设二维随机变量(X,Y)具有概率密度f(x,y)=6xy,(0 数学
Cov(x,y)=EXY-EXEY挨个求出来不就可以了吗?
EXY=1/3 EY=3/5 Ex=2/5
Cov(x,y)=7/75
绛旓細鍙埄鐢ㄨ仈鍚堟鐜囧瘑搴︾殑浜岄噸绉垎涓1锛屾眰鍑簁=2銆傝竟闄呭瘑搴﹀嚱鏁扮殑姹傝В锛屾湰璐ㄥ氨鏄冨療绉垎锛屽彧瑕佽浣忚竟缂樻鐜囧瘑搴﹀氨鏄鑱斿悎瀵嗗害鍑芥暟姹傜Н鍒嗭紝褰撴垜浠眰鍏充簬Y鐨勮竟闄呭瘑搴﹀嚱鏁版椂灏辨槸瀵逛簬f锛坸锛寉锛鐨勮仈鍚堝瘑搴﹀嚱鏁板叧浜嶺姹傜Н鍒嗭紝姹俌鐨勮竟闄呭瘑搴﹀嚱鏁板垯鍚岀悊銆傜浜岄儴鍒嗘槸姹闅忔満鍙橀噺鍑芥暟鐨勫瘑搴︼紝涓鑸敤鍒嗗竷鍑芥暟娉曪紝鍗冲厛鐢...
绛旓細Cov(X,Y)=E(XY)-E(X)E(Y)=1/6-(5/12)²=-1/144銆傚洜涓哄垎甯冨嚱鏁 F(x0,y0)=P{X<x0&&Y<y0} 涓嶇x0锛寉0璋佸ぇ璋佸皬锛屾寚鐨勬槸 Y=y0鐩寸嚎浠ヤ笅銆乆=x0鐩寸嚎涔嬪彸鍖哄煙鍐呯殑绉垎锛岃岃繖涓尯鍩熷唴铏界劧 x>y澶勫瘑搴﹀嚱鏁颁负0锛屼絾杩樻槸鏈 x<y鐨勭偣鐨勩備緥濡傦細璁句簩缁撮殢鏈哄彉閲(X,Y)鐨勬鐜囧瘑搴︿负...
绛旓細鏍规嵁瑙勮寖鎬у拰褰掍竴鎬 k=1/3锛沺锛坸y锛=1-p锛坸锛-p锛坹锛=1-1/2-1/3 =1/6 E(xy锛=E锛坸锛*E锛坹锛=1/6 瀹氫箟 涓鑸紝璁綞鏄竴涓殢鏈鸿瘯楠岋紝瀹冪殑鏍锋湰绌洪棿鏄疭={e}锛璁綳=X锛坋锛夊拰Y=Y(e)S鏄畾涔夊湪S涓婄殑闅忔満鍙橀噺锛岀敱瀹冧滑鏋勬垚鐨勪竴涓悜閲锛圶锛孻锛锛屽彨鍋浜岀淮闅忔満鍙橀噺鎴栦簩缁撮殢鏈哄悜閲忥紱鏈...
绛旓細2014-11-06 璁句簩缁撮殢鏈哄彉閲(X,Y)鍏锋湁鑱斿悎姒傜巼瀵嗗害f(x,y)={c(... 2012-01-10 璁句簩缁撮殢鏈哄彉閲(X,Y)鐨勬鐜囧瘑搴︿负f (x,y)=6x,0... 2016-05-27 璁句簩缁撮殢鏈哄彉閲(X,Y)鏈嶄粠鍖哄煙D={(x,y)|0鈮鈮1... 2018-01-09 璁鹃殢鏈哄彉閲廥-N(0 1)姹俌=e^x姒傜巼瀵嗗害? 2015-04-30 璁句簩缁撮殢鏈哄彉閲(X,Y...
绛旓細EX=鈭埆[0<=y<=x<=1] xf(x,y)dxdy=鈭玔0->1]鈭玔0->x] 12xy²dydx=4/5 EY=鈭埆[0<=y<=x<=1] yf(x,y)dxdy=鈭玔0->1]鈭玔0->x] 12y³dydx=3/5 E(X²+Y²)=鈭埆[0<=y<=x<=1] (x²+y²)f(x,y)dxdy=鈭玔0->1]鈭玔0...
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀
绛旓細璇︾粏杩囩▼rt锛屽笇鏈涜兘甯埌浣犺В鍐抽棶棰
绛旓細璇︾粏杩囩▼濡傚浘rt鈥︹﹀笇鏈涜兘甯埌浣犺В鍐抽棶棰
绛旓細=k鈭(1~2){(1+y)/8} dy =k{(1+y)²/16}|(1~2)=5k/16 =5/64 3)杩欓噷闇瑕佹妸y浣滃叏瀹氫箟鍩熺Н鍒 P=k鈭(1~3)鈭(0~1/2)(3x²+xy)dxdy =k鈭(1~3){(1+y)/8} dy =(16-4)/64 =12/64 =3/16 4)1<=y<=3-2x 0<=x<=1 瑙佸浘涓粦鑹插尯鍩(濡傛灉鎯冲厛绉x...
绛旓細鐒跺悗濡傚浜庨殢鏈哄彉閲廥鐨勫垎甯冨嚱鏁癋锛x锛锛屽鏋滃瓨鍦ㄩ潪璐熷嚱鏁癴锛坸锛夈備娇瀵逛簬浠绘剰瀹炴暟x锛屾湁F锛坸锛夛紳鈭紙锛嶁垶锛寈锛塮锛坱锛塪t鍒橷鎴愪负杩炵画鍨嬮殢鏈哄彉閲忋傚叾涓嚱鏁癴锛坸锛夌О涓篨鐨勬鐜囧瘑搴﹀嚱鏁帮紝绠绉版鐜囧瘑搴︼紟杩欐槸姒傜巼瀵嗗害鐨勫畾涔夈備妇渚嬶細宸茬煡浜岀淮闅忔満鍙橀噺锛圶,Y锛夊叿鏈夋鐜囧瘑搴(x,y)= 2e-(2x+y),x>0,...
