fx(x,y)表示什么?它和f'x(x,y)有什么关系? f''xy(x,y)与fxy(x,y)有什么区别?
\u6982\u7387\u8bba\u4e2d\u7684fX(x)\u662f\u4ec0\u4e48\u610f\u601d?\u5b83\u548cf(x)\u6709\u4ec0\u4e48\u533a\u522b\u5728\u4e00\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u4e2d,f(x)\u8868\u793a\u968f\u673a\u53d8\u91cfX\u7684\u5bc6\u5ea6\u51fd\u6570.
fX(x)\u548cfY(y)\u5728\u201c\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u53ca\u5176\u5bc6\u5ea6\u51fd\u6570\u201d\u4e2d\u51fa\u73b0.
fX(x)\u662fX\u7684\u8fb9\u7f18\u5bc6\u5ea6\u51fd\u6570\uff1bfY(y)\u662fY\u7684\u8fb9\u7f18\u5bc6\u5ea6\u51fd\u6570.
\u4e00\u4e2a\u662f\u4e8c\u5143\u4e8c\u9636\u5bfc\u51fd\u6570\uff0c\u4e00\u4e2a\u662f\u4e8c\u5143\u51fd\u6570\u3002
前者代表隐函数对x求偏导,后者是二元函数对x求偏导在一维连续型随机变量中,f(x)表示随机变量X的密度函数.
fX(x)和fY(y)在“二维连续型随机变量及其密度函数”中出现.
fX(x)是X的边缘密度函数;fY(y)是Y的边缘密度函数.
是不是都是偏导数
绛旓細f(x,y)dx=鈭(0,1)dx=1锛屽叾涓-1<y<1銆(2)锛屸埖fX(x)*fY(y)=2x鈮爁(x,y)锛屸埓X銆乊涓嶇浉浜掔嫭绔嬨(3)锛屸埖0<x<1锛-x<y<x锛屸埓0<x+y<2x锛屽嵆0<z<2x锛0<x<1銆傗埓F(Z=z)=P(0<z<2x)銆傗埓鐢卞瘑搴﹁绠楀叕寮忥紝鏈塮Z(z)=F'(Z=z)=fX(z)*[dx/dz]=z/2锛屽叾涓0<z<2銆
绛旓細鈭磃X(x)=[2e^(-2x)]鈭(0,鈭)e^(-y)dy=2e^(-2x)锛寈>0锛沠X(x)=0锛寈鍏跺畠銆傗埓X鐨勮竟闄呭垎甯冨嚱鏁FX(x)=鈭(0,x)fX(x)dx=1-e^(-2x)锛岋紝x>0锛汧X(x)=0锛寈鍏跺畠銆傚悓鐞嗭紝Y鐨勮竟闄呭瘑搴﹀嚱鏁fY(y)=鈭(-鈭,鈭)f(x,y)dx=鈭(-鈭,鈭)2e^(-2x-y)dx銆傗埓fX(x)=[e^(-y)]...
绛旓細濡傛灉浜岀淮闅忔満鍙橀噺X,Y鐨勫垎甯冨嚱鏁癋{x锛寉}涓哄凡鐭ワ紝閭d箞闅忔満鍙橀噺x锛寉鐨勫垎甯冨嚱鏁Fx{x}鍜孎y{y}鍒嗗埆鍙敱F{x锛寉}姹傚緱銆傚垯Fx{x}鍜孎y{y}涓哄垎甯冨嚱鏁癋{x锛寉}鐨勮竟缂樺垎甯冨嚱鏁般傝竟缂樺瘑搴﹀嚱鏁版眰瑙f柟娉曟槸锛氭牴鎹彉閲忕殑鍙栧艰寖鍥达紝瀵硅仈鍚堟鐜囧瘑搴﹀嚱鏁扮Н鍒嗭紝瀵箉绉垎寰楀埌X鐨勮竟缂樻鐜囧瘑搴︺傝竟缂樻鐜囧瘑搴︿篃绉版鐜囧瘑搴...
