Î÷·½¾­¼Ãѧ΢¹Û²¿·Ö¿ÎºóÏ°Ìâ´ð°¸

ÔÚÒÔÉÏÌÖÂÛÁ˵¥¸öÉÌÆ·Êг¡ºÍµ¥¸öÉú²úÒªËØÊг¡µÄ¾ùºâ¼Û¸ñ¾ö¶¨¼°Æä×÷ÓÃÖ®ºó£¬Ò»°ã¾ùºâÀíÂÛÌÖÂÛÁËÒ»¸ö¾­¼ÃÉç»áÖÐËùÓеĵ¥¸öÊг¡µÄ¾ùºâ¼Û¸ñ¾ö¶¨ÎÊÌ⣬Æä½áÂÛÊÇ£ºÔÚÍêÈ«¾ºÕù¾­¼ÃÖУ¬´æÔÚ×ÅÒ»×é¼Û¸ñ(P1£¬P2£¬¡­£¬Pn)£¬Ê¹µÃ¾­¼ÃÖÐËùÓеÄn¸öÊг¡Í¬Ê±ÊµÏÖ¹©ÇóÏàµÈµÄ¾ùºâ״̬¡£ÕâÑù£¬Î¢¹Û¾­¼Ãѧ±ãÍê³ÉÁ˶ÔÆäºËÐÄ˼Ïë¼´¡°¿´²»¼ûµÄÊÖ¡±Ô­ÀíµÄÖ¤Ã÷¡£

ÔÚÉÏÃæʵ֤Ñо¿µÄ»ù´¡ÉÏ£¬Î¢¹Û¾­¼ÃѧÓÖ½øÈëÁ˹淶Ñо¿²¿·Ö£¬¼´¸£Àû¾­¼Ãѧ¡£¸£Àû¾­¼ÃѧµÄÒ»¸öÖ÷ÒªÃüÌâÊÇ£ºÍêÈ«¾ºÕùµÄÒ»°ã¾ùºâ¾ÍÊÇÅÁÀÛÍÐ×îÓÅ״̬¡£Ò²¾ÍÊÇ˵£¬ÔÚÅÁÀÛÍÐ×îÓŵľ­¼ÃЧÂʵÄÒâÒåÉÏ£¬½øÒ»²½¿Ï¶¨ÁËÍêÈ«¾ºÕùÊг¡¾­¼ÃµÄÅäÖÃ×ÊÔ´µÄ×÷Óá£

ÔÚÌÖÂÛÁËÊг¡»úÖƵÄ×÷ÓÃÒÔºó£¬Î¢¹Û¾­¼ÃѧÓÖÌÖÂÛÁËÊг¡Ê§ÁéµÄÎÊÌâ¡£Êг¡Ê§Áé²úÉúµÄÖ÷ÒªÔ­Òò°üÀ¨Â¢¶Ï¡¢Íⲿ¾­¼Ã¡¢¹«¹²ÎïÆ·ºÍ²»ÍêÈ«ÐÅÏ¢¡£ÎªÁË¿Ë·þÊг¡Ê§Áéµ¼ÖµÄ×ÊÔ´ÅäÖõÄÎÞЧÂÊ£¬¾­¼Ãѧ¼ÒÓÖ̽ÌÖºÍÌá³öÁËÏàÓ¦µÄ΢¹Û¾­¼ÃÕþ²ß¡£

