概率论！设随机变量X服从[2,6]上的均匀分布，则其密度函数为？谢谢！ 设随机变量x服从(-2,2)上的均匀分布，则随机变量Y=X^...
\u8bbe\u968f\u673a\u53d8\u91cfx\u670d\u4ece[0,2]\u5747\u5300\u5206\u5e03\u6c42y=x^2\u5bc6\u5ea6\u51fd\u6570\u5177\u4f53\u56de\u7b54\u5982\u4e0b\uff1a
\u968f\u673a\u53d8\u91cf\u5728\u4e0d\u540c\u7684\u6761\u4ef6\u4e0b\u7531\u4e8e\u5076\u7136\u56e0\u7d20\u5f71\u54cd\uff0c\u53ef\u80fd\u53d6\u5404\u79cd\u4e0d\u540c\u7684\u503c\uff0c\u6545\u5176\u5177\u6709\u4e0d\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\uff0c\u4f46\u8fd9\u4e9b\u53d6\u503c\u843d\u5728\u67d0\u4e2a\u8303\u56f4\u7684\u6982\u7387\u662f\u4e00\u5b9a\u7684\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u968f\u673a\u53d8\u91cf\u53d6\u67d0\u4e2a\u6570\u503c\u6216\u843d\u5165\u67d0\u4e2a\u6570\u503c\u533a\u95f4\u8fd9\u6837\u7684\u57fa\u672c\u4e8b\u4ef6\u7684\u96c6\u5408\uff0c\u5e94\u5f53\u5c5e\u4e8e\u6240\u8003\u8651\u7684\u4e8b\u4ef6\u57df\u3002
\u6709\u4e9b\u968f\u673a\u73b0\u8c61\u9700\u8981\u540c\u65f6\u7528\u591a\u4e2a\u968f\u673a\u53d8\u91cf\u6765\u63cf\u8ff0\u3002\u4f8b\u5982\u5bf9\u5730\u9762\u76ee\u6807\u5c04\u51fb\uff0c\u5f39\u7740\u70b9\u7684\u4f4d\u7f6e\u9700\u8981\u4e24\u4e2a\u5750\u6807\u624d\u80fd\u786e\u5b9a\uff0c\u56e0\u6b64\u7814\u7a76\u5b83\u8981\u540c\u65f6\u8003\u8651\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u4e00\u822c\u79f0\u540c\u4e00\u6982\u7387\u7a7a\u95f4(\u03a9,F,p)\u4e0a\u7684n\u4e2a\u968f\u673a\u53d8\u91cf\u6784\u6210\u7684n\u7ef4\u5411\u91cfX=(x1,x2,\u2026\uff0cxn)\u4e3an\u7ef4\u968f\u673a\u5411\u91cf\u3002
\u968f\u673a\u53d8\u91cf\u53ef\u4ee5\u770b\u4f5c\u4e00\u7ef4\u968f\u673a\u5411\u91cf\u3002\u79f0n\u5143x1,x2,\u2026\uff0cxn\u7684\u51fd\u6570\u4e3aX\u7684(\u8054\u5408)\u5206\u5e03\u51fd\u6570\u3002\u53c8\u5982\u679c(x1,x2)\u4e3a\u4e8c\u7ef4\u968f\u673a\u5411\u91cf\uff0c\u5219\u79f0x1+ix2(i2=-1)\u4e3a\u590d\u968f\u673a\u53d8\u91cf\u3002
\u4f60\u7ed9\u8fd9\u4e2a\u7b54\u6848\u4e0d\u5bf9
\u8bbe-2<x<2\u65f6\uff0cf(x)=k
1=\u222b(-2\u52302)f(x)dx=4k
\u6240\u4ee5k=1/4
FY(y)=P(Y<y)=P(x^2<y)
\u5f53y\u22640\u65f6\uff0cFY(y)=0
fY(y)=[FY(y)]'=0
\u5f530<y\u22644\u65f6
FY(y)=P(x^2<y)=P(-\u221ay<x<\u221ay)=\u222b(-\u221ay\u5230\u221ay)f(x)dx=1/2*\u221ay
fY(y)=[FY(y)]'=1/(4*\u221ay)
\u5f53y\u22651\u65f6\uff0cFY(y)=1
fY(y)=[FY(y)]'=0
\u6240\u4ee5\u7b54\u6848\u662f
1/(4*\u221ay)\uff0c0<y\u22644
0\uff0c \u5176\u4ed6
绛旓細瀵嗗害鍑芥暟涓篺(x)={1/4(2
绛旓細瀵嗗害鍑芥暟涓篺(x)={1/4(2<=x<=6)銆0(鍏跺畠)}銆
绛旓細E(2X²)+3E(Y)=2E(X²)+3E(Y)=2脳(1/2)+3/4=7/4锛涙敞鎰忥細E(X)=1/2 E(X²)=D(X)+E²(X)=1/4+1/4=1/2 //: 鍧囨柟鍊硷紳鏂瑰樊+鍧囧肩殑骞虫柟 E(Y)=1/4
绛旓細2銆佷綘濂斤紒X鏈嶄粠鍙傛暟涓何荤殑娉婃澗鍒嗗竷鏃禘(X)=位锛孍(X^2)=位+位^2锛鐢变簬E[(X-2)(X-3)]=E(X^2-5X+6)=E(X^2)-5E(X)+6=(位^2)-4位+6=2锛屾墍浠ュ彲浠ヨВ鍑何=2銆傜粡娴庢暟瀛﹀洟闃熷府浣犺В璇峰強鏃堕噰绾炽3銆丏锛圶锛夋寚鏂瑰樊锛孍锛圶锛夋寚鏈熸湜銆傛柟宸槸鍦姒傜巼璁鍜岀粺璁℃柟宸 閲闅忔満鍙橀噺鎴栦竴缁勬暟鎹...