绛旓細鍏蜂綋鍥炵瓟濡傚浘锛氫簨浠堕殢鏈哄彂鐢熺殑鏈虹巼锛屽浜庡潎鍖鍒嗗竷鍑芥暟锛屾鐜囧瘑搴︾瓑浜庝竴娈靛尯闂(浜嬩欢鐨勫彇鍊艰寖鍥)鐨勬鐜囬櫎浠ヨ娈靛尯闂寸殑闀垮害锛屽畠鐨勫兼槸闈炶礋鐨勶紝鍙互寰堝ぇ涔熷彲浠ュ緢灏忋
绛旓細F锛坸锛寉锛鍙岄噸绉垎涓1 涓斿埄鐢ㄨ繕鍘熸硶 浠锛漷an锛坢锛塧bsm F锛坸锛寉锛=P(X<x,y =x鎴栬匶>=y)=1-P(X>=x锛-P锛圷> =y)+2P(X>=x锛塒锛圷> =y)-P(X>=x锛塒锛圷>=y) < =1-P(X>=x锛塒锛圷>=y) < =1-([1-P(X<x锛塢[1-p锛坹<y)] =x锛-P(X>=x锛塒锛圷>=y)>=...
绛旓細f鏄嫳鏂噁action鐨勬剰鎬濓紝鍑芥暟鐨勬剰鎬 鎷彿閲岄潰鏄嚜鍙橀噺 璧锋潵灏辨槸faction锛x锛锛屾槸琛ㄧず鍏充簬x鐨勫嚱鏁帮紝绠鍐欐垚f锛坸锛夛紝渚嬪f锛坸锛=3x+1 鍚屾牱鐨f锛坸锛寉锛夎〃绀鍏充簬x锛寉鐨勫嚱鏁帮紝涔熷氨鏄繖涓嚱鏁伴噷闈㈠寘鍚x鍜y涓や釜鍙橀噺锛屼緥濡俧锛坸锛寉锛=x+2y+3 鍑芥暟浠h〃涓涓暟鍊硷紝涓鏃﹀彉閲忕‘瀹氾紝鍑芥暟鍊煎氨纭畾浜嗭紝鍙橀噺涓...
绛旓細=lim(y鈫掆垶)[1-e^(-4x)][1-e^(-2y)]=1-e^(-4x)锛寈>0銆FX(x)=0,x涓哄叾瀹冦傚悓鐞嗭紝Y鐨勮竟缂樺垎甯冨嚱鏁FY(y)=lim(x鈫掆垶)F(X,Y)=lim(x鈫掆垶)[1-e^(-4x)][1-e^(-2y)]=1-e^(-2y)锛寉>0銆丗Y(y)=0,y涓哄叾瀹冦傚張锛屸埖F(X,Y)=FX(x)*FY(y)锛屸埓X銆乊鐩镐簰鐙珛銆
绛旓細涓嶅瓨鍦紱鍥犱负锛歠xy(x,y)=fyx(x,y);fxy(x,y)=4;fyx(x,y)=3;鎵浠ヤ笉瀛樺湪f(x,y).
绛旓細fx(x)=1 0<x<1 fx(x)=0 鍏跺畠fY(y)=e^(-y) ,y>0 fY(y)=0 鍗风Н鍏紡锛 fz(z)=鈭fx(x)fy(z-x)dx,绉垎闄愪负-鈭<x<+鈭 鍥犱负 0<x0,鎵浠ワ紝鍗风Н鍏紡鐨勭Н鍒嗛檺涓0<x<z,鏃朵袱涓绉嚱鏁板潎涓嶄负0 fz(z)=鈭玣x(x)fy(z-x)dx X=1锛孻=e^(-y锛鎵浠ワ細Z=1+e^(-y锛夛紙y>...
绛旓細Fx(x) = 鈭f(x,y)*dy 姹傚崟鍙橀噺鐨勬湡鏈涳紝鍙互鍙傝冧互涓嬪叕寮忥細E(x) = 鈭玿*Fx(x)*dx=鈭埆x*f(x,y)*dxdy 璁锛圶锛孻锛鏄簩缁撮殢鏈哄彉閲忥紝x锛寉鏄换鎰忓疄鏁帮紝浜屽厓鍑芥暟锛F(x,y)=P({X鈮鈭℡鈮})=P(X鈮,Y鈮)锛岃绉颁簩缁撮殢鏈哄彉閲(X锛孻)鐨勫垎甯冨嚱鏁帮紝鎴栫О涓X鍜Y鐨勮仈鍚堝垎甯冨嚱鏁般