(2)¹ØÓÚ΢¹Û¾­¼ÃѧµÄºËÐÄ˼Ïë¡£

΢¹Û¾­¼ÃѧµÄºËÐÄ˼ÏëÖ÷ÒªÊÇÂÛÖ¤×ʱ¾Ö÷ÒåµÄÊг¡¾­¼ÃÄܹ»ÊµÏÖÓÐЧÂʵÄ×ÊÔ´ÅäÖá£Í¨³£ÓÃÓ¢¹ú¹Åµä¾­¼Ãѧ¼ÒÑǵ±¡¤Ë¹ÃÜÔÚÆä1776Äê³ö°æµÄ¡¶¹úÃñ²Æ¸»µÄÐÔÖʺÍÔ­ÒòµÄÑо¿¡·Ò»ÊéÖÐÌá³öµÄ¡¢ÒÔºóÓÖ±»³ÆΪ¡°¿´²»¼ûµÄÊÖ¡±Ô­ÀíµÄÄÇÒ»¶Î»°£¬À´±íÊö΢¹Û¾­¼ÃѧµÄºËÐÄ˼Ï룬ÆäÔ­ÎÄΪ£º¡°Ã¿È˶¼ÔÚÁ¦Í¼Ó¦ÓÃËûµÄ×ʱ¾£¬À´Ê¹ÆäÉú²úÆ·Äܵõ½×î´óµÄ¼ÛÖµ¡£Ò»°ãµØ˵£¬Ëû²¢²»ÆóͼÔö½ø¹«¹²¸£Àû£¬Ò²²»ÖªµÀËûËùÔö½øµÄ¹«¹²¸£ÀûΪ¶àÉÙ¡£ËûËù×·ÇóµÄ½ö½öÊÇËû¸öÈ˵ݲÀÖ£¬½ö½öÊÇËû¸öÈ˵ÄÀûÒæ¡£ÔÚÕâÑù×öʱ£¬ÓÐÒ»Ö»¿´²»¼ûµÄÊÖÒýµ¼ËûÈ¥´Ù½øÒ»ÖÖÄ¿±ê£¬¶øÕâÖÖÄ¿±ê¾ø²»ÊÇËûËù×·ÇóµÄ¶«Î÷¡£ÓÉÓÚËû×·ÖðËû×Ô¼ºµÄÀûÒ棬Ëû¾­³£´Ù½øÁËÉç»áÀûÒ棬ÆäЧ¹ûÒª±ÈËûÕæÕýÏë´Ù½øÉç»áÀûÒæʱËùµÃµ½µÄЧ¹ûΪ´ó¡£¡±

µÚÈýÕ ЧÓÃÂÛ

1.½â´ð£º°´ÕÕÁ½ÉÌÆ·µÄ±ß¼ÊÌæ´úÂÊMRSµÄ¶¨Ò幫ʽ£¬¿ÉÒÔ½«Ò»·Ý¿ÏµÂ»ù¿ì²Í¶Ô³ÄÉÀµÄ±ß¼ÊÌæ´úÂÊд³É£º

¦¤YMRSXY£½£­ ¦¤X ÆäÖУ¬X±íʾ¿ÏµÂ»ù¿ì²ÍµÄ·ÝÊý£»Y±íʾ³ÄÉÀµÄ¼þÊý£»MRSXY±íʾÔÚά³ÖЧÓÃˮƽ²»±äµÄÇ°ÌáÏ£¬Ïû·ÑÕßÔö¼ÓÒ»·Ý¿ÏµÂ»ù¿ì²ÍÏû·ÑʱËùÐèÒª·ÅÆúµÄ³ÄÉÀµÄÏû·ÑÊýÁ¿¡£

ÔÚ¸ÃÏû·ÑÕßʵÏÖ¹ØÓÚÕâÁ½ÖÖÉÌÆ·µÄЧÓÃ×î´ó»¯Ê±£¬ÔÚ¾ùºâµãÉÏÓÐMRSXY£½

20

¼´ÓÐ MRSXY£½£½

80

Ëü±íÃ÷£¬ÔÚЧÓÃ×î´ó»¯µÄ¾ùºâµãÉÏ£¬¸ÃÏû·ÑÕß¹ØÓÚÒ»·Ý¿ÏµÂ»ù¿ì²Í¶Ô³ÄÉÀµÄ±ß¼ÊÌæ´úÂÊMRSΪ¡£ 2.

