mardia_dm1633_assignment3.Rmd

```{r}

library(markovchain)
library(expm) #allows you to perform A%^%x matrix multiplications


statesNames = c("S1","S2","S3")
tmatrix=matrix(c(0.5,0.5,0,0,0.5,0.5,0.5,0,0.5),
 nrow = 3, ncol = 3, byrow = TRUE,dimnames=list(statesNames,statesNames))
tmatrix
mcC = new("markovchain", transitionMatrix =tmatrix) #once you are in state S4, you will stay there
is.irreducible(mcC)
period(mcC)

#True represents that the transition matrix is Irreducible
#The period being 1 represents it is aperiodic, if it was greater than 1 it would be periodic
#Hence the transition matrix is irreducible and aperiodic.

```

```{r}
#Define a intial state of pi
pi=matrix(c(0.34,0.33,0.33),byrow=TRUE,ncol=3)
pi%*%(tmatrix%^%100)
pi%*%(tmatrix%^%1000)

#We can see that this is the stationary distribution of transition matrix

```