“AÑO DE LA DIVERSIFICACIÓN PRODUCTIVA Y DEL FORTALECIMIENTO DE LA EDUCACIÓN” UNIVERSIDAD NACIONAL JOSÉ FAUSTINO SÁNCHEZ CARRIÓN
FACULTAD DE INGENIERÍA INDUSTRIAL, SISTEMAS E INFORMÁTICA ESCUELA ACADÉMICO ACADÉMICO PROFESIONAL DE INGENIERÍA INDUSTRIAL
MODELO DE MARKOV
CURSO: INVESTIGACIÓN DE OPERACIONES II DOCENTE: SOSA PALOMINO, ALCIBÍADES ESTUDIANTES: ALCEDO MUÑOZ, CRISTHIAN
COLLANTES BONATTI, DANNY
FALERO FALERO PAICO, EUSEBIO EUSE BIO
GERVACIO GERVACIO VERAMENDI, JUNIOR
HUASCO MARTEL, JUAN
LASTRA CELINO, DAV DAVID ID
OTERO ELLEN, OSCAR
CICLO: VII HUACHO - PERÚ !"#
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
INTRODUCCIÓN
L$% &$'()$% '( M$*+ %( .)&/01() '()2* '( /% '()3.)$'% 4*&(%% (%2&5%2.&%6 D.&7% (%20'.$) (/ &34*2$3.()2 '( $*.$8/(% $/($2*.$% $ / /$*9 '(/ 2.(34 : ;2,<=6 S( '(>.)() &3 0)$ &/(&&.?) '( $*.$8/(% $/($2*.$% @: ;2,<=, 2
I, ')'( : ;2,<= 40('(
∈
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
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
OBJETIVOS
OBJETIVO GENERAL •
D(%$**//$* (/ 3'(/ '( M$*+ &) 0) &$% $4/.&$2.6
OBJETIVOS ESPECÍFICOS •
C)&(* 1 >$3./.$*.$*)% &) (/ 3'(/ '( M$*+6
•
I)2(*4*(2$* 1 &)2*$%2$* /% *(%0/2$'% '( 3'(/ '( M$*+6
•
D$* $ &)&(* /$ 3(* '(&.%.?) 8$%5)'%( () /% *(%0/2$'% 1$ 82().'%6
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
CADENA DE MARKOV
L$% &$'()$% '( M$*+ %) 0)$% 7(**$3.()2$% 4$*$ $)$/.$* (/ &34*2$3.()2 1 (/ 98.(*) '( '(2(*3.)$'% 2.4% '( 4*&(%% (%2&5%2.&%, (%2 (%, 4*&(%% 0( (/0&.)$) '( >*3$ ) '(2(*3.).%2.&$% $ / /$*9 '(/ 2.(34 () 2*) $ 0) &)0)2 '( (%2$'%6 U)$ &$'()$ '( M$*+, M$*+, 4* / 2$)2, *(4*(%()2$ 0) %.%2(3$ '( $*.$ %0 (%2$' $ / /$*9 '(/ 2.(3 2.(34 4,, %.() %.()' ' &$'$ &$'$ &$38 &$38. . 0)$ 0)$ 2*$)% 2*$)%.& .&.? .?)) '(/ '(/ %.%2 %.%2(3 (3$6 $6 D.&7 D.&7% % &$38 &$38. .%% ) (%25 (%25)) 4*('(2(*3.)$', $0)0( %. / (%2$ /$ 4*8$8./.'$' '(/ 4*?.3 (%2$' () >0)&.?) '( /% (%2$'% $)2(*.*(%, 4*8$8./.'$' 0( (% &)%2$)2( $ / /$*9 '(/ 2.(34 ;%.%2(3$ 739)( () (/ 2.(34=6 E()20$/3()2(, () 0)$ 2*$)%.&.?), (/ )0( (%2$' 40('( %(* (/ 3.%3 0( (/ $)2(*.* 1 (% 4%.8/( 0( (.%2$ /$ 4%.8./.'$' '( .)>/0.* () /$% 4*8$8./.'$'(% '( 2*$)%.&.?) $&20$)' $'(&0$'$3()2( $'(&0$'$3()2( %8*( (/ %.%2(3$ ;'(&.%.?)=6 ;EPPEN, GOULD SCHMIDT !!!= R(&.8() %0 )38*( '(/ 3$2(352.& *0% A)'*(. A)'*((.2&7 M$*+ ;"#K-"=, 0( /$% .)2*'0 () "! "!66
ORIGEN DE LA TEORÍ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
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
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
Mod!o d M"#$o% U)$ 3'(/ '( M$*+ 4* (/ )38*( '( A)'*(1 M$*+, (% 0) %.%2(3$ 3$2(352.& 0( %0>*( 2*$)%.&.)(% '( 0) (%2$' $ 2*, ()2*( 0) )Q3(* >.).2 )03(*$8/( '( (%2$'% 4%.8/(%6 S( 2*$2$ '( 0) 4*&(% $/($2*. 9()(*$/3()2( &$*$&2(*.$' &3 %.) 3(3*.$ (/ %.90.()2( (%2$' '(4()'( %?/ '(/ %(&0()&.$ '( $&)2(&.3.()2% 0( /$ 4*(&('.(*)6 L$ 4*8$8./.'$' '( 2*$)%.&.) (%2$ '(>.).'$ $%.