ͼ3¡ª1 ijÏû·ÑÕߵľùºâ

½â´ð£º(1)ͼÖеĺá½Ø¾à±íʾÏû·ÑÕßµÄÊÕÈëÈ«²¿¹ºÂòÉÌÆ·1µÄÊýÁ¿Îª30µ¥Î»£¬ÇÒÒÑÖªP1£½2Ôª£¬ËùÒÔ£¬Ïû·ÑÕßµÄÊÕÈëM£½2Ôª¡Á30£½60Ôª¡£

(2)ͼÖеÄ×ݽؾà±íʾÏû·ÑÕßµÄÊÕÈëÈ«²¿¹ºÂòÉÌÆ·2µÄÊýÁ¿Îª20µ¥Î»£¬ÇÒÓÉ(1)ÒÑÖªÊÕÈëM£½60Ôª£¬Ëù

M60

ÒÔ£¬ÉÌÆ·2µÄ¼Û¸ñP2£½£½£½3Ôª¡£

2020

(3)ÓÉÓÚÔ¤ËãÏß·½³ÌµÄÒ»°ãÐÎʽΪP1X1£«P2X2£½M

ËùÒÔ£¬ÓÉ(1)¡¢(2)¿É½«Ô¤ËãÏß·½³Ì¾ßÌåдΪ£º2X1£«3X2£½60¡£

22

(4)½«(3)ÖеÄÔ¤ËãÏß·½³Ì½øÒ»²½ÕûÀíΪX2£½£­X1£«20¡£ºÜÇå³þ£¬Ô¤ËãÏßµÄбÂÊΪ£­¡£

33

(5)ÔÚÏû·ÑÕßЧÓÃ×î´ó»¯µÄ¾ùºâµãEÉÏ£¬ÓÐMRS12£½£¬¼´ÎÞ²îÒìÇúÏßбÂʵľø¶ÔÖµ¼´MRSµÈÓÚÔ¤ËãÏßб

PXPYP1P2

P1P12

Âʵľø¶ÔÖµ¡£Òò´Ë£¬MRS12£½£½¡£

P2P23

3.½â´ð£º(1)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßA¶øÑÔ£¬ÈȲèÊÇÖÐÐÔÉÌÆ·£¬Òò´Ë£¬ÈȲèµÄÏû·ÑÊýÁ¿²»»áÓ°ÏìÏû·ÑÕßAµÄЧÓÃˮƽ¡£Ïû·ÑÕßAµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(a)¡£Í¼3¡ª2ÖеļýÍ·¾ù±íʾЧÓÃˮƽÔö¼ÓµÄ·½Ïò¡£

(2)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßB¶øÑÔ£¬¿§·ÈºÍÈȲèÊÇÍêÈ«»¥²¹Æ·£¬ÆäЧÓú¯ÊýÊÇU£½min{x1£¬x2}¡£Ïû·ÑÕßBµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(b)¡£

(3)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßC¶øÑÔ£¬¿§·ÈºÍÈȲèÊÇÍêÈ«Ìæ´úÆ·£¬ÆäЧÓú¯ÊýÊÇU£½2x1£«x2¡£Ïû·ÑÕßCµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(c)¡£

(4)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßD¶øÑÔ£¬¿§·ÈÊÇÑá¶ñÆ·¡£Ïû·ÑÕßDµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(d)¡£ ͼ3¡ª2 ¹ØÓÚ¿§·ÈºÍÈȲèµÄ²»Í¬Ïû·ÑÕßµÄÎÞ²îÒìÇúÏß 4.

ͼ3¡ª3

½â´ð£ºÒ»°ã˵À´£¬·¢¸øÏû·ÑÕßÏÖ½ð²¹Öú»áʹÏû·ÑÕß»ñµÃ¸ü´óµÄЧÓá£ÆäÔ­ÒòÔÚÓÚ£ºÔÚÏÖ½ð²¹ÖúµÄÇé¿öÏ£¬Ïû·ÑÕß¿ÉÒÔ°´ÕÕ×Ô¼ºµÄÆ«ºÃÀ´¹ºÂòÉÌÆ·£¬ÒÔ»ñµÃ¾¡¿ÉÄÜ´óµÄЧÓá£Èçͼ3¡ª3Ëùʾ¡£

