求概率统计大神们解这道最大似然估计值题！！
\u6709\u5173\u6982\u7387\u8bba\u7684\u9898\u76ee\uff0c\u6c42\u5927\u795e\u89e3\u7b54\uff01\uff01~\u56e0\u4e3aX1.X2\uff0cX3,....Xn\u662f\u603b\u4f53\u7684\u6837\u672c\uff0c\u6240\u4ee5\u5b83\u4eec\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff0cX~N(\u03bc\uff0c\u03c3²)\uff0c
\u6240\u4ee5X\u5e73\u5747\u503c~N(\u03bc\uff0c\u03c3²/n)\u3002\u56e0\u4e3aXn+1~N(\u03bc\uff0c\u03c3²)\u4e0eX\u5e73\u5747\u503c\u72ec\u7acb\uff0c\u6240\u4ee5
Xn+1\uff0dX\u5e73\u5747\u503c~N(0\uff0c(n+1)\u03c3²/n).\u6240\u4ee5\uff08Xn+1\uff0dX\u5e73\u5747\u503c\uff09/\u221a(n+1\u03c3²/n)~N(0\uff0c1)
(n-1)S²/\u03c3²~x²(n-1),\u6240\u4ee5\uff08Xn+1\uff0dX\u5e73\u5747\u503c\uff09/\u221a(n+1\u03c3²/n)/\u221a(n-1)S²/\u03c3²/(n-1)~t(n-1)
\u4e0a\u9762\u7684\u5f0f\u5b50\u662f\u7531\u516c\u5f0fX/\u221aY/N~t(N) \u5176\u4e2dX~N(0\uff0c1)\uff0cY~x²(N)
\u5316\u7b80\u5f97\uff08Xn+1\uff0dX\u5e73\u5747\u503c\uff09/S\u221an/(n+1)
l(t)=\u03a3{ln(6)+ln(xi)-3ln(t)+ln(t-xi)}
l'(t)=-3n/t+\u03a3(1/(t-xi))
3n/t=\u03a3(j=1~n)[{\u8fde\u4e58(i=1~n)(t-xi)}/(t-xj)]/\u03a3(k=1~n)(t-xk)
\u6c42\u6700\u5927\u62df\u7136\u8981\u6c42\u4e00\u5143i\u6b21\u65b9\u7a0b\u7684\u89e3
利用导数求出当θ=5/6时
f(x1=1,x2=2,x3=1 | θ)取的最大值，
即θ最大似然估计为5/6
绛旓細鐭╀及璁℃硶 EX=鈭玿f(x)dx=(胃+1)/(胃+2)--->胃=(1-2EX)/(EX-1)鏋澶т技鐒娉 L(x,胃)=(胃+1)^n(x1.x2...xn)^胃 Ln(L(x,胃))=nLn(胃+1)+胃(Ln(x1.x2...xn))∂Ln(L)/∂胃=0--->胃=n/[Ln((x1.x2...xn)^(-1))]-1 鏂瑰樊宸茬煡锛岀敤U妫楠屾硶 ...
绛旓細1銆佺煩浼拌 EX=鈭玿f(x)dx=鈭玿尾x^(尾-1)dx=尾/(尾+1)=x(骞冲潎锛--尾=x(骞冲潎)/(1-x(骞冲潎锛)2銆鏈澶т技鐒浼拌 L(尾)=TT尾xi^(尾-1)-->LnL(尾)=nLn尾+鈭(尾-1)Ln(xi)d(LnL(尾))/d尾=0--->n/尾+鈭慙n(xi)=0-->尾=n/鈭慙n(1/xi)
绛旓細鍒氭墠浣犻棶鐨勫扡鏄冀鐜涘嚱鏁 鐢ㄦ潵绠鍖栧畾绉垎鐨勮绠 杩欓鍒╃敤鎬讳綋鐭╋紳瀵瑰簲鐨勬牱鏈煩 璁＄畻涓や釜鍙傛暟鐨勭煩浼拌 鍒╃敤浼肩劧鍑芥暟 璁＄畻涓や釜鍙傛暟鐨勬瀬澶т技鐒浼拌 杩囩▼濡備笅锛
绛旓細鏈澶т技鐒浼拌锛屽彧鏄竴绉姒傜巼璁哄湪缁熻瀛︾殑搴旂敤锛屽畠鏄弬鏁颁及璁＄殑鏂规硶涔嬩竴銆傝鐨勬槸宸茬煡鏌愪釜闅忔満鏍锋湰婊¤冻鏌愮姒傜巼鍒嗗竷锛屼絾鏄叾涓叿浣撶殑鍙傛暟涓嶆竻妤氾紝鍙傛暟浼拌灏辨槸閫氳繃鑻ュ共娆¤瘯楠岋紝瑙傚療鍏剁粨鏋滐紝鍒╃敤缁撴灉鎺ㄥ嚭鍙傛暟鐨勫ぇ姒傚笺傛渶澶т技鐒朵及璁℃槸寤虹珛鍦ㄨ繖鏍风殑鎬濇兂涓婏細宸茬煡鏌愪釜鍙傛暟鑳戒娇杩欎釜鏍锋湰鍑虹幇鐨勬鐜囨渶澶э紝鎴戜滑褰撶劧涓...
