1銆�  瑷�(sh猫)锛戯紣浠剁敘(ch菐n)鍝佷腑鏈夛紨浠朵笉鍚堟牸鍝�锛屽緸涓换鍙栧叐浠讹紝宸茬煡鍙栧嚭鐨勫叐浠朵腑鏈変竴浠朵笉鍚堟牸鍝�锛屾眰鍙︿竴浠朵篃鏄笉鍚堟牸鍝佺殑姒傜巼銆傦紙锛�.锛掞級

    銆�鎬濊矾銆�鍦�”宸茬煡鍙栧嚭鐨勫叐浠朵腑鏈変竴浠朵笉鍚堟牸鍝�”鐨勬儏娉佷笅锛屽彟涓€浠舵湁鍏╃ó鎯呮硜(1)鏄笉鍚堟牸鍝�,鍗充竴浠剁偤鍚堟牸鍝�,涓€浠剁偤涓嶅悎鏍煎搧(2)鐐哄悎鏍煎搧,鍗冲叐浠堕兘鏄悎鏍煎搧.灏�(du矛)浜�(1),C(1,4)*(1,6)/C(2,10)=8/15;灏�(du矛)浜�(2),C(2,4)/C(2,10)=2/15.鎻愬晱瀵�(sh铆)闅涗笂鏄眰鍦ㄩ€欏叐绋儏娉佷笅,(1)鐨勬鐜�,鍓�(2/15)/(8/15+2/15)=1/5

2銆�  瑷�(sh猫)A鏄�3闅庣煩闄�锛�b1,b2,b3鏄窔鎬х劇(w煤)闂�(gu膩n)鐨�3缍悜閲忕祫锛屽凡鐭�Ab1=b1+b2, Ab2=-b1+2b2-b3, Ab3=b2-3b3, 姹� |A| 锛堢瓟妗堬細|A|=-8锛�

銆�鎬濊矾銆�A= 锛堢瓑寮忓叐閭婃眰琛屽垪寮忕殑鍊�,鍥�?y脿n)?/span>b1,b2,b3绶氭€х劇(w煤)闂�(gu膩n),鎵€浠ュ叾琛屽垪寮忕殑鍊间笉鐐洪浂,绛夊紡鍏╅倞姝ｅソ绱勫幓,寰�-8锛�

3銆�  鏌愪汉鑷ū鑳介爯(y霉)瑕嬫湭渚�(l谩i)锛屼綔鐐哄皪(du矛)浠栫殑鑰冮(y脿n)锛屽皣1鏋氱‖骞ｆ媼10娆�锛屾瘡涓€娆¤畵浠栦簨鍏�
闋�(y霉)瑷€绲�(ji茅)鏋�锛�10娆′腑浠栬(shu艒)灏�(du矛)7娆� 锛屽鏋滃(sh铆)闅涗笂浠栧苟涓嶈兘闋�(y霉)瑕嬫湭渚�(l谩i)锛屽彧鏄毃渚跨寽娓�(c猫)锛� 鍓囦粬浣滃嚭閫欐ǎ濂界殑绛旀鐨勬鐜囨槸澶氬皯锛熺瓟妗堢偤11/64銆�

    銆�鎬濊矾銆�鍘熼瑾�(shu艒)浠栨槸濂界殑绛旀,鍗冲寘鎷簡7娆�,8娆�,9娆�,10娆＄殑姒傜巼. 鍗� C(7 10)0.5^7x0.5^3+......C(10 10)0.5^10, 鍗崇偤11/64.

4銆�  鎴愮瓑姣旀暩(sh霉)鍒椾笁鍊�(g猫)鏁�(sh霉)鐨勫拰鐐烘甯告暩(sh霉)K,姹傞€欎笁鍊�(g猫)鏁�(sh霉)涔樼⿳鐨勬渶灏忓€�

    銆�鎬濊矾銆�a/q+a+a*q=k(k鐐烘鏁存暩(sh霉))
鐢辨姹傚緱a=k/(1/q+1+q)
鎵€姹傚紡=a^3,姹傛渶灏忓€煎彲瑕嬬啊(ji菐n)鍖栫偤姹�a鐨勬渶灏忓€�.
灏�(du矛)a姹傚皫(d菐o),鐨勯榛�(di菐n)鐐�q=+1,q=-1.
鍏朵腑q=-1鏅�(sh铆)a鍙栨サ灏忓€�-k,寰炶€屾湁鎵€姹傛渶灏忓€肩偤a=-k^3.(mba涓嶈姹傝瓑鏄庢渶鍊�)

