鐢辨暩(sh霉)瀛�0,1,2,3,4,5绲勬垚鐒￠噸寰�(f霉)鏁�(sh霉)瀛楃殑鍏綅鏁�(sh霉)锛屽叾涓€�(g猫)浣嶆暩(sh霉)瀛楀皬浜庡崄浣嶆暩(sh霉)瀛楃殑鍏辨湁澶氬皯鍊�(g猫)锛�

銆�鎬濊矾銆� 5锛�/2=300

鐢ㄦ帓鍒楃祫鍚堢殑灏�(du矛)绋辨€濇兂鍙互鐞嗚В涓婇潰鐨勮В娉�,鑸夊€�(g猫)绨″柈渚嬪瓙锛�5鍊�(g猫)浜烘帓闅�(du矛)锛岀敳蹇呴爤鎺掑湪涔欏乏閭婄殑鎺掓硶锛�5浜哄叏鎺掑垪鏅�(sh铆)锛岀敳涓嶅湪涔欑殑宸﹂倞灏卞湪涔欑殑鍙抽倞锛屾晠鎺掓硶鏄�1/2*5锛併€�

琚嬪瓙涓(bi膩o)铏�(h脿o)1-9鐨勭悆锛屽緸涓笉鏀惧洖鍙�4鍊�(g猫)锛屾眰鎵€鍙栫殑4鍊�(g猫)鐞冩(bi膩o)铏�(h脿o)鍜岀殑鏈熸湜銆傦紙E=20锛�

銆�鎬濊矾銆�瑷�xi鐐虹i娆″彇鐨勭悆锛�i=1锛�2锛�3锛�4
E(Y=x1+x2+x3+x4)=E(x1)+E(x2)+E(x3)+E(x4)=4*(1/9)*(1+2+3+...+9)=20

锛�閫欓亾椤屾湁鏀惧洖鍜岀劇鏀惧洖鐨勭瓟妗堢浉鍚�锛�

瑷�(sh猫)n鍊�(g猫)浜烘帓鎴愪竴鎺掞紝鐢蹭箼鏄叾涓叐鍊�(g猫)浜�锛屾眰閫�n鍊�(g猫)浜虹殑浠绘剰鎺掑垪涓�锛岀敳涔欎箣闁撴伆鏈�r鍊�(g猫)浜虹殑姒傜巼銆�

銆�鎬濊矾1銆�1銆佸厛灏囩敳銆佷箼2浜烘帓鍒楋細P锛�2锛�2锛�
2銆佺敳涔欎箣闁�R浜猴細P锛�r,n-2锛�
3銆佸皣鐢蹭箼鍙婁箣闁�r浜虹湅浣滀竴鏁撮珨锛岃垏鍏朵粬n-r-2鍋氭帓鍒�
鎵€姹�P=P锛�2锛�2锛�*P锛�r,n-2锛�*(n-r-1)!/n!=2*(n-r-1)/n(n-1)

銆�鎬濊矾2銆�P= =

琚嬩腑鏈夌櫧鐞�5鍙�锛岄粦鐞�6鍙紝闄哥簩(x霉)鍙栧嚭3鐞�锛屾眰
(1)銆侀爢搴�?y脿n)妤硅瘞缂€璇樻瘝鎬�?/span>
(2)銆�2鍙粦鐞冪殑姒傜巼
(3)銆佹湁鏀惧洖鐨勫彇3娆�锛屾眰鍙栧緱鍏╁彧榛戠悆鐨勬鐜�銆�

銆�鎬濊矾銆�(1) P=6*5*5/11*10*9=5/33
(2) P=C(2,5)C(1,5)/C(3,11)=5/11
鐢ㄧ祫鍚堝紡瀛愶細闄哥簩(x霉)鍙�3鐞冪瓑鍍�(ji脿)浜庝竴娆″彇涓夌悆锛屾湁2鐞�?y脿n)妤硅瘶姣嶆€�?锛屼笉鑰冩叜闋嗗簭
涔熷彲浠ョ敤鎺掑垪寮忓瓙锛岀浉鐣�(d膩ng)浜庨粦鐧介粦+榛戦粦鐧�+鐧介粦榛戜箣鍜�
3*6*5*5/11*10*9

鏈�15鐞�锛�5鍊�(g猫)鐐虹櫧鐞冿紝鎶婂畠鍊戦毃姗�(j墨)瑁濋€�(j矛n)5鍊�(g猫)鐩掑瓙锛屾瘡鐩�3鍊�(g猫)锛岃X鐐烘湁鐧界悆鐨勭洅瀛愭暩(sh霉)锛屽墖E锛�X锛�=锛�

銆�鎬濊矾銆�15鍊�(g猫)鐞冩斁鍏�5鍊�(g猫)鐩掑瓙锛屾瘡鐩�3鍊�(g猫)锛屽叡鏈� c(3,15)*c(3,12)*c(3,9)*c(3,6)*c(3,3)绋�
瑷�(sh猫) xi=1锛岀i鍊�(g猫)鐩掑瓙鍏�(n猫i)鏈夌櫧鐞� ,
xi=0锛岀i鍊�(g猫)鐩掑瓙鍏�(n猫i)鐒＄櫧鐞�(i=1,2,3,4,5)
xi=1鏅�(sh铆)锛岀i鍊�(g猫)鐩掑瓙鍏�(n猫i)鍙兘鏈夌櫧鐞�1锛�2锛屾垨3鍊�(g猫)
灏�(du矛)鎳�(y墨ng)鐨勫彲鑳界偤c(1,5)c(2,10)*c(3,12)*c(3,9)*c(3,6)*c(3,3)绋�,
c(2,5)c(1,10)*c(3,12)*c(3,9)*c(3,6)*c(3,3)绋�锛屽拰c(3,5)*c(0,10)*c(3,12)*c(3,9)*c(3,6)*c(3,3)绋� 銆�
涔熷彲浠ュ厛姹�xi=0;灏�(du矛)鎳�(y墨ng)鐐�c(0,5)c(3,10)*c(3,12)*c(3,9)*c(3,6)*c(3,3)绋� .
P{xi=1}=1-p{xi=0}=67/91;
E(xi)=67/91
鏁呮湁鐧界悆鐨勭洅瀛愬€�(g猫)鏁�(sh霉)浣�E(x1+x2+x3+x4+x5)=5*67/91=3.68