(%2$' $&20$/ 1 ) () /$
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
L$ &0$/ 2.()( &3 .)2(*4*(2$&.) / %.90.()2(, /$ 4*4$8./.'$' '( (%2$* () (/ (%2$' () (/ 2.(34 ), '$' 0( %( (%20 .).&.$/3()2( () (/ (%2$' . () (/ 33()2 .)3('.$2 $)2(*.* )"6 L$ &$'()$ '( 3$*+ (% 0) 4*&(% (%2&$%2.&, 1$ 0( /$% $*.$8/(% : ",:,X,:) 40('( .)2(*4*(2$*%( &3 0)$ %0&(%.?) '( $*.$8/(% $/($2*.$% &01$% &$*$&2(*%2.&$% 40('() $*.$* $ / /$*9 '(/ 2.(346
E(34/
S($ :2 /$ >$3./.$ '( (%2$'% '(/ &/.3$, ')'( : ",:,X,:) *(4*(%()2$*$) /% (%2$'% '(/ &/.3$ () (/ '$ ", '$ 7$%2$ (/ '$ )6
P#o&'d"d d M"#$o%: S( '.&( 0( 0) 4*&(% &034/( /$ 4*4.('$' '( M$*+ &0$)' 2'$ /$ 7.%2*.$ 4$%$'$ '(/ 4*&(% %( 40('( *(%03.* () /$ 4%.&.?) $&20$/ 0( &04$ (/ 4*&(% 4$*$ 4'(* &$/&0/$* /$ 4*8$8./.'$' '( &$38.$* $ 2* (%2$', (% '(&.*, %( &034/( /$ 4*4.('$' %.90.()2(
(P"#" )*+ , *-'!'"/ U)$$ '( /$% U) /$% 4*.) 4*.)&. &.4$ 4$/( /(%% 02./ 02./.' .'$' $'(% (% 0( 0( 2.() 2.()(( (/ 3'( 3'(/ / '( M$*+ M$*+ (% (%2$ (%2$8/ 8/(& (&(* (* /$% /$% 4%.8./.'$'(% '( &0$/0.(* (()2 >020* &)&.()' /% (()2% 4$%$'%6 E%2 40('( 1 $>(&2$ /$% '(&.%.)(% 0( 4'*$3% 23$* 8$%5)')% () /$ .)&(*2.'038*( 0( 4*&$) 4%((* $*.% (()2% >020*% 1 2'% 2.()() %0 9*$' '( 4*8$8./.'$' '( 0( %0&('$)6
O2* '( /% >$&2*(% 0( $/2(*$ /$ 23$ '( '(&.%.)(% (% &0$)' (%2% 4%.8/(% (()2% >020*% %( () $/2(*$'% &) (/ 4$% '(/ 2.(34, 4$*$ (.2$* (%2( $&)2(&.3.()2 (.%2( (%2( 3'(/ (/
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
E%2$ '(4()'()&.$ '(/ (()2 $)2(*.* '.%2.)90( $ /$% &$'()$% '( M5*+ '( /$% %(*.(% '( (()2% .)'(4()'.()2(%, .)'(4()'.()2(%, &3 2.*$* 0)$ 3)('$ $/ $.*( 0) '$'6
(0U1 TIPO ES/ E/ M'( M'(/ / '( M$*+ M$*+ (% 0) 2.4 2.4 '( 3'( 3'(/ / 4*8 4*8$8 $8./ ./% %2.& 2.& 0( 0( %( 0%$ 0%$ 4$*$ 4$*$ 4*(' 4*('(& (&.* .* /$ (/0&.?) (/0&.?) 1 1 (/ &34*2$3.()2 $ &*2 1 $ /$*9 4/$ '( '(2(*3.)$'% %.%2(3$% %.%2(3$%66