ÔÚͼ3¡ª3ÖУ¬Ö±ÏßABÊÇ°´ÊµÎï²¹ÖúÕÛËãµÄ»õ±ÒÁ¿¹¹³ÉµÄÏÖ½ð²¹ÖúÇé¿öϵÄÔ¤ËãÏß¡£ÔÚÏÖ½ð²¹ÖúµÄÔ¤Ëã

**

ÏßABÉÏ£¬Ïû·ÑÕ߸ù¾Ý×Ô¼ºµÄÆ«ºÃÑ¡ÔñÉÌÆ·1ºÍÉÌÆ·2µÄ¹ºÂòÁ¿·Ö±ðΪx1ºÍx2£¬´Ó¶øʵÏÖÁË×î´óµÄЧÓÃˮƽU2£¬¼´ÔÚͼ3¡ª3ÖбíÏÖΪԤËãÏßABºÍÎÞ²îÒìÇúÏßU2ÏàÇеľùºâµãE¡£

¶øÔÚʵÎï²¹ÖúµÄÇé¿öÏ£¬Ôòͨ³£²»»á´ïµ½×î´óµÄЧÓÃˮƽU2¡£ÒòΪ£¬Æ©È磬µ±ÊµÎï²¹ÖúµÄÉÌÆ·×éºÏΪFµã(¼´Á½ÉÌÆ·ÊýÁ¿·Ö±ðΪx11¡¢x21)£¬»òÕßΪGµã(¼´Á½ÉÌÆ·ÊýÁ¿·Ö±ðΪx12ºÍx22)ʱ£¬ÔòÏû·ÑÕßÄÜ»ñµÃÎÞ²îÒìÇúÏßU1Ëù±íʾµÄЧÓÃˮƽ£¬ÏÔÈ»£¬U1

MU1P1

5.½â´ð£º¸ù¾ÝÏû·ÑÕßµÄЧÓÃ×î´ó»¯µÄ¾ùºâÌõ¼þ £½

MU2P2

dTUdTU22

ÆäÖУ¬ÓÉU£½3X1X2¿ÉµÃMU1£½£½3X2 MU2£½£½6X1X2

dX1dX2

2

3X220

ÓÚÊÇ£¬ÓÐ £½

6X1X2304

ÕûÀíµÃ X2£½X1 (1)

3

4

½«Ê½(1)´úÈëÔ¤ËãÔ¼ÊøÌõ¼þ20X1£«30X2£½540£¬µÃ20X1£«30¡¤X1£½540

3

½âµÃ X1£½9

½«X1£½9´úÈëʽ(1)µÃX2£½12

Òò´Ë£¬¸ÃÏû·ÑÕßÿÄ깺ÂòÕâÁ½ÖÖÉÌÆ·µÄÊýÁ¿Ó¦¸ÃΪ X1=9£¬X2=12

***22

½«ÒÔÉÏ×îÓŵÄÉÌÆ·×éºÏ´úÈëЧÓú¯Êý£¬µÃU£½3X1(X2)£½3¡Á9¡Á12£½3 888

Ëü±íÃ÷¸ÃÏû·ÑÕßµÄ×îÓÅÉÌÆ·¹ºÂò×éºÏ¸øËû´øÀ´µÄ×î´óЧÓÃˮƽΪ3 888¡£

d

6. ½â´ð£º(1)ÓÉÏû·ÑÕßAµÄÐèÇóº¯ÊýQA£½20£­4P£¬¿É±àÖÆÏû·ÑÕßAµÄÐèÇó±í£»ÓÉÏû·ÑÕßBµÄÐèÇóº¯Êýd

