data<-c(0.1,0,0,0,0.1,0,0.4,0,0,0.4,0,0,0.3,0,0.3,0,0,0,0.2,0.2,0.1,0.4,0.3,0.2,1)
mat<-matrix(data, nrow=5, byrow=T)
rownames(mat)<-c("5", "7", "-4","15","f(y)")
colnames(mat)<-c("-1", "6", "2", "20","f(x)")
mat
mu_x<-5*mat[1,5]+7*mat[2,5]+(-4)*mat[3,5]+15*mat[4,5]
mu_y<-(-1)*mat[5,1]+6*mat[5,2]+2*mat[5,3]+20*mat[5,4]
mu_x
mu_y
var_x<-5^2*mat[1,5]+7^2*mat[2,5]+(-4)^2*mat[3,5]+15^2*mat[4,5]-mu_x^2
var_y<-(-1)^2*mat[5,1]+6^2*mat[5,2]+2^2*mat[5,3]+20^2*mat[5,4]-mu_y^2
var_x
var_y

p_xy<-data[c(1:4,6:9,11:14,16:19)]
p_xy
xy<-c(-5,30,10,100,-7,42,14,140,4,-24,-8,-80,-15,90,30,300)

x<-c(5,7,-4,15)
y<-c(-1,6,2,20)
z<-matrix(data=NA, nrow=4, ncol=4, byrow=T)
for(i in 1:4) {
  for(j in 1:4) {
      z[i,j]<-x[i]*y[j]
    }
    }
xy_z<-c(z[1,],z[2,],z[3,],z[4,])
xy_z
mu_xy<-sum(p_xy*xy_z)
mu_xy
cov_xy<-sum(p_xy*xy_z)-(mu_x*mu_y)
cov_xy
corr_xy<-cov_xy/sqrt(var_x*var_y)
corr_xy