M"-#' D T#"2,'3'42: U)$ 3$2*. '( 2*$)%.&.?) 4$*$ 0)$ &$'()$ '( M$*+ '( ) (%2$' (% 0)$ 3$2*. '( ) : ) &) 2'% /% *(9.%2*% ) )(9$2.% 1 &) /$ 4*4.('$' $'.&.)$/ '( 0( /$ %03$ '( /% *(9.%2*% '( &$'$ &/03)$ ; >./$= (% "6 ;EPPEN, GOULD SCHMIDT !!!= !!!= P* ((34/ /$% %.90.()2(% %) 3$2*.&(% '( 2*$)%.&.?)6
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
U) &)0)2 >.).2 '( M (%2$'%, (7$0%2.% 1 3020$3()2( (&/01()2(% ;((34/ (%2$'% '( /$ ()>(*3('$'=
C.&/ '( 3$*+ ;4$%= ;4$%= 4(*.' '( 2.(34 0( %.*( '( 8$%( 4$*$ ($3.)$* ($3.)$* /$% 2*$)%.&.)(% ()2*( (%2$'% ;((34/, 0) 3(%=
P*8$8./.'$'(% '( 2*$)%.&.?) ()2*( (%2$'%, () 0) &.&/ ;3$2*. P=
D.%2*.80&.? D.%2*.80&.?)) .).&.$/ .).&.$/ '(/ %.%2(3$ ()2*( /% M (%2$'% (%2$'% 4%.8/(%6 4%.8/(%6 ;HAMDY ;HAMDY A6 TAH AHA A !!=
P#o3,o, P#o3,o, ,-o36,-'3o, U)$ %0&(%.?) '( 8%(*$&.)(% 8%(*$&.)(% :", :, 6 6 %( '()3.)$ 4*&(% (%2&5%2.& (%2&5%2.&
S. /% $/*(% '( (%2$% 8%(*$&.)(% ) %( 40('() 4*('(&.* ($&2$3()2(6
P(* %( 40('() (%4(&.&$* /$% 4*8$8./.'$'(% 4$*$ /% '.%2.)2% $/*(% 4%.8/(% () &0$/0.(* .)%2$)2( '( 2.(346 x 1 : v . a quedefine quedefine el estad estadoinici oinicial al del proce proceso so x n : v . a que defineel defineel estad estado o del proc procesoen esoen el instan instante te deltiempo deltiempo n
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
FINITAS: C$*$&2(*.$'$% 4* 0( /$ &0**()&.$ '( /% (()2% 2(*3.)$) () /% (%2$'% $8%*8()2(%6 S0(/() &0**.* '(%40% '( 0) (%2$' '( 4*&(%% E3 () /$ ()2$ '( 3$)$)$%, /$% 3$)$)$% 2(*3.)$) %.()' ()'.'$% %( 4.(*'() 4* 40'*.&.?)6
INFINITAS: L$ &0**()&.$ '( /% (()2% %( &)%.'(*$ .)'(2(*3.)$', 4(* 2.()'() $ 0)$ %.20$&.?) '( (%2$8./.$&.?)6 E3 /% (%2$'% '( &/.3$, 40('() %(* %/($' )08/$' 0( &0**( (/ '$ $ '$, /$% 4*(>(*()&.$% 4* &$)$/(% &$)$/(% 2(/(.%.%6 2(/(.%.%6
D7'2'3'o2, 2 !o, P#o3,o, P#o3,o, d M"#$o% E,-"do,: L$% &)'.&.)(% () /$% &0$/(% %( ()&0()2*$ 0) ()2( %0&(%% 4%.8/(%6 E2,"8o,: L$% &0**()&.$% *(4(2.'$% '( 0) (()2 0( %( (%20'.$6 P#o9"9'!'d"d d T#"2,'3'42: L$ 4*8$8./.'$' '( 4$%$* '( 0) (%2$' $&20$/ $/ %.90.()2( () 0) 4(*' 2.(34, 1 %( '()2$ 4* 4* 4. ;/$ 4*8$8./.'$' '( 4$%$* 4$%$* '(/ (%2$' . $/ (%2$' () 0)$ 0)$ 2*$)%.&.?) 4(*'=
