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
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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...
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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...
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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...
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