5銆�  鎿蹭簲鏋氱‖骞ｏ紝宸茬煡鑷冲皯鍑虹従(xi脿n)鍏╁€�(g猫)姝ｉ潰锛屽墖姝ｉ潰鎭板ソ鍑虹従(xi脿n)涓夊€�(g猫)鐨勬鐜�銆�

銆�鎬濊矾銆�鍙互鏈夊叐绋柟娉曪細
1.鐢ㄥ彜鍏告鍨� 妯ｆ湰榛�(di菐n)鏁�(sh霉)鐐�C锛�3锛�5锛�锛屾ǎ鏈附鏁�(sh霉)鐐�C锛�2锛�5锛�C锛�3锛�5锛�C锛�4锛�5锛�C锛�5锛�5锛夛紙涔熷氨鏄(shu艒)姝ｉ潰鏈濅笂鐐�2锛�3锛�4锛�5鍊�(g猫)锛�锛岀浉闄ゅ氨鍙互浜�锛�
2.鐢ㄦ浠舵鐜� 鍦ㄨ嚦灏戝嚭鐝�(xi脿n)2鍊�(g猫)姝ｉ潰鐨勫墠鎻愪笅锛屾濂戒笁鍊�(g猫)鐨勬鐜�銆傝嚦灏�2鍊�(g猫)姝ｉ潰鍚戜笂鐨勬鐜囩偤13/16锛�P锛�AB锛夌殑姒傜巼鐐�5/16锛屽緱5/13

鍋囪ō(sh猫)浜嬩欢A锛氳嚦灏戝嚭鐝�(xi脿n)鍏╁€�(g猫)姝ｉ潰锛�B锛氭伆濂藉嚭鐝�(xi脿n)涓夊€�(g猫)姝ｉ潰銆�
A鍜�B婊胯冻璨濆姫鍔涚崹(d煤)绔嬭│椹�(y脿n)姒傚瀷锛屽嚭鐝�(xi脿n)姝ｉ潰鐨勬鐜�p=1/2
P(A)=1-(1/2)^5-(C5|1)*(1/2)*(1/2)^4=13/16
A鍖呭惈B锛�P(AB)=P(B)=(C5|3)*(1/2)^3*(1/2)^2=5/16
鎵€浠ワ細P(B|A)=P(AB)/P(A)=5/13銆�

6銆�  瑷�(sh猫)鏈�n鍊�(g猫)鐞冨拰n鍊�(g猫)鑳借鐞冪殑鐩掑瓙锛屽畠鍊戝悇绶ㄦ湁搴忚櫉(h脿o)1,2,....n浠婇毃姗�(j墨)灏囩悆鍒嗗垾鏀惧湪鐩掑瓙涓�锛屾瘡鍊�(g猫)鐩掓斁涓€鍊�(g猫)锛屾眰鍏╁€�(g猫)搴忚櫉(h脿o)鎭板ソ涓€鑷寸殑鏁�(sh霉)灏�(du矛)鍊�(g猫)鏁�(sh霉)鐨�鏁�(sh霉)瀛�(xu茅)鏈熸湜銆傦紙绛旀锛�1锛�

銆�鎬濊矾銆�1/nⁿ锛�N鍊�(g猫)鐞冮€�(j矛n)N鍊�(g猫)鐩掓湁N鐨�N娆℃柟绋帓鍒�锛屽皪(du矛)铏�(h脿o)鍏ュ骇鍙湁1绋帓鍒�銆�

7銆�  鑻ユ柟绋�x²+p*x+37=0鎭版湁鍏╁€�(g猫)姝ｆ暣鏁�(sh霉)瑙�x1,x2,鍓�((x1+1)*(x2+1))/p=?
(a) -2, (b) -1 (c)-1/2 (d)1

銆�鎬濊矾銆�椤岀洰瑾�(shu艒)鏈夊叐鍊�(g猫)姝ｆ暣鏁�(sh霉)鐨勬牴锛屾晠鍙兘鏄�1鍜�37锛�p=-38

8銆�  瑷�(sh猫)F(n)=(n+1) ^n-1(n鐐鸿嚜鐒舵暩(sh霉)),鍓�F(n):
(a) 鍙兘琚�n鏁撮櫎 (b)鑳借n*n鏁撮櫎 .....

