±äÒìÖ¸±êÖÐµÄÆ½¾ù²îÊǸ÷±êÖ¾Öµ( )¡£

¢ÙÀë²îµÄƽ¾ùÊý ¢Ú¶ÔÆäËãÊõƽ¾ùÊýµÄƽ¾ùÀë²î

¢Û¶ÔÆäËãÊõƽ¾ùÊýÀë²î¾ø¶ÔÖµ ¢Ü¶ÔÆäËãÊõƽ¾ùÊýÀë²î¾ø¶ÔÖµµÄƽ¾ùÊý 20£®±êÖ¾±äÒìÖ¸±êÖеıê×¼²îÊǸ÷±êÖ¾Öµ¶ÔËãÊõƽ¾ùÊýµÄ( )¡£ ¢ÙÀë²îƽ·½µÄƽ¾ùÊý ¢ÚÀë²îƽ¾ùÊýµÄƽ·½¸ù

¢ÛÀë²îƽ·½Æ½¾ùÊýµÄƽ·½¸ù ¢ÜÀë²îƽ¾ùÊýƽ·½µÄƽ·½¸ù 21£®ÔÚ³éÑùÍÆ¶ÏÖÐÓ¦ÓñȽϹ㷺µÄÖ¸±êÊÇ( )¡£ ¢ÙÈ«¾à ¢Úƽ¾ù²î ¢Û±ê×¼²î ¢Ü±ê×¼²îϵÊý

22£®Èç¹ûͳ¼Æ×ÊÁϾ­¹ý·Ö×飬²¢ÐγÉ×é¾à·ÖÅä(·Ö²¼)ÊýÁУ¬ÔòÈ«¾àµÄ¼ÆËã·½·¨ ÊÇ( )¡£

¢ÙÈ«¾à=×î´ó×éÖÐÖµÒ»×îС×éÖÐÖµ ¢ÚÈ«¾à=×î´ó±äÁ¿ÖµÒ»×îС±äÁ¿Öµ ¢ÛÈ«¾à=×î´ó±êÖ¾ÖµÒ»×îС±êÖ¾Öµ ¢ÜÈ«¾à=×î´ó×éÉÏÏÞÒ»×îС×éÏÂÏÞ

23£®ÔÚͳ¼Æ×ÊÁϾ­¹ý·Ö×é²¢ÐγɷÖÅäÊýÁÐʱ£¬¼ÆËã±ê×¼²îµÄ¹«Ê½Îª( )¡£ ¢Ù

?(X?X)n2f£» ¢Ú

?(X?X)?f?(Xn2f

¢Û

?(X?X)f?f £» ¢Ü

?X)2

24£®±êÖ¾±äÒìÖ¸±êÖУ¬¼ÆËã·½·¨¼òµ¥µÄÊÇ( )¡£ ¢Ùƽ¾ù²î ¢Ú±ê×¼²î ¢Û±äÒìÈ«¾à ¢Ü±ê×¼²îϵÊý 25£®Æ½¾ù²îµÄ¼ÓȨƽ¾ùʽµÄ¹«Ê½ÊÇ( )¡£ (X?X)f¢Ù??f(X?X)£» ¢Ú??f2f

¢Û?X?Xf£» ¢Ü

?f?(X?X)?f2f

26£®ÔÚ¼ÆËãÆ½¾ù²îʱ£¬ËùÒÔ²ÉÓÃÀë²îµÄ¾ø¶ÔÖµ ¢Ù

?(X?X)£¬ÕâÊÇÒòΪ( )¡£

?(X?X)?0 ¢Ú?(X?X)?0 ?(X?X)?0 ¢Ü?(X?X)?0

28

¢Û

27£®±ê×¼²îµÄ¼ÓȨƽ¾ùʽµÄ¹«Ê½ÊÇ( )¡£

¢Ù

?(X?X)?f2f ¢Ú

?(X?X)f

?f2(X?X)f ¢Û?(X?X)f ¢Ü?

?f?f28. ƽ¾ù²î(A?D)µÄȡֵ·¶Î§ÊÇ( )¡£

¢ÙA ? D=0 ¢Ú A ? D¡Ü0 ¢Û A¡¤D¡Ý0 ¢Ü 0¡ÜA¡¤D¡Ü1 29. ±ê×¼²î( ¦Ò)µÄȡֵ·¶Î§ÊÇ( )¡£

¢Ù¦Ò=0 ¢Ú¦Ò¡Ü0 ¢Û ¦Ò¡Ý0 ¢Ü 0¡Ü¦Ò¡Ü1 30. ÊǷDZêÖ¾µÄ±ê×¼²îÊÇ( )¡£ ¢Ù

p(1?p) ¢Úp(1Ò»p) ¢Û (p?1) ¢Ü1Ò»p

31. ÊǷDZêÖ¾µÄƽ¾ùÊý(p)µÄȡֵ·¶Î§ÊÇ( )¡£ ¢Ù p¡Ý0 ¢Úp¡Ü0 ¢Ûp>l ¢Ü0¡Üp¡Ü1 32. ÊǷDZêÖ¾µÄ±ê×¼²î¢Ù

p(1?p)µÄȡֵ·¶Î§( )¡£

p(1?p)¡Ý0 ¢Úp(1?p)¡Ül p(1?p)¡Ü1 ¢Ü 0¡Üp(1?p)¡Ü0.5

¢Û0¡Ü

33. ÒÑÖªÁ½¸ö×ÜÌ寽¾ùÊý²»µÈ£¬µ«±ê×¼²îÏàµÈ£¬Ôò( )¡£ ¢Ùƽ¾ùÊý´ó£¬´ú±ílÉú´ó ¢Úƽ¾ùÊýС£¬´ú±íÐÔ´ó ¢Ûƽ¾ùÊý´ó£¬´ú±íÐÔС ¢ÜÒÔÉ϶¼¶Ô (Èý)¶àÏîÑ¡ÔñÌâ