QB£½30£­5P£¬¿É±àÖÆÏû·ÑBµÄÐèÇó±í¡£ÖÁÓÚÊг¡µÄÐèÇó±íµÄ±àÖÆ¿ÉÒÔʹÓÃÁ½ÖÖ·½·¨£¬Ò»ÖÖ·½·¨ÊÇÀûÓÃÒѵõ½Ïû·ÑÕßA¡¢BµÄÐèÇó±í£¬½«Ã¿Ò»¼Û¸ñˮƽÉÏÁ½¸öÏû·ÑÕßµÄÐèÇóÊýÁ¿¼Ó×ÜÀ´±àÖÆÊг¡ÐèÇó±í£»ÁíÒ»ÖÖ·½·¨ÊÇÏÈ

ddd½«Ïû·ÑÕßAºÍBµÄÐèÇóº¯Êý¼Ó×ÜÀ´ÇóµÃÊг¡ÐèÇóº¯Êý£¬¼´Êг¡ÐèÇóº¯ÊýQ£½QA£«QB£½(20£­4P)£«(30£­5P)£½

d50£­9P£¬ È»ºóÔËÓÃËùµÃµ½µÄÊг¡ÐèÇóº¯ÊýQ£½50£­9PÀ´±àÖÆÊг¡ÐèÇó±í¡£ÕâÁ½ÖÖ·½·¨ËùµÃµ½µÄÊг¡ÐèÇó±íÊÇÏàͬµÄ¡£°´ÒÔÉÏ·½·¨±àÖƵÄ3ÕÅÐèÇó±íÈçÏÂËùʾ¡£

Ïû·ÑÕßAµÄÐèÇó±í

dP QA 0 20 1 16 2 12 3 8 4 4 5 0 ,Ïû·ÑÕßBµÄÐèÇó±í

dP QB 0 30 1 2 3 4 5 6 ,Êг¡µÄÐèÇó±í

P 0 1 2 3 4 5 6

d25 20 15 10 5 0 Q£½50£­9P 50 41 32 23 14 5 0 (2)ÓÉ(1)ÖеÄ3ÕÅÐèÇó±í£¬Ëù»­³öµÄÏû·ÑÕßAºÍB¸÷×ÔµÄÐèÇóÇúÏßÒÔ¼°Êг¡µÄÐèÇóÇúÏßÈçͼ3¡ª4Ëùʾ¡£

ͼ3¡ª4

d

ÔÚ´Ë£¬ÐèÒªÌرðÖ¸³öµÄÊÇ£¬Êг¡ÐèÇóÇúÏßÓÐÒ»¸öÕ۵㣬¸Ãµã·¢ÉúÔÚ¼Û¸ñP£½5ºÍÐèÇóÁ¿Q£½5µÄ×ø±êµãλÖ᣹ØÓÚÊг¡ÐèÇóÇúÏßµÄÕâÒ»ÌØÕ÷£¬¿ÉÒÔ´ÓÁ½¸ö½Ç¶ÈÀ´½âÊÍ£ºÒ»¸ö½Ç¶ÈÊÇ´ÓͼÐÎÀ´Àí½â£¬Êг¡ÐèÇóÇúÏßÊÇÊг¡Éϵ¥¸öÏû·ÑÕßÐèÇóÇúÏßµÄˮƽ¼Ó×Ü£¬¼´ÔÚP¡Ü5µÄ·¶Î§£¬Êг¡ÐèÇóÇúÏßÓÉÁ½¸öÏû·ÑÕßÐèÇóÇúÏßˮƽ¼Ó×ܵõ½£»¶øµ±P£¾5ʱ£¬Ö»ÓÐÏû·ÑÕßBµÄÐèÇóÇúÏß·¢Éú×÷Óã¬ËùÒÔ£¬ËûµÄÐèÇóÇúÏß¾ÍÊÇÊг¡ÐèÇóÇúÏß¡£ÁíÒ»¸ö

ddd½Ç¶ÈÊÇ´ÓÐèÇóº¯Êý¿´£¬ÔÚP¡Ü5µÄ·¶Î§£¬Êг¡ÐèÇóº¯ÊýQ£½QA£«QB£½(20£­4P)£«(30£­5P)£½50£­9P³ÉÁ¢£»¶ø

