#Markov Chain - Simple
# n is the number of rv's to be generated.
For the class of 2/2: A template
--------------
MCS <- function(n)
{
        PP <- matrix(0, 3, 3)
# Transition matrix PP
        PP[[1, 1]] <- 0.3
        PP[[1, 2]] <- 0.4
        PP[[1, 3]] <- 0.2
        PP[[2, 1]] <- 0.3
        PP[[2, 2]] <- 0.3
        PP[[2, 3]] <- 0.4
        PP[[3, 1]] <- 0.01
        PP[[3, 2]] <- 0.01
        PP[[3, 3]] <- 0.98
# 2 is the starting state
        i <- 2
        ret <- NULL
        for(k in 1:n) {
                xn <- sample(3, 1, prob = as.vector(PP[i,  ]), replace
                         = T)
                ret <- c(ret, xn)
                i <- xn
        }
        return(ret)
}


#=================================
> MCS(400)
  [1] 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3 1 2 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
 [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
 [75] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[112] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[149] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[186] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[223] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[260] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3
[297] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 2 2 3 3
[334] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3
[371] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3