鍦�n*n鍊�(g猫)灏忔牸瀛愮殑妫嬬洡涓�,闅ㄦ(j墨)鍦板妰鍑虹敱鑻ュ共鍊�(g猫)灏忔柟鏍肩祫鎴愮殑鐭╁舰,姹�:鎭板ソ绲勬垚姝ｆ柟褰㈢殑姒傜巼.

銆�鎬濊矾銆�瑷�(sh猫)xi=i,yj=j鐐哄彇鍑虹殑鐭╁舰鐨勯暦鍜屽銆�
鍓�i=1,2,3,....n;j=1,2,3,...n.
x1鏈�n-1+1=n绋彲鑳�锛�x2鏈�n-2+1绋彲鑳�锛�...xn鏈�n-n+1=1绋彲鑳�
鍏辨湁n+(n-1)+...+1=n(n+1)/2
鏁�p{xi=i}=(n-i+1)/(n(n+1)/2)
鍚岀悊P{yj=j}=(n-j+1)/(n(n+1)/2)
姝ｆ柟褰㈢偤i=j
p{x=i,y=i}=P{x=i}P{y=i}
P{姝ｆ柟褰�}=∑p{x=i,y=i}=∑(n+1-i) ²/(n(n+1锛�/2)^2i=1,2,3,....,n
鍥�?y脿n)?sum;(n-i+1) ²=n ²+(n-1) ²+....+1=n(n+1)(2n+1)/6
鎵€浠�P{姝ｆ柟褰�}=(n(n+1)(2n+1)/6)/(n(n+1锛�/2) ²=

10鍊�(g猫)鐩稿悓鐨勫皬鐞冩斁鍏ョ法铏�(h脿o)鐐�1銆�2銆�3鐨勪笁鍊�(g猫)鐩掑瓙鍏�(n猫i)锛岃姹傛瘡鍊�(g猫)鐩掑瓙鐨勭悆鏁�(sh霉)涓嶅皬浜庡畠鐨勭法铏�(h脿o)鏁�(sh霉)锛屽墖涓嶅悓鐨勬斁娉曞叡鏈夛紙锛夌ó锛�

銆�鎬濊矾1銆�1铏�(h脿o)鐩掑瓙鍙互鏀�1—5鍊�(g猫)鐞�锛�2铏�(h脿o)鐩掑瓙鍙互鏀�2—6鍊�(g猫)鐞�锛�3铏�(h脿o)鐩掑瓙鍙互鏀�3—7鍊�(g猫)鐞�锛屾垜鐨勭瓟妗堝叡15绋€�

銆�鎬濊矾2銆�涓夊€�(g猫)鐩掑瓙蹇呴爤鍒嗗垾鑷冲皯鏀�1锛�2锛�3鍊�(g猫)鐞�锛屽墿涓�4 鍊�(g猫)涓嶅悓鐨勬斁娉曞嵆鎵€姹傛暩(sh霉)銆�
1锛� 鍙斁鍦ㄤ竴鍊�(g猫)鐩� 瀛愪腑锛�C锛�3锛�1锛�
2锛� 鏀惧湪鍏╁€�(g猫)鐩掑瓙涓細C锛�3锛�2锛�*3
3锛� 鏀惧湪涓夊€�(g猫)鐩掑瓙涓細C锛�3锛�1锛�
姝や笁闋�(xi脿ng)鐩稿姞寰�15銆�

648鐨勬绱勬暩(sh霉)鐨勫€�(g猫)鏁�(sh霉)鏄�______銆�(20)

648=2³*3⁴
銆�鎬濊矾銆�姝ｇ磩鏁�(sh霉)鐐�4*5=20鍊�(g猫).

锛�2鏈�3鍊�(g猫),鍏辨湁鍙�0,1,2,3鍊�(g猫)鍥涚ó鍙兘.
3鏈�4鍊�(g猫),鍏辨湁鍙�0,1,2,3,4鍊�(g猫)5绋彲鑳�.    鎵€浠�4*5=20锛�

5ⁿ + 13ⁿ 锛� n 鏄伓鏁�(sh霉)锛夐櫎浠�3鐨勪綑鏁�(sh霉)鏄�_____銆� (2)

銆�鎬濊矾銆�5ⁿ =(6-1) ⁿ = (-1) ⁿ =1,13 ⁿ =(12+1) ⁿ =1 ⁿ =1 浣�2

瑷�(sh猫)闆嗗悎A鐨勫厓绱犲€�(g猫)鏁�(sh霉)鐐� 锛屽墖闆嗗悎A鐨勫惈濂囨暩(sh霉)鍊�(g猫)鍏冪礌鐨勫瓙闆嗙殑鍊�(g猫)鏁�(sh霉)鏄� ______銆�

銆�鎬濊矾銆�c(1,n)+c(3,n)+....=1/2*[c(0,n)+c(1,n)+c(2,n)+...+c(n,n)]=1/2*2 ⁿ =2 ^n-1