设随机变量(X,Y)的分布律为P(X=1,Y=10)=P(X=2,Y=5)=0.5试求ρ 设(X,Y)的联合分布律为P(X=1,Y=10)=P(X=2...
\u968f\u673a\u53d8\u91cf(X,Y)\u7684\u8054\u5408\u5206\u5e03\u5f8b\u4e3aP(X=1,Y=0)=0.1,P(X=1,Y=2)=0.2,P(X=2,Y=0)=a,P(X=2,Y=2)=b,\u5219E(X+2)\u7b49\u4e8e\uff1f\u5177\u4f53\u56de\u7b54\u5982\u56fe\uff1a
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\u6269\u5c55\u8d44\u6599\uff1a
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\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u968f\u673a\u53d8\u91cf
EX=1\u00d70.5+2\u00d70.5=1.5
E\uff08X²\uff09=1²\u00d70.5+2²\u00d70.5=2.5
DX=E\uff08X²\uff09-\uff08EX\uff09²=0.25
EY=5\u00d70.5+10\u00d70.5=7.5
E\uff08Y²\uff09=5²\u00d70.5+10²\u00d70.5=62.5
DY=E\uff08Y²\uff09-\uff08EY\uff09²=6.25
E\uff08XY\uff09=1\u00d75\u00d70=1\u00d710\u00d70.5=2\u00d75\u00d70.5+2\u00d710\u00d70=10
\u56e0\u4e3acov\uff08X\uff0cY\uff09-EX\u00d7EY=-1.25
\u6240\u4ee5\uff1aP=cov\uff08X\uff0cY\uff09/\u221aDX\u221aDY=-11.25\u00f7\u221a0.25\u00d7\u221a6.25=-1
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因为只有这两组取值，可以得出Y=15-5X，所以相关系数为-1。如果一定要计算的话，可以参考下图列出概率表并计算期望、方差、协方差，最后求出相关系数。
绛旓細Y鐨勮竟缂鍒嗗竷寰嬩负锛歒 1 4 P 1/2 1/2 鏄撴眰寰楋紝E(X)=0锛孍(Y)=5/2锛孍(XY)=-2路4路1/4+(-1)路1路1/4+1路1路1/4+2路1路1/4=0 鈭礐ov(X锛孻)=E(XY)-E(X)路E(Y)=0 鈭碭涓嶻涓嶇浉鍏炽(2)P(X=-2锛孻=1)=0鈮燩(X=-2)路P(Y=1)鈭碭涓嶻涓嶇浉浜掔嫭绔嬨闅忔満鍙橀噺X鍜...
绛旓細棣栧厛a+b=1-1/4-1/4=1/2 P{X=0|Y=0}=1/2琛ㄧず鍦╕=0鐨勬儏鍐典笅锛孹=0鐨勬鐜囦负1/2锛岄偅涔坅=1/4 鍒檅=1/4
绛旓細a+0.2=0.3,鏁卆=0.1;0.3+0.4+0.1+b=1锛屾晠b=0.2.P(X=-1)=0.3,P(X=0)=0.4,P(X=2)=0.3;P(Y=1)=0.5,P(Y=3)=0.5 浠わ紱a+1/6+1/12+ +1/6+1/6+1/6+ +1/12+1/6+b=1,寰楋細a+b+1=1锛屽嵆锛歛+b=0銆傚洜涓篴>=0, b>=0,鏁呯煡閬撳繀鏈夛細a=0锛宐=0...
绛旓細杈圭紭鍒嗗竷寰嬶紝浠x涓渚锛寈鍙0鐨勬鐜囨槸1锛6锛屽彇锛1姒傜巼鏄1锛3锛1锛12锛5锛12锛屽彇2鐨勬鐜囧氨鏄5锛12锛岄偅涔堝仛涓涓〃锛岀涓琛屾槸鍙兘鐨勫彇鍊0锛1锛2锛庣浜岃鎶婄浉搴旀鐜囧～杩涘幓銆備簩缁寸鏁ｅ瀷闅忔満鍙橀噺鐨勫垎甯绉颁负杈圭紭鍒嗗竷寰嬶紝鐢卞畾涔夊彲浠ョ煡閬撹竟缂樺垎甯冨緥锛屽叾瀹炲氨鏄殢鏈哄彉閲忚嚜宸鐨勫垎甯冿紝姹傝竟缂樺垎甯冨緥涔熷氨鏄...
