R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

Sigma<-matrix(0.6,10,10)+0.4*diag(10)
Sigma
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  1.0  0.6  0.6  0.6  0.6  0.6  0.6  0.6  0.6   0.6
##  [2,]  0.6  1.0  0.6  0.6  0.6  0.6  0.6  0.6  0.6   0.6
##  [3,]  0.6  0.6  1.0  0.6  0.6  0.6  0.6  0.6  0.6   0.6
##  [4,]  0.6  0.6  0.6  1.0  0.6  0.6  0.6  0.6  0.6   0.6
##  [5,]  0.6  0.6  0.6  0.6  1.0  0.6  0.6  0.6  0.6   0.6
##  [6,]  0.6  0.6  0.6  0.6  0.6  1.0  0.6  0.6  0.6   0.6
##  [7,]  0.6  0.6  0.6  0.6  0.6  0.6  1.0  0.6  0.6   0.6
##  [8,]  0.6  0.6  0.6  0.6  0.6  0.6  0.6  1.0  0.6   0.6
##  [9,]  0.6  0.6  0.6  0.6  0.6  0.6  0.6  0.6  1.0   0.6
## [10,]  0.6  0.6  0.6  0.6  0.6  0.6  0.6  0.6  0.6   1.0
mu=rep(0,10)
mu
##  [1] 0 0 0 0 0 0 0 0 0 0
#a
##Mulginal Distribution is multivariate normal
#Mean
mu_12 = mu[1:2]
mu_12
## [1] 0 0
#Covariance
Sigma_12 = Sigma[1:2,1:2]
Sigma_12
##      [,1] [,2]
## [1,]  1.0  0.6
## [2,]  0.6  1.0
#b
a=3:10
b=1:2
x_a = rep(1,8)
##Mean
mu[b] + Sigma[b,a]%*%solve(Sigma[a,a])%*%(x_a-mu[a])
##           [,1]
## [1,] 0.9230769
## [2,] 0.9230769
#Covariance
Sigma[b,b]-Sigma[b,a]%*%solve(Sigma[a,a])%*%Sigma[a,b]
##            [,1]       [,2]
## [1,] 0.44615385 0.04615385
## [2,] 0.04615385 0.44615385
#c
a = rep(1,10)
#Mean
t(a)%*%mu
##      [,1]
## [1,]    0
##Covariance
t(a)%*%Sigma%*%a
##      [,1]
## [1,]   64