绛旓細姒傜巼璁闂,宸茬煡闅忔満鍙橀噺X鏈嶄粠鍙傛暟涓2鐨勬寚鏁板垎甯,姹侲(e^(-2x))鎴戞眰鏉ユ眰鍘婚兘鏄1/4涓轰粈涔堢瓟妗堟槸1/2姹傚ぇ绁炴寚鏁!!!... 姒傜巼璁洪棶棰,宸茬煡闅忔満鍙橀噺X鏈嶄粠鍙傛暟涓2鐨勬寚鏁板垎甯,姹侲(e^(-2x)) 鎴戞眰鏉ユ眰鍘婚兘鏄1/4 涓轰粈涔堢瓟妗堟槸1/2 姹傚ぇ绁炴寚鏁!!! 灞曞紑 ...
绛旓細绗竴棰樹綘鏄寚鐭╂瘝鍑芥暟鍚э紝閫塁锛屽氨鏄寜瀹氫箟姹傘傜浜棰樺鏁版鎬佸垎甯(浣犲啓鐨凩N鏄繖涓剰鎬濆惂锛)鐨勬湡鏈涙柟宸湁鍏紡锛屽鏋滀綘瑕佺洿鎺ョ畻鐨勮瘽姣旇緝楹荤儲锛屼綘闇瑕佺畻鍑烘潵EX鍜孍(X^2)锛屽叾涓渶瑕佸弽澶嶇敤鍒板噾骞虫柟鐨勬妧宸с
绛旓細瑙ｅ緱EX=P=锛X涓婃柟涓妯級锛3锛夊洜涓篍锛圶涓婃柟涓妯級=EX1=P锛屾墍浠ワ紝涓ょ浼拌閮芥槸P鐨勬棤鍋忎及璁°傛ц川锛氱煩浼拌鏄埄鐢ㄦ牱鏈煩鏉ヤ及璁℃讳綋涓浉搴旂殑鍙傛暟銆傞鍏堟帹瀵兼秹鍙婄浉鍏冲弬鏁扮殑鎬讳綋鐭╋紙鍗虫墍鑰冭檻鐨闅忔満鍙橀噺鐨勫箓鐨勬湡鏈涘硷級鐨勬柟绋嬨傜劧鍚庡彇鍑轰竴涓牱鏈苟浠庤繖涓牱鏈及璁℃讳綋鐭┿傛帴鐫浣跨敤鏍锋湰鐭╁彇浠ｏ紙鏈煡鐨勶級鎬讳綋鐭...
绛旓細-2x) dx =1-(1-y)=y 3銆佸綋y<0鏃 F(y)=P(e^(-2X)鈮1-y)=P(X鈮(-1/2)ln(1-y)) 娉細(-1/2)ln(1-y)鏄釜璐熸暟 =0 缁间笂锛欶(y)=1 y>1 x 0鈮鈮1 0 y<0 鍥犳Y涓(0,1)涓婄殑鍧囧寑鍒嗗竷銆
绛旓細绛旀鏄細P锛x<y锛=2/3 鍏蜂綋瑙ｆ硶濡備笅锛氳В棰樻濊矾锛氭眰鍑篨Y鑱斿悎姒傜巼瀵嗗害浠ュ悗,鍦ㄥ潗鏍囪酱XY涓婄敾鍑篩=-X-1鐨勭嚎,鍐嶆牴鎹甔鍜孻鐨勫彇鍊艰寖鍥磇e,鍗砐>0,Y>0,鎶婅仈鍚堟鐜囧瘑搴﹀湪鍥存垚鐨勪笁瑙掑舰鍐呰繘琛2閲嶇Н鍒,鍗冲彲绠楀嚭鏈鍚庣瓟妗堛
绛旓細娉婃澗鍒嗗竷鍏紡锛氶殢鏈哄彉閲廥鐨姒傜巼鍒嗗竷涓猴細P{X=k}=位^k/(k锛乪^位)k=0锛1锛..鍒欑ОX鏈嶄粠鍙傛暟涓何伙紙位0锛夌殑娉婃澗鍒嗗竷锛宬浠ｈ〃鐨勬槸鍙橀噺鐨勫硷紝涓旀槸鑷劧鏁般傛硦鏉惧垎甯冨叕寮忥細P{X=k}=位^k/(k锛乪^位)銆璁鹃殢鏈哄彉閲廥鏈嶄粠鍙傛暟涓2鐨勬硦鏉惧垎甯,E(X),D(X)=?姹傝缁嗚В绛1銆佸叿浣撳洖绛斿鍥撅細浣嶇疆鍙傛暟纬...
