ejercicio 5.14 (colas)

174 days ago by roschaefer

Sea X una cadena de Markov con espacio de estado {a,b,c,d,e,f} probilidades de transicion dadas por: 
       
P<-matrix(c(0.3, 0.5, 0.0, 0.0, 0.0, 0.2,0.0, 0.5, 0.0, 0.5, 0.0, 0.0,0.0, 0.0, 1.0, 0.0, 0.0, 0.0,0.0, 0.3, 0.0, 0.0, 0.0, 0.7,0.1, 0.0, 0.1, 0.0, 0.8, 0.0,0.0, 1.0, 0.0, 0.0, 0.0, 0.0),ncol=6,byrow=TRUE) dimnames(P)<-list(c("a","b","c","d","e","f"),c("a","b","c","d","e","f")) P 
        
    a   b   c   d   e   f
a 0.3 0.5 0.0 0.0 0.0 0.2
b 0.0 0.5 0.0 0.5 0.0 0.0
c 0.0 0.0 1.0 0.0 0.0 0.0
d 0.0 0.3 0.0 0.0 0.0 0.7
e 0.1 0.0 0.1 0.0 0.8 0.0
f 0.0 1.0 0.0 0.0 0.0 0.0
    a   b   c   d   e   f
a 0.3 0.5 0.0 0.0 0.0 0.2
b 0.0 0.5 0.0 0.5 0.0 0.0
c 0.0 0.0 1.0 0.0 0.0 0.0
d 0.0 0.3 0.0 0.0 0.0 0.7
e 0.1 0.0 0.1 0.0 0.8 0.0
f 0.0 1.0 0.0 0.0 0.0 0.0
a.- Catalogar los estados recurrentes. los estados recurrentes son c, b, d, f. b.- Catalogar los conjutos irreducible. conjunto irreducible {b,d,f} {c} c.- Catalogar los estados transitorios los estados transitorios son a, e. d.- Calcule la matriz F 
       
P.<-matrix(c(0.3, 0.5, 0.0, 0.0, 0.2, 0.0 ,0.0, 0.5, 0.5, 0.0, 0.0,0.0, 0.0, 0.3, 0.0, 0.0, 0.7,0.0,0.1, 0.0, 0.0, 0.8, 0.0,0.1,0.0, 1.0, 0.0, 0.0, 0.0, 0.0,0.0, 0.0, 0.0, 0.0, 0.0,1),ncol=6,byrow=TRUE) P. 
        
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]  0.3  0.5  0.0  0.0  0.2  0.0
[2,]  0.0  0.5  0.5  0.0  0.0  0.0
[3,]  0.0  0.3  0.0  0.0  0.7  0.0
[4,]  0.1  0.0  0.0  0.8  0.0  0.1
[5,]  0.0  1.0  0.0  0.0  0.0  0.0
[6,]  0.0  0.0  0.0  0.0  0.0  1.0
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]  0.3  0.5  0.0  0.0  0.2  0.0
[2,]  0.0  0.5  0.5  0.0  0.0  0.0
[3,]  0.0  0.3  0.0  0.0  0.7  0.0
[4,]  0.1  0.0  0.0  0.8  0.0  0.1
[5,]  0.0  1.0  0.0  0.0  0.0  0.0
[6,]  0.0  0.0  0.0  0.0  0.0  1.0
Q<-P.[1:5,1:5] Q 
        
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.3  0.5  0.0  0.0  0.2
[2,]  0.0  0.5  0.5  0.0  0.0
[3,]  0.0  0.3  0.0  0.0  0.7
[4,]  0.1  0.0  0.0  0.8  0.0
[5,]  0.0  1.0  0.0  0.0  0.0
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.3  0.5  0.0  0.0  0.2
[2,]  0.0  0.5  0.5  0.0  0.0
[3,]  0.0  0.3  0.0  0.0  0.7
[4,]  0.1  0.0  0.0  0.8  0.0
[5,]  0.0  1.0  0.0  0.0  0.0
w <- solve(diag(ncol(Q))-Q) w 
        
Error in solve.default(diag(5) - Q) : 
  Lapack routine dgesv: system is exactly singular
Error: object 'w' not found
Error in solve.default(diag(5) - Q) : 
  Lapack routine dgesv: system is exactly singular
Error: object 'w' not found