1.

makeStates <- function(x,nc) cut(x,breaks=nc,labels=FALSE)

findP <- function(x) 
{
   k <- max(x)
   n1 <- length(x) - 1
   p <- matrix(nrow=k,ncol=k,0)
   nvec <- rep(0,k)
   for (m in 1:n1) {
      i <- x[m]
      nvec[i] <- nvec[i] + 1
      j <- x[m+1]   
      p[i,j] <- p[i,j] + 1
   }
   for (i in 1:k) {
      p[i,] <- p[i,] /nvec[i] 
   }
   p
}