绛旓細Cov(X,Y)=E(XY)-E(X)E(Y)銆備簩浣嶇鏁ｅ瀷闅忔満鍙樻暟(X,Y)鑱斿悎鍒嗗竷寰 棣栧厛鏍规嵁宸茬煡锛氬彲姹(0.4/0.4+a)=0.8 a=0.1 鏍规嵁浜岀淮鑱斿悎鍒嗗竷鎵鏈夋鐜囧煎敮涓鍙眰b=0.1 澶т竴宸ョ▼鏁板锛氳浜岀淮绂绘暎鍨嬮殢鏈哄彉鏁帮紙X銆Y锛夌殑鑱斿悎鍒嗗竷寰嬩负 E(X)=0脳锛0.20+0.05+0.10锛+1脳锛0.05+0.10+0....
绛旓細鏍规嵁闅忔満鍙橀噺鍑芥暟鐨勬湡鏈涘叕寮忓彲鐭(Z)=E(X+Y)=鈭(xi+yj)pij=(1+1)脳0.1+(1+2)脳0.25+(1+3)脳0.15+(2+1)脳0.15+(2+2)脳0.2+(2+3)脳0.15=3.55锛屼綘閭ｄ釜绛旀鑲畾鏄敊鐨勩
绛旓細姒傜巼璁!璁鹃殢鏈哄彉閲廥涓嶻鏈嶄粠鍚屼竴鍒嗗竷,鍏鍒嗗竷寰嬩负X(Y)~ 涓婂浘鍚р﹀笇鏈涙湁澶х鑳借祼鏁!... 涓婂浘鍚р﹀笇鏈涙湁澶х鑳借祼鏁! 灞曞紑 1涓洖绛 #璇濋# 鎵撳伐浜哄繀鐪嬬殑鑱屽満銆庣淮鏉冦忔寚鍗!abc552518 2013-04-28 路 TA鑾峰緱瓒呰繃1271涓禐 鐭ラ亾灏忔湁寤烘爲绛斾富 鍥炵瓟閲:654 閲囩撼鐜:66% 甯姪鐨勪汉:329涓 鎴戜篃鍘荤瓟棰...
绛旓細1銆佺敱浜鍒嗗竷寰涓悇涓鐜囦箣鍜屼负1锛屽洜姝=1/8 2銆佷笉鐙珛锛岀敱浜嶱(X=1)=3/8,P(Y=1)=3/8 鎵浠(X=1)P(Y=1)=9/64 鑰孭(X=1,Y=1)=1/8 涓よ呬笉鐩哥瓑锛屽洜姝や笉鐙珛 3銆丒(X)=-1脳3/8+0+1脳3/8=0 鍚岀悊绠楀緱E(Y)=0 E(Y²)=3/4 鎵浠(Y)=E(Y²)-[E(Y)...
绛旓細P(XY=4)=0.1锛圶=2,Y=2锛,鈭 E(XY)=锛-2锛*0.5+锛-1锛*0.2+1*0.1+2*0.1+4*0.1=-0.5 鈭 鏈缁堝彲寰桬(XY)=-0.5 銆婃鐜囪涓庢暟鐞嗙粺璁°嬫槸涓虹悊宸ョ搴旂敤鍨嬫湰绉戜汉鎵嶅煿鍏昏岀紪鍐欑殑姒傜巼璁轰笌鏁扮悊缁熻鏁欐潗銆傚叏涔﹀叡10绔狅紝鍐呭鍖呮嫭锛氶殢鏈轰簨浠跺強鍏舵鐜囷紝闅忔満鍙橀噺鍙婂叾鍒嗗竷锛闅忔満鍚戦噺鍙婂叾...
绛旓細鈭X锛孻鏄浉浜掔嫭绔嬶紝鍒橮(X锛濆害1,Y锛2)锛漃(X锛1)路P(Y锛2)P(X锛1)锛1/6+1/9+1/18P(Y锛2)锛1/9+伪P(X锛1)路P(Y锛2)锛(1/6+1/9+1/18)路(1/9+伪)瑙ｅ緱伪锛2/9銆傚悓鐞嗭紝p锛1/9 qE(X)锛1x(1/6+1/9+1/18)+2x(1/3x2/9x1/9)锛2/9 ...
