{
library(akima)
# code to compute the joint and conditional PDF
# example problem 3.9 page 76 of the text book
nx=50
ny=50
nxy=nx*ny
x=seq(0,1,length=nx)
y=seq(0,1,length=ny)
jpdf=1:nxy
xy=matrix(0,nrow=nxy,ncol=2)
k=0
for(i in 1:nx) {
  for(j in 1:ny) {
     k=k+1
     xy[k,1]=x[i]
     xy[k,2]=y[j]
     #jpdf[k]=exp(-(xy[k,1]+xy[k,2]))
     jpdf[k]=0.4*(2*xy[k,1]+3*xy[k,2])
  }
}
zz=interp(xy[,1],xy[,2],jpdf)
persp(zz)
#conditional slize at x=0.5
#f(y | x) = f(x,y)/f(x)
xc=0.5
fygx=1:ny
for(i in 1:ny){
   fygx[i]=0.4*(2*xc+3*y[i])/((4*xc/5) + (3/5))
}

}