#x1<-rnorm(10,0,1)
x1<-c(0.941,-0.007,-1.660,-0.713,-2.311,0.956,0.215,0.347,-0.412,-0.494)
#[1]  0.941420501 -0.006570378 -1.659617475 -0.713084619 -2.311091870
# [6]  0.955634729  0.214630869  0.347359396 -0.411664170 -0.494051406
mx1<-mean(x1)
#x2<-rnorm(10,0,1)
x2<-c(2.253,-0.039,-1.304,2.732,-2.027,0.556,-0.173,-1.792,-1.242,-0.615)
#[1]  2.25288125 -0.03872519 -1.30422579  2.73273153 -2.02963616  0.55574747
# [7] -0.17270893 -1.79212356 -1.24162188 -0.61493527
mx2<-mean(x2)
xw<-matrix(c(x1-mx1,x2-mx2),10,2)
sum(x1-mx1)
w<-t(xw)%*%xw
rho<-w[1,2]/(sqrt(w[1,1]*w[2,2]))
rho
#> rho
#[1] 0.4687826
mle<-w/10
mle
#> mle
#          [,1]      [,2]
#[1,] 0.9999700 0.7195707
#[2,] 0.7195707 2.3562270
unbiased<-w/9
unbiased
#> unbiased
#         [,1]     [,2]
#[1,] 1.111078 0.799523
#[2,] 0.799523 2.618030
eigen.w<-eigen(w)
#eigen.w
lam<-c(eigen.w$values)
lam
#> lam
#[1] 26.668554  6.893415
hmat<-matrix(eigen.w$vectors,2,2)
#lam; hmat
lam/10;lam/9
mx1;mx2