dd

µ±P£¾5ʱ£¬Ö»ÓÐÏû·ÑÕßBµÄÐèÇóº¯Êý²Å¹¹³ÉÊг¡ÐèÇóº¯Êý£¬¼´Q£½QB£½30£­5P¡£

7¡¢½â´ð£º¸ù¾ÝÏû·ÑÕßЧÓÃ×î´ó»¯µÄ¾ùºâÌõ¼þMU1/MU2=P1/P2

dTU3?88ÆäÖУ¬ÓÉÒÔÖªµÄЧÓú¯ÊýU?xx ¿ÉµÃ£ºMU1??x1x2

dx18dTU58?8 MU2??x1x2

dx283?88x1x23x2PP18?1 ?ÓÚÊÇ£¬ÓУºÕûÀíµÃ£º335x1P258?8P2x1x28¼´ÓÐx2?5535881255335p1x1 £¨1£© 3p2£¨1£©Ê½´úÈëÔ¼ÊøÌõ¼þP1X1+P2X2=M£¬ÓУº

P1x1?P25P1x1?M3M5M3P2½âµÃ£ºx1?´úÈ루1£©Ê½µÃ x2?

8P18P2ËùÒÔ£¬¸ÃÏû·ÑÕß¹ØÓÚÁ½ÉÌÆ·µÄÐèÇóº¯ÊýΪx1?3M5M x2? 8P18P28. ½â´ð£ºÓÉÓÚÎÞ²îÒìÇúÏßÊÇÒ»ÌõÖ±Ïߣ¬ËùÒÔ¸ÃÏû·ÑÕßµÄ×îÓÅÏû·ÑÑ¡ÔñÓÐÈýÖÖÇé¿ö£¬ÆäÖеĵÚÒ»¡¢µÚ¶þ

ÖÖÇé¿öÊôÓڱ߽ǽ⡣

µÚÒ»ÖÖÇé¿ö£ºµ±MRS12>P1/P2ʱ£¬¼´a> P1/P2ʱ£¬Èçͼ£¬Ð§ÓÃ×î´óµÄ¾ùºâµãEµÄλÖ÷¢ÉúÔÚºáÖᣬËü±íʾ´ËʱµÄ×îÓŽâÊÇÒ»¸ö±ß½Ç½â£¬¼´ X1=M/P1£¬X2=0¡£Ò²¾ÍÊÇ˵£¬Ïû·ÑÕß½«È«²¿µÄÊÕÈ붼¹ºÂòÉÌÆ·1£¬²¢ÓÉ´Ë´ïµ½×î´óµÄЧÓÃˮƽ£¬¸ÃЧÓÃˮƽÔÚͼÖÐÒÔʵÏß±íʾµÄÎÞ²îÒìÇúÏß±ê³ö¡£ÏÔÈ»£¬¸ÃЧÓÃˮƽ¸ßÓÚÔڼȶ¨µÄÔ¤ËãÏßÉÏÆäËûÈκÎÒ»¸öÉÌÆ·×éºÏËùÄÜ´ïµ½µÄЧÓÃˮƽ£¬ÀýÈçÄÇЩÓÃÐéÏß±íʾµÄÎÞ²îÒìÇúÏßµÄЧÓÃˮƽ¡£

