设随机变量X与Y相互独立，且服从同一分布，X的分布律为 求：设X与Y是同分布的随机变量，P(X=1)=0.3, P(...
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P(Z=1)= P(X=1, Y=0)+ P(X=0, Y=1)+ P(X=1, Y=1)= 3/4.
P(Z=0) =:P(X=0, Y=0) =1/4..
Z的分布律: P(Z=0)=1/4, P(Z=1) = 3/4.
x,y互相独立
设x的密度函数为f(x),y的密度函数为f(y)
它们的联合密度函数为f(x,y)=f(x)f(y)
f(y,x)=f(y)f(x)=f(x,y)
f(x,y)关于y=x对称
p(x<=y)的区域是直线y=x的下侧
p(x<=y)=积分f(x,y)dxdy=(1/2)整个平面的积分f(x,y)
p(x<=y)=1/2
绛旓細銆愮瓟妗堛戯細鍥犱负X涓嶻鐙珛鍚屽垎甯冿紝鏁匬{a锛渕in(X锛Y)鈮}=P{min(X锛孻)鈮}P{min(X锛孻)鈮}=1-P{min(X锛孻)锛瀊}-[1-P{min(X锛孻)锛瀉}]=P{min(X锛孻)锛瀉}-P}min(X锛孻)锛瀊}=P(X锛瀉锛孻锛瀉)-P(X锛瀊锛孻锛瀊)=P(X锛瀉)P(Y锛瀉)-P(X锛瀊)P(Y锛瀊)=[P(X锛瀉)]2...
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绛旓細1) E(尉)=E(X+Y)=E(X)+E(Y)=0+0=0锛2) E(畏)=E(X-Y)=E(X)-E(Y)=0-0=0锛3) D(尉)=E[尉-E(尉)]²=E[X²+2XY+Y²]=D(X)+D(Y)=1+1=2;4) D(畏)=E[畏-E(畏)]²=E[X²-2XY+Y²]=D(X)+D(Y)=1+1=2;
绛旓細X+Y ~ B(2, p)銆傝繖鏄洜涓猴紝闅忔満鍙橀噺X鍜孻鐩镐簰鐙珛du锛屼笖鍧囨湇浠庝簬B(1,p)锛孹+Y鐩稿綋浜庣嫭绔嬮噸澶嶅仛浜嗕袱娆℃姏纭竵鐨勫疄楠岋紝涓2閲嶈礉鍔埄姒傚舰锛屾晠X+Y ~ B(2, p)銆傚叧蹇冪殑涔熻鏄叾鐐瑰拰鏁颁负7锛岃屽苟涓嶅叧蹇冨叾瀹為檯缁撴灉鏄惁鏄紙1锛6锛夋垨锛2锛5锛夋垨锛3锛4锛夋垨锛4锛3锛夋垨锛5锛2锛夋垨锛6锛1锛...
绛旓細銆愮瓟妗堛戯細姝ｆ佸垎甯冪殑绾挎х粍鍚堬紟鍥犱负X锛孻鐩镐簰鐙珛锛屼笖閮芥湇浠庢鎬佸垎甯冿紝鎵浠ュ畠浠殑绾挎х粍鍚圵=2X-Y鏈嶄粠姝ｆ佸垎甯冿紝浠庤屽嚱鏁癦=W+3涔熸湇浠庢鎬佸垎甯冿紟璁＄畻鏁板瓧鐗瑰緛锛屽緱 E(Z)=2E(X)-E(Y)+3=5锛孌(Z)=4D(X)+D(Y)=17锛庝簬鏄紝姹傚緱鍑芥暟z鐨勬鐜囧瘑搴︺傛眰浜岀淮闅忔満鍙橀噺鐨勫嚱鏁扮殑鍒嗗竷锛屼竴鑸渶瑕佷粠鍒嗗竷...
绛旓細姒傜巼缁熻锛屾鐜囧垎甯冮棶棰,璁鹃殢鏈哄彉閲廥涓嶻鐩镐簰鐙珛锛屼笖鍧囨湇浠庝簬鍙傛暟涓簆鐨0-1鍒嗗竷B(1,p)(0姒傜巼缁熻锛屾鐜囧垎甯冮棶棰橈紝璁鹃殢鏈哄彉閲廥涓嶻鐩镐簰鐙珛锛屼笖鍧囨湇浠庝簬鍙傛暟涓簆鐨0-1鍒嗗竷銆侱(XY)=E[(XY)^2]-[E(XY)]^2 =E(X^2*Y^2)-[E(X)*E(Y)]^2 =E(X^2)*E(Y^2)-(EX)^2*E(Y)^2 ...
绛旓細绛旀鏄細P锛坸<y锛=2/3 鍏蜂綋瑙ｆ硶濡備笅锛氳В棰樻濊矾锛氭眰鍑XY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X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
绛旓細璁鹃殢鏈哄彉閲廥涓嶻鐩镐簰鐙珛锛屼笖鍧囨湇浠庡弬鏁拔=1鐨勬寚鏁板垎甯冿紝姹傝瘉锛氬嚱鏁癢=X锛媃涓庝篃鐩镐簰鐙珛銆傚洜涓篨涓嶻鐩镐簰鐙珛 鎵浠涓嶻鐨勭浉鍏崇郴鏁=0 鍒欐牴鎹浉鍏崇郴鏁板畾涔 Cov(X锛Y)=0 D锛2X-Y锛=4D(X)+D(Y)-4Cov(X锛孻)D锛2X-Y锛=4D(X)+D(Y)=12 闅忔満浜嬩欢鏁伴噺鍖栫殑濂藉鏄彲浠ョ敤鏁板鍒嗘瀽鐨勬柟娉曟潵鐮旂┒...
绛旓細P{min{X,Y}鈮1}=1-P{min{X,Y}>1}=1-P{X>1,Y>1} 鈭闅忔満鍙橀噺X涓嶻鐩镐簰鐙珛,涓鍧囨湇浠庡尯闂碵0,3]涓婄殑鍧囧寑鍒嗗竷 鈭碢{min{X,Y}鈮1}=1-P{min{X,Y}>1}=1-P{X>1,Y>1}=1-[1/3*(3-1)]^2=5/9
