《概率论公式大全》Word文档.pdf

该【《概率论公式大全》Word文档 】是由【小屁孩】上传分享，文档一共【12】页，该文档可以免费在线阅读，需要了解更多关于【《概率论公式大全》Word文档 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..????A???AA???AA????吸收律:A?(AB)?AA?(A?B)?AA?B?AB?A?(AB)反演律:A?B?ABAB?A?Bnnnn?A??A?A??Aiiiii?1i?1i?1i?(A)?1?P(A)若A?B?P(B?A)?P(B)?P(A)对任意两个事件A,B,有P(B?A)?P(B)?P(AB)加法公式:对任意两个事件A,B,有P(A?B)?P(A)?P(B)?P(AB):..P(A?B)?P(A)?P(B)nnnP(?A)??P(A)??P(AA)??P(AAA)???(?1)n?1P(AA?A)iiijijk12ni?1i?11?i?j?n1?i?j?k?(AB)??PBA?P(A)乘法公式??P(AB)?P(A)PBA(P(A)?0):..????P(AA?A)?P(A)PAA?PAAA?A12n121n12n?1(P(AA?A)?0)12n?1全概率公式nnP(A)??P(AB)??P(B)?P(AB)iiii?1i?1Bayes公式P(B)P(AB)?kkP(AB)n?k?P(B)P(AB)P(BA)P(A)iiki?(a?X?b)?P(X?b)?P(X?a)?F(b)?F(a)(1)0–1分布P(X?k)?pk(1?p)1?k,k?0,1(2)二项分布B(n,p):..若P(A)=pP(X?k)?Ckpk(1?p)n?k,k?0,1,?,nn*Possion定理limnp???0nn???klimCkpk(1?p)n?k?e??nnnk!n??有k?0,1,2,?(3)Poisson分布P(?):..?kP(X?k)?e??,k?0,1,2,?k!(1)均匀分布U(a,b)?1?,a?x?bf(x)??b?a??0,其他?0,??x?aF(x)??,b?a??1?(2)指数分布E(?)??e??x,x?0?f(x)???0,其他??0,x?0F(x)??1?e??x,x?0?(3)正态分布N(m,s2)1(x??)2?f(x)?e2?2???x???2??1(t??)2x?F(x)??e2?2dt2????:..*N(0,1)—标准正态分布1x2??(x)?e2???x???2?1t2x??(x)??e2dt???x???2???:..二维随机变量(X,Y)的分布函数xyF(x,y)???f(u,v)dvdu????边缘分布函数与边缘密度函数x??F(x)???f(u,v)dvduX??????f(x)??f(x,v)dvX??y??F(y)???f(u,v)dudvY??????f(y)??f(u,y)duY??(1)区域G上的均匀分布,U(G)?1?,(x,y)?Gf(x,y)??A?0,其他?(2)二维正态分布1?(x??)2(x??)(y??)(y??)2?1??1?2?12?2?f(x,y)??e2(1??2)?????2???2????11222???1??212???x???,???y???:..(x,y)?f(x)f(yx)f(x)?0XXYX?f(y)f(xy)f(y)?0YXYY????f(x)??f(x,y)dy??f(xy)f(y)dyXXYY????????f(y)??f(x,y)dx??f(yx)f(x)dxYYXX????f(x,y)f(yx)f(x)??YXXf(xy)f(y)f(y)XYYY:..f(x,y)f(xy)f(y)??XYYf(yx)f(x)f(x)??E(X)??xpkkk?1??E(X)??xf(x)dx??随机变量函数的数学期望X的k阶原点矩E(Xk)X的k阶绝对原点矩E(|X|k)X的k阶中心矩E((X?E(X))k)X的方差:..E((X?E(X))2)?D(X)X,Y的k+l阶混合原点矩E(XkYl)X,Y的k+l阶混合中心矩??E(X?E(X))k(Y?E(Y))lX,Y的二阶混合原点矩E(XY)X,Y的二阶混合中心矩X,Y的协方差:..E?(X?E(X))(Y?E(Y))?X,Y的相关系数?(X?E(X))(Y?E(Y))?E??????XYD(X)D(Y)??X的方差D(X)=E((X-E(X))2)D(X)?E(X2)?E2(X)协方差cov(X,Y)?E?(X?E(X))(Y?E(Y))??E(XY)?E(X)E(Y)1???D(X?Y)?D(X)?D(Y)?2相关系数cov(X,Y)??XYD(X)D(Y):..(注:素材和资料部分来自网络,供参考。请预览后才下载,期待你的好评与关注!)