銆�鎬濊矾銆�鐢ㄤ簩闋�(xi脿ng)寮忓畾鐞嗗幓鍋氱浜岄锛屽彧鑰冩叜n鐨勭郴鏁�(sh霉)锛屾湁涓€鍊�(g猫)鍚�n鐨勯爡(xi脿ng).绯绘暩(sh霉)涓倓鏈変竴鍊�(g猫)n.绛旀鎳�(y墨ng)鐐�b銆�

9銆�  涓€寮电洅瀛愪腑鏈�4寮靛崱鐗�锛屽叾涓叐寮靛崱鐗囧叐闈㈤兘鏄磪鑹诧紝涓€寮靛崱鐗囧叐闈㈤兘鏄稜鑹�锛屼竴寮靛崱鐗囦竴闈㈢磪涓€闈㈢稜銆備换鍙栧叾涓竴寮� 锛岃瀵熷叾涓€闈㈢殑椤忚壊锛屽鏋滆瑙€瀵熺殑涓€闈㈡槸缍犵殑锛屾眰鍙︿竴闈篃鏄稜鑹茬殑姒傝珫銆�
銆�鎬濊矾銆�瑷�(sh猫)A=琚瀵熺殑涓€闈㈡槸缍犵殑锛�B=鍏╅潰閮芥槸缍�
鍓囬渶姹�P锛�B/A锛�=P锛�AB锛�/P锛�A锛�=P锛�B锛�/P锛�A锛�=1/4锛�1/2=1/2锛屾墍绲︾瓟妗堝嵒2/3锛�

10銆�              瑷�(sh猫)锛℃槸锛旓紛锛撶煩闄ｄ笖锛诧紙锛★級锛濓紥锛岋饥锛� 姹傦疾锛堬肌锛級

    銆�鎬濊矾銆�R(B)=3
so: R(AB)=R(A)=2

11銆�              鍦ㄦ埧闁撲腑鏈�10鍊�(g猫)浜�,鍒嗗垾浣╂埓寰�1铏�(h脿o)鍒�10铏�(h脿o)鐨勭磤(j矛)蹇电珷,浠婚伕3浜鸿閷勫叾绱€(j矛)蹇电珷铏�(h脿o)纰�,

姹�:(1)鏈€灏忚櫉(h脿o)纰肩偤5鐨勬鐜�锛�(2)鏈€澶ц櫉(h脿o)纰肩偤5鐨勬鐜�.

銆�鎬濊矾銆�鏈€灏忚櫉(h脿o)纰肩偤5 鐨勬鐜囷細
铏�(h脿o)纰�5宸茬⒑瀹�锛屽彟澶�2浜虹殑铏�(h脿o)纰兼噳(y墨ng)寰�6銆�7銆�8銆�9銆�10涓伕鍑�
鏁呯祫鍚堢殑鍊�(g猫)鏁�(sh霉)鐐�  鎵€浠ユ鐜囩偤 /C 锛�10/120锛�1/12
鍚屾ǎ鏈€澶ц櫉(h脿o)纰肩偤5鐨勬鐜囷細
铏�(h脿o)纰�5宸茬⒑瀹�锛屽彟澶�2浜虹殑铏�(h脿o)纰兼噳(y墨ng)寰�1銆�2銆�3銆�4涓伕鍑�
鏁呯祫鍚堢殑鍊�(g猫)鏁�(sh霉)鐐�C 鎵€浠ユ鐜囩偤C /C 锛�6/120锛�1/20

12銆�              寰�5 闆欎笉鍚岀殑闉嬪瓙涓换鍙�4 鍙�,姹傞€�4鍙瀷瀛愪腑鑷冲皯鏈夊叐鍙厤鎴愪竴闆欑殑姒傜巼鏄灏�

鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘�锛岃珛(q菒ng)鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€�(g猫)浜鸿榛�(di菐n)锛岃垏鏈恫(w菐ng)绔欑劇(w煤)闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊(sh铆)锛屽皪(du矛)鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷(sh铆)鎬�銆佸畬鏁存€�銆佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛(q菒ng)璁€鑰呭儏浣滃弮鑰�锛屽苟璜�(q菒ng)鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