·(特征函数)，设p元随机向量X~F(x),则其特征函数定义为 fe)=Eet'x,t∈R肥，i=VT 矩： ·期望EX=(EX1,,EXp) ·协方差cou(X)=(E(X:-EX)(X,-EX)) ·若Xpx1,Ygx1为随机向量，则它们的协方差cou(X,Y)=(E(X: EX)(y-Ey)】 Etr(AXB)=tr(A(EX)B);cov(AX)=Acov(X)A' ·E(X'AX)='Aμ+tr(A),其中∑=cou(X) cov(AX,BY)=Acou(X,Y)B' Previous Next First Last Back Forward 3• (特征函数), 设 p 元随机向量 X ∼ F(x), 则其特征函数定义为 f(t) = Eeit ′X, t ∈ R p , i = √ −1 矩: • 期望 EX = (EX1, . . . , EXp) ′ • 协方差 cov(X) = ( (E(Xi − EXi)(Xj − EXj ))ij) • 若 Xp×1, Yq×1 为随机向量, 则它们的协方差 cov(X, Y ) = ( (E(Xi− EXi)(Yj − EYj ))ij) • Etr(AXB) = tr(A(EX)B), cov(AX) = Acov(X)A ′ • E(X ′AX) = µ ′Aµ + tr(AΣ), 其中 Σ = cov(X) • cov(AX, BY ) = Acov(X, Y )B ′ Previous Next First Last Back Forward 3