µÚ¶þÖÖÇé¿ö£ºµ±MRS12

µÚÈýÖÖÇé¿ö£ºµ±MRS12=P1/P2ʱ£¬a= P1/P2ʱ£¬Èçͼ£¬ÎÞ²îÒìÇúÏßÓëÔ¤ËãÏßÖصþ£¬Ð§ÓÃ×î´ó»¯´ïµ½¾ùºâµã¿ÉÒÔÊÇÔ¤ËãÏßÉϵÄÈκÎÒ»µãµÄÉÌÆ·×éºÏ£¬¼´×îÓŽâΪX1¡Ý0£¬X2¡Ý0£¬ÇÒÂú×ãP1X1+P2X2=M¡£´ËʱËù´ïµ½µÄ×î´óЧÓÃˮƽÔÚͼÖÐÒÔʵÏß±íʾµÄÎÞ²îÒìÇúÏß±ê³ö¡£ÏÔÈ»£¬¸ÃЧÓÃˮƽ¸ßÓÚÔڼȶ¨µÄÔ¤ËãÏßÉÏÆäËûÈκÎÒ»ÌõÎÞ²îÒìÇúÏßËùÄÜ´ïµ½µÄЧÓÃˮƽ£¬ÀýÈçÄÇЩÓÃÐéÏß±íʾµÄÎÞ²îÒìÇúÏßµÄЧÓÃˮƽ¡£

ͼ3¡ª5

9. ½â£º£¨1£©ÓÉÌâÒâ¿ÉµÃ£¬ÉÌÆ·µÄ±ß¼ÊЧÓÃΪ£º MU??U1?0.5?q ?Q2?U?3 ?MMU1ÓÚÊÇ£¬¸ù¾ÝÏû·ÑÕß¾ùºâÌõ¼þ??£¬ÓУºq?0.5?3p

P2»õ±ÒµÄ±ß¼ÊЧÓÃΪ£º??ÕûÀíµÃÐèÇóº¯ÊýΪq?1/36p

£¨2£©ÓÉÐèÇóº¯Êýq?1/36p£¬¿ÉµÃ·´ÐèÇóº¯ÊýΪ£ºp?£¨3£©ÓÉ·´ÐèÇóº¯Êý£¬¿ÉµÃÏû·ÑÕßÊ£ÓàΪ£º

41?0.51111q?dq??4?q???

0612333221?0.5q 6CS??40ÒÔp=1/12,q=4´úÈëÉÏʽ£¬ÔòÓÐÏû·ÑÕßÊ£ÓࣺCs=1/3

10.½â´ð£º£¨1£©ÓÉÏû·ÑÕßµÄЧÓú¯ÊýU?xx£¬ËãµÃ£ºMUx????U?U??x??1y?,MUy???x?y??1 ?Q?yÏû·ÑÕßµÄÔ¤ËãÔ¼Êø·½³ÌΪPx?Py?M £¨1£© ¸ù¾ÝÏû·ÑÕßЧÓÃ×î´ó»¯µÄ¾ùºâÌõ¼þ

?MUxPx???MUyPy £¨2£© ?Pxx?Pyy?M???x??1y?Px??µÃ??x?y??1Py £¨3£© ?Pxx?Pyy?M?½â·½³Ì×飨3£©£¬¿ÉµÃ

x??M/px £¨4£© y??M/py £¨5£©

ʽ£¨4£©¼´ÎªÏû·ÑÕß¹ØÓÚÉÌÆ·xºÍÉÌÆ·yµÄÐèÇóº¯Êý¡£ ÉÏÊöÐèÇóº¯ÊýµÄͼÐÎÈçͼ

£¨2£©ÉÌÆ·xºÍÉÌÆ·yµÄ¼Û¸ñÒÔ¼°Ïû·ÑÕßµÄÊÕÈëͬʱ±ä¶¯Ò»¸ö±ÈÀý£¬Ï൱ÓÚÏû·ÑÕßµÄÔ¤ËãÏß±äΪ

?pxx??pyy??M £¨6£©

ÆäÖÐ

?Ϊһ¸ö·ÇÁã³£Êý¡£

´ËʱÏû·ÑÕßЧÓÃ×î´ó»¯µÄ¾ùºâÌõ¼þ±äΪ

?x??1y?px??x?y??1py £¨7£© ?pxx??pyy??MÓÉÓÚ£¬¹Ê·½³Ì×飨7£©»¯Îª

??x??1y?Px?? ??x?y??1Py £¨8£© ?Pxx?Pyy?M?

ÁªÏµ¿Í·þ£º779662525#qq.com(#Ì滻Ϊ@) ËÕICP±¸20003344ºÅ-4