i.i.d正态随机变量 设随机变量，…，Ypi.i.d~N(O,1),则随机向量Y=(Y,,Yp)y 的密度为 f(,,)=】 左t-=Ba)a-y 设Y~Np(0,I),则有 ·EY=0,cou(Y)=Ip. ·E(Y'AY)=tr(A): ·设a为p元向量，A为对称矩阵，则cou(aY,YAY)=0. ·设A,B为对称矩阵，则cou(Y'AY,Y'BY)=2tr(AB). Previous Next First Last Back Forwardi.i.d 正态随机变量 设随机变量 Y1, . . . , Yp i.i.d ∼ N(0, 1), 则随机向量 Y = (Y1, . . . , Yp) ′ 的密度为 f(y1, . . . , yp) = ∏p i=1 1 √ 2π exp{−1 2 y 2 i } = (2π) −p/2 exp{−1 2 y ′ y} 设 Y ∼ Np(0, I), 则有 • EY = 0, cov(Y ) = Ip. • E(Y ′AY ) = tr(A). • 设 a 为 p 元向量, A 为对称矩阵, 则 cov(a ′Y, Y ′AY ) = 0. • 设 A, B 为对称矩阵, 则 cov(Y ′AY, Y ′BY ) = 2tr(AB). Previous Next First Last Back Forward 5