绛旓細螤鏄箻绉鍙 螤(i=1~n) Ti =T1*T2*T3...Tn 姹傛渶澶ф嫙鐒朵竴鑸槸涓よ竟姹傝嚜鐒跺鏁帮紝鎶婁箻绉彉鎴愪簡姹傚拰鍐嶆眰瀵硷紝浣垮鏁颁负0姹傛渶澶瀵规暟鎷熺劧锛屽苟楠岃瘉瀵兼暟鍦0鐐规椂鍑芥暟鍙栫殑鏋佸兼槸鏈澶у 濡傛灉涓や釜鎷熺劧浼拌閲忥紝瑕佹眰瀵规暟鎷熺劧鍑芥暟鐨勪袱涓亸瀵硷紝瑙ｄ袱涓亸瀵肩瓑浜0鐨勬柟绋嬶紝鐒跺悗鍒嗗埆楠岃瘉鏄惁鏄渶澶у鏁版嫙鐒 ...
绛旓細鍙堬紝X'=E(X)锛屸埓位鐨勭煩浼拌位'=(1/n)鈭憍i锛宨=1,2锛屸︼紝n銆傗憽鏋澶т技鐒浼拌銆備綔浼肩劧鍑芥暟L(x,位)=鈭廝(Xi=k)=[e^(-n位)](位^鈭憍i)/鈭廩(xi)!]銆傚啀姹∂[lnL(x,位)]/∂位銆佸苟浠ゅ叾鍊间负0锛屸埓-n+(1/位)鈭憍i=0銆傗埓位鐨勬瀬澶т技鐒朵及璁∥'=(1/n)鈭憍i锛宨=1,...
绛旓細鏈澶т技鐒浼拌 鏄竴绉缁熻鏂规硶 ,瀹冪敤鏉ユ眰涓涓牱鏈泦鐨勭浉鍏姒傜巼瀵嗗害鍑芥暟鐨勫弬鏁.杩欎釜鏂规硶鏈鏃╂槸閬椾紶瀛﹀浠ュ強缁熻瀛﹀缃楃撼寰仿疯垂闆 鐖靛＋鍦1912骞磋嚦1922骞撮棿寮濮嬩娇鐢ㄧ殑.鈥滀技鐒垛濇槸瀵筶ikelihood 鐨勪竴绉嶈緝涓鸿创杩戞枃瑷鏂囩殑缈昏瘧,鈥滀技鐒垛濈敤鐜颁唬鐨勪腑鏂囨潵璇村嵆鈥鍙兘鎬鈥.鏁呰,鑻ョО涔嬩负鈥滄渶澶у彲鑳芥т及璁♀濆垯鏇村姞...
绛旓細璁炬讳綋X鏈嶄粠娉婃澗鍒嗗竷P(位)锛孭(X鈮1) 鐨鏈澶т技鐒浼拌閲忔槸1位xixi锛乪−位=e−n位n蟺i锛1位xixi锛佲埓lnL锛−n位+ni...鍥犱负X鏈嶄粠鍙傛暟涓何荤殑娉婃澗鍒嗗竷锛涙墍浠(X锛漨)锛澪籱m!e−位锛岋紙m=0锛1锛2锛屸︼級璁緓1锛寈2锛屸n鏄潵鑷讳綋鐨勪竴缁勬牱鏈娴嬪煎垯鏈澶т技鐒跺嚱鏁颁负...
绛旓細EX=0脳胃2+1脳2胃锛1-胃锛+2脳胃2+3脳锛1-2胃锛=3-4胃 鏁咃細胃锛¼锛3−EX锛壩哥殑鐭╀及璁￠噺涓猴細胃=¼锛3-X锛夋牴鎹粰瀹氱殑鏍锋湰瑙傚療鍊艰绠楋細X=1/8锛3+1+3+0+3+1+2+3锛=2 鍥犳胃鐨勭煩浼拌鍊间负锛毼=¼锛3-X锛=¼瀵逛簬缁欏畾鐨勬牱鏈硷紝浼肩劧鍑芥暟涓猴細L锛...
绛旓細鏈澶т技鐒浼拌锛屽彧鏄竴绉姒傜巼璁哄湪缁熻瀛︾殑搴旂敤锛屽畠鏄弬鏁颁及璁＄殑鏂规硶涔嬩竴銆傝鐨勬槸宸茬煡鏌愪釜闅忔満鏍锋湰婊¤冻鏌愮姒傜巼鍒嗗竷锛屼絾鏄叾涓叿浣撶殑鍙傛暟涓嶆竻妤氾紝鍙傛暟浼拌灏辨槸閫氳繃鑻ュ共娆¤瘯楠岋紝瑙傚療鍏剁粨鏋滐紝鍒╃敤缁撴灉鎺ㄥ嚭鍙傛暟鐨勫ぇ姒傚笺傛渶澶т技鐒朵及璁℃槸寤虹珛鍦ㄨ繖鏍风殑鎬濇兂涓婏細宸茬煡鏌愪釜鍙傛暟鑳戒娇杩欎釜鏍锋湰鍑虹幇鐨勬鐜囨渶澶э紝鎴戜滑褰撶劧涓...
