Discussion 10 - Markov Chains

Intro to Probabilities page 451

Chapter 11.4 Exercise 1

• Compute Py, P2y, and P4y and show that the results are approaching a constant vector. What is this vector?

ans:

The vector approaches {0.33,0.33}

library(matlib)
library(MASS) 
p<- matrix(c(0.5, 0.5, 0.25, 0.75), nrow = 2, ncol = 2, byrow=T)
p

##      [,1] [,2]
## [1,] 0.50 0.50
## [2,] 0.25 0.75

y <- matrix(c(1,0), nrow=2,ncol=1, byrow=T)
y

##      [,1]
## [1,]    1
## [2,]    0

p %*% y

##      [,1]
## [1,] 0.50
## [2,] 0.25

psquare <- p %*% p

psquare %*% y

##        [,1]
## [1,] 0.3750
## [2,] 0.3125

pto4 <- psquare %*% psquare

pto4 %*% y

##           [,1]
## [1,] 0.3359375
## [2,] 0.3320312

pto16 <-pto4%*% pto4

pto16 %*% y

##           [,1]
## [1,] 0.3333435
## [2,] 0.3333282