1. ƽ¾ùÖ¸±êµÄÏÔÖøÌØµãÊÇ( )¡£

¢ÙijһÊýÁ¿±êÖ¾ÔÚ×ÜÌ嵥λ֮¼äµÄÊýÁ¿²îÒì³éÏó»¯ ¢Ú×ÜÌå¸÷µ¥Î»Ä³Ò»ÊýÁ¿±êÖ¾µÄ´ú±íÖµ ¢Û×ÜÌåÄÚ¸÷µ¥Î»µÄÆ·ÖʱêÖ¾²îÒì³éÏó»¯ ¢Ü×ÜÌåÖ¸±êÖµµÄÊýÁ¿²îÒì³éÏó»¯

¢ÝÒìÖÊ×ÜÌåµÄ¸÷µ¥Î»±êÖ¾ÖµµÄ²îÒì³éÏó»¯ 2£®Æ½¾ùÖ¸±êµÄ×÷ÓÃÖ÷ÒªÓÐ( )¡£

¢ÙÀûÓÃÆ½¾ùÖ¸±ê£¬¿ÉÒÔ¶ÔÈô¸ÉͬÀàÏÖÏóÔÚ²»Í¬µ¥Î»¡¢µØÇø¼ä½øÐбȽÏÑо¿ ¢ÚÀûÓÃÆ½¾ùÖ¸±ê£¬¿ÉÑо¿Ä³Ò»×ÜÌåijÖÖÊýÖµµÄƽ¾ùˮƽµÄ±ä»¯ ¢ÛÀûÓÃÆ½¾ùÖ¸±ê£¬¿ÉÒÔ·ÖÎöÏÖÏóÖ®¼äµÄÒÀ´æ¹ØÏµ

¢Üƽ¾ùÖ¸±ê¿É×÷ΪijЩ¿ÆÑ§Ô¤²â¡¢¾ö²ßºÍÄ³Ð©ÍÆËãµÄÒÀ¾Ý ¢ÝÀûÓÃÆ½¾ùÖ¸±ê£¬¿ÉÒÔ·´Ó³×ÜÌå´ÎÊý·Ö²¼µÄ¼¯ÖÐÇ÷ÊÆ 3£®¼òµ¥ËãÊõƽ¾ùÊýËùÒÔ¼òµ¥ÊÇÒòΪ( )¡£

29

¢ÙËùÒÀÒÔ¼ÆËãµÄ×ÊÁÏÒÑ·Ö×é ¢Ú¸÷±äÁ¿ÖµµÄƵÂÊÏàµÈ ¢Û¸÷±äÁ¿ÖµµÄƵÂʲ»µÈ ¢ÜËùÒÀÒÔ¼ÆËãµÄ×ÊÁÏδ·Ö×é ¢Ý¸÷±äÁ¿ÖµµÄ´ÎÊý·Ö²¼²»Í¬

4£®¼ÓȨËãÊõƽ¾ùÊý¼ÆË㹫ʽÓÐ( )¡£ ¢Ù?Xf ¢Ú?fXff? ¢Û?nX ¢Ü

?m 1?Xmf5. ¼ÓȨËãÊõƽ¾ùÊýµÈÓÚ¼òµ¥ËãÊõƽ¾ùÊýµÄÌõ¼þÊÇ( )¡£ ¢Ù¸÷×é±äÁ¿Öµ²»Ïàͬ ¢Ú¸÷×é´ÎÊýÏàµÈ ¢Û¸÷×éȨÊý¶¼Ïàͬ ¢ÜÔÚ·Ö×éµÄ×éÊý½ÏÉÙ ¢Ý¸÷×é´ÎÊý²»ÏàµÈ

6£®¼ÓȨËãÊõƽ¾ùÊýµÄ´óС( )¡£

¢ÙÊܸ÷×é´ÎÊý¶àÉÙµÄÓ°Ïì ¢ÚÊܸ÷×é±êÖ¾Öµ´óСµÄÓ°Ïì ¢ÛÊܸ÷×é±êÖ¾ÖµºÍ´ÎÊýµÄ¹²Í¬Ó°Ïì ¢Ü²»Êܸ÷×é±êÖ¾ÖµµÄÓ°Ïì ¢ÝÓë¸÷×é´ÎÊý·Ö²¼¶àÉÙÎÞ¹ØÏµ

7£®ÔÚ×é¾àÊýÁеÄÌõ¼þÏ£¬¼ÆËãÖÐλÊýµÄ¹«Ê½Îª( )¡£ ¢Ù

?fMe?L?2?Sm?1fm?i ¢ÚM?fe?U?2?Sm?1fm?i

?f¢Û Me?L?2?Sm?1fm?f?i ¢Ü Me?U?2?Sm?1fm?i

¢ÝM?U?e?f2?Sm?1fm?i

8£®µ÷ºÍƽ¾ùÊýµÄ¼ÆË㹫ʽÓÐ( )¡£ ¢Ù ¢Ü

?Xn ¢Ú ¢Ý

?Xf?fn ¢Û

?Xf?f

?m1?Xf

1?XX1X2?Xn?1Xn

n9£®¼¸ºÎƽ¾ùÊýµÄ¼ÆË㹫ʽÓÐ( )¡£ ¢ÙnX1?X2??Xn?1Xn ¢Ú

30

ÁªÏµ¿Í·þ£º779662525#qq.com(#Ìæ»»Îª@) ËÕICP±¸20003344ºÅ-4