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概率公式整理1.随机事件及其概率吸收律:AABAAAA)(ABAAAAA)()(ABABABA反演律:BABABAABniiniiAA11niiniiAA112.概率的定义及其计算:)(1)(APAP若BA)()()(APBPABP对任意两个事件A,B,有)()()(ABPBPABP加法公式:对任意两个事件A,B,有)()()()(ABPBPAPBAP)()()(BPAPBAP)()1()()()()(2111111nnnnkjikjinjijiniiniiAAAPAAAPAAPAPAP3.条件概率ABP)()(APABP乘法公式)0)(()()(APABPAPABP)0)(()()(12112112121nnnnAAAPAAAAPAAPAPAAAP全概率公式niiABPAP1)()()()(1iniiBAPBPBayes公式)(ABPk)()(APABPkniiikkBAPBPBAPBP1)()()()(4.随机变量及其分布分布函数计算)()()()()(aFbFaXPbXPbXaP5.离散型随机变量(1)0–1分布1,0,)1()(1kppkXPkk(2)二项分布),(pnB若P(A)=pnkppCkXPknkkn,,1,0,)1()(*Possion定理0limnnnp有,2,1,0!)1(limkkeppCkknnknknn(3)Poisson分布)(P,2,1,0,!)(kkekXPk6.连续型随机变量(1)均匀分布),(baU其他,0,1)(bxaabxf1,,0)(abaxxF(2)指数分布)(E其他,00,)(xexfx0,10,0)(xexxFx(3)正态分布N(,2)xexfx222)(21)(xttexFd21)(222)(*N(0,1)—标准正态分布xexx2221)(xtexxtd21)(227.多维随机变量及其分布二维随机变量(X,Y)的分布函数xydvduvufyxF),(),(边缘分布函数与边缘密度函数xXdvduvufxF),()(dvvxfxfX),()(yYdudvvufyF),()(duyufyfY),()(8.连续型二维随机变量(1)区域G上的均匀分布,U(G)其他,0),(,1),(GyxAyxf(2)二维正态分布yxeyxfyyxx,121),(2222212121212)())((2)()1(212219.二维随机变量的条件分布0)()()(),(xfxyfxfyxfXXYX0)()()(yfyxfyfYYXYdyyfyxfdyyxfxfYYXX)()(),()(dxxfxyfdxyxfyfXXYY)()(),()()(yxfYX)(),(yfyxfY)()()(yfxfxyfYXXY)(xyfXY)(),(xfyxfX)()()(xfyfyxfXYYX10.随机变量的数字特征数学期望1)(kkkpxXEdxxxfXE)()(随机变量函数的数学期望X的k阶原点矩)(kXEX的k阶绝对原点矩)|(|kXEX的k阶中心矩)))(((kXEXEX的方差)()))(((2XDXEXEX,Y的k+l阶混合原点矩)(lkYXEX,Y的k+l阶混合中心矩lkYEYXEXE))(())((X,Y的二阶混合原点矩)(XYEX,Y的二阶混合中心矩X,Y的协方差))())(((YEYXEXEX,Y的相关系数XYYDXDYEYXEXE)()())())(((X的方差D(X)=E((X-E(X))2))()()(22XEXEXD协方差))())(((),cov(YEYXEXEYX)()()(YEXEXYE)()()(21YDXDYXD相关系数)()(),cov(YDXDYXXY
本文标题:概率论公式总结
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