Discussion week 10

# Exercise 3-P 414:


P = matrix(c(.5, .25, .25,
             .5, .25, .25,
             .5, .25, .25), nrow = 3, ncol = 3, byrow=T)

P

##      [,1] [,2] [,3]
## [1,]  0.5 0.25 0.25
## [2,]  0.5 0.25 0.25
## [3,]  0.5 0.25 0.25

\[P^2\]

P2 = P %*% P
P2

##      [,1] [,2] [,3]
## [1,]  0.5 0.25 0.25
## [2,]  0.5 0.25 0.25
## [3,]  0.5 0.25 0.25

\[P^3\]

P3 = P2 %*% P
P3

##      [,1] [,2] [,3]
## [1,]  0.5 0.25 0.25
## [2,]  0.5 0.25 0.25
## [3,]  0.5 0.25 0.25

\[P^7\]

P7 = P3 %*% P
P7

##      [,1] [,2] [,3]
## [1,]  0.5 0.25 0.25
## [2,]  0.5 0.25 0.25
## [3,]  0.5 0.25 0.25

\[p=p^n\]