Act3 JuanPaaaa

library(expm)

#estados
estados = c("S,A","S,B","R,A","R,B")

datos = c(0.49,0.21,0.21,0.09,0.175,0.525,0.075,0.225,0.35,0.15,0.35,0.15,0.125,0.375,0.125,0.375)

#Matriz
monster = matrix(datos, ncol = 4, nrow = 4, byrow = T)
monster

      [,1]  [,2]  [,3]  [,4]
[1,] 0.490 0.210 0.210 0.090
[2,] 0.175 0.525 0.075 0.225
[3,] 0.350 0.150 0.350 0.150
[4,] 0.125 0.375 0.125 0.375

# Punto B -----------------------------------------------------------------

alpha = c(0,1,0,0)
trespasos = monster%^%3
trespasos

          [,1]      [,2]      [,3]      [,4]
[1,] 0.3166690 0.3113310 0.1875810 0.1844190
[2,] 0.2594425 0.3685575 0.1536825 0.2183175
[3,] 0.3126350 0.3073650 0.1916150 0.1883850
[4,] 0.2561375 0.3638625 0.1569875 0.2230125

final = alpha%*%trespasos
final[1]

[1] 0.2594425

#Cadena
library(markovchain)


# Punto C -----------------------------------------------------------------


cmtd = new(Class = "markovchain", states = estados, transitionMatrix = monster)
estable = steadyStates(cmtd)
estable

           S,A       S,B       R,A       R,B
[1,] 0.2840909 0.3409091 0.1704545 0.2045455

costos = c(50000,50000,120000,120000)

valor_esperado = estable%*%costos
valor_esperado

      [,1]
[1,] 76250