data<-c(0.167, 0.083, 0.083, 0.333, 0.083, 0.5, 0.083, 0.667, 0.25, 0.583, 0.167, 1)
mat<-matrix(data, nrow=3, byrow=T)
rownames(mat)<-c("1", "3", "ÇÕ°è")
colnames(mat)<-c("0", "1", "2", "ÇÕ°è")
mat
mu_x<-1*mat[1,4]+3*mat[2,4]
mu_y<-0*mat[3,1]+1*mat[3,2]+2*mat[3,3]
mu_x
mu_y
var_x<-1^2*mat[1,4]+3^2*mat[2,4]- mu_x^2
var_y<-0^2*mat[3,1]+1^2*mat[3,2]+2^2*mat[3,3]-mu_y^2
var_x
var_y
p_xy<-c(0.167, 0.083, 0.083, 0.083, 0.5, 0.083)
xy<-c(0,1,2,0,3,6)
cov_xy<-sum(p_xy*xy)-(mu_x*mu_y)
cov_xy
corr_xy<-cov_xy/sqrt(var_x*var_y)
corr_xy

frac <- c("1/6","1/12","1/12","1/3","1/12","1/2","1/12","2/3","1/4","7/12","1/6","1")
dd<-sapply(frac, function(x) eval(parse(text=x)))
d<-as.numeric(dd)
matd<-matrix(d, nrow=3, byrow=T)
rownames(matd)<-c("1", "3", "ÇÕ°è")
colnames(matd)<-c("0", "1", "2", "ÇÕ°è")
matd
mu_x_d<-1*matd[1,4]+3*matd[2,4]
mu_y_d<-0*matd[3,1]+1*matd[3,2]+2*matd[3,3]
mu_x_d
mu_y_d
var_x_d<-1^2*matd[1,4]+3^2*matd[2,4]- mu_x_d^2
var_y_d<-0^2*matd[3,1]+1^2*matd[3,2]+2^2*matd[3,3]-mu_y_d^2
var_x_d
var_y_d
frac_d <- c("1/6","1/12","1/12","1/12","1/2","1/12")
ddd<-sapply(frac_d, function(x) eval(parse(text=x)))
d_d<-as.numeric(ddd)
p_xy_d<-d_d
xy<-c(0,1,2,0,3,6)
cov_xy_d<-sum(p_xy_d*xy)-(mu_x_d*mu_y_d)
cov_xy_d
corr_xy_d<-cov_xy_d/sqrt(var_x_d*var_y_d)
corr_xy_d