228 D.W.Diamond and R.E.Verrecchia,Information aggregation and rational expectations A price random variable of this form implies that the covariances between p and the random variables i,X,,and are given by c1≡cov[P,闪=ho', c2≡cov[庐，]=-yV, c3≡cov[产，x]=-(y/T)V, c4=COv[P,]=B(ho1+(Ts)1). (6) Thus,the vectorZ=(,,-[+]yo)has a joint five-variate Normal distribution with mean m=(yo,0,0,yo,0)and covariance matrix ho1 00 h6' Ci 0 TV V 0 C2 M= 0 VV 0 C3 00 ho1+s-1 C2 C3 Ca H-1 Partition the vectors Z,m,and the matrix M as follows: m /M11M12 m= M= m M21M22 where Z=(,X).m,=(yo,0)and M,:is a two-by-two matrix,and the sizes of the other matrices and vectors are determined.Let F,=F(a,X|=x,立=y,庐=P) represent trade t's distribution function for the joint random variables i and conditional on observing=x=y:and p=P.LetZ=(x y,P).It is a well-known result [see,e.g.,Mood-Graybill (1963,p.213)]that the conditional distribution of ii and &given Z,is a Bivariate Normal with mean m=m,+M2M22 (Z-m2),and convariance matrix M1= M11-M12M22 M21.In particular,this implies that the mean and variance of i conditional on observing==y,and P=P is given by =yo+(1/K)[(cic3(ho1+s-1)-ho 'c4c3)x +(e1c4+ho'{c3-VH-1})(y.-o) +(ho1e4-V{ho1+s-1}c1)P-{a+}yo门， (7)228 D.W Diamond and R.E. Verrecchia, Information aggregation and rational expectations A price random variable of this form implies that the covariances between P and the random variables C, 8, &, and A are given by c,~cov[P,izJ=/3h~‘, c,ECOV[B,X]= -yV, c3 =cov [P, Z,] = - (y/T)V, C~~COV[&yJ=/Y{h,‘+(Ts)-‘}. (6) Thus, the vector Z = (t?, x, gt, j$ P - [a + /I] yo) has a joint five-variate Normal distribution with mean m = (y,,, O,O, y,, 0) and covariance matrix ;i && J. Partition the vectors Z, m, and the matrix M as follows: where Z: = (G,x), m1 = (y,,O) and Ml1 is a two-by-two matrix, and the sizes of the other matrices and vectors are determined. Let represent trade t’s distribution function for the joint random variables u” and w conditional on observing 2, = xt, j$ = y,, and P = P. Let Z,* = (xt, y,, P). It is a well-known result [see, e.g., Mood-Graybill (1963, p. 213)] that the conditional distribution of u’ and 1, given Zy, is a Bivariate Normal with mean rn: = m, + M,,M;,’ (Zz -m,), and convariance matrix Mf, = MI, -M,,M;,‘Mz,. In particular, this implies that the mean and variance of C conditional on observing zt = x,, yt = y,, and P = P is given by ~,=y,+(1/K)[(c,c,{h,‘+s-‘}-h,‘c,c,)x, + (Vc,c,+h,‘{c:- VK’})(y,-yo) +(h~‘~lc,-I/{h~‘+s~‘}cl)(P-{a+~)yo)], (7)