M"-#' d -#"2,'3'42 P;: S( '(>.)( &3 0)$ 3$2*. &0$'*$'$ + [ + &01% (/(3()2% %) &'< '( /$ %.90.()2( >*3$
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
E/ (/(3()2 () /$ >./$ ., &/03)$ , 4. P ;:) S\:)]" S.=, *(4*(%()2$ /$ 4*8$8./.'$' '( 2*$)%.&.?) '( 0) 4$%6 E% 0)$ 3$2*. &0$'*$'$ &01% (/(3()2% %) ) )(9$2.% 1 2$/ 0( /$ %03$ '( /% (/(3()2% '( &$'$ >./$ (% .90$/ $ "6
S=59o!o, *-'!'"do,: "6
&'<: P*8$8./.'$' '( &$38.$* '(/ (%2$' . $/ (%2$' 6
6
P: M$2*. >*3$'$ 4* /% $/*(% '( 4. ;M$2*. '( 2*$)%.&.?)=6
6
S' -;: P*8$8./.'$' '( ()&)2*$*%( () (/ (%2$' . () (/ 4(*.' 2
ESTADOS ABSORBENTES: U) (%2$' %( //$3$ $8%*8()2( %. 4.+ ", (% '(&.*, %. 0)$ ( 0( (/ (%2$' //(9$ $ +, 4(*3$)(&( $7 $7 4$*$ %.(34*(6
MODELO MATEMATICO: CADENA INFINITA S" ;2= ^ S ;2= ^X ^ S ) ;2= " 4." ^ 4. ^X ^ 4.)
"
) (%2$'% 6
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
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
S? @ [ 1 0 0 ] S> @
S @
[ 10 0 ]
[
p 11 p 21 p 31
[
p 12 p 22 p 32
p 11 [ p 11 p 12 p 13 ] p 21 p 31
]
p 13 p 23 =[ p 11 p 12 p 13 ] p 33
p 12 p 22 p 32
p 13 p 23 p 33
]
=[ x y z ]
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
L$ 4*8$8./.'$' &)'.&.)$/ P;:)^" % _ :) %=, '( 0( /$ &$'()$ (%2$*5 () (/ (%2$' % () (/ 2.(34 ) ^ " %. (%25 () (/ (%2$' %. () (/ 2.(34 ) %( &)&( &3 0)$ 4*8$8./.'$' '( 2*$)%.&.?)6 S. 4$*$ 0)$ &$'()$ '( M$*+ (%2$ 4*8$8./.'$' '( 2*$)%.&.?) 2.()( (/ 3.%3 $/* 4$*$ 2' /% 2.(34% ) ;) ", , ,666= '(&.3% 0( /$ &$'()$ 2.()( 4*8$8./.'$'(% '( 2*$)%.&.?) (%2$&.)$*.$%6
S( &)%.'(*$ /$% %.90.()2(% >*30/
%$ S = S 6 P S = " ∑ i
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
P$*$ '$* %/0&.?) $/ %.%2(3$ '( (&0$&.?), '(4()'( 0( 32' 02./.$ (/ $)$/.%2$6
. #9o! M"#$o%'"2o P$*$ 02./.$* (%2( 32' %( 2.()( 0( 2()(* () &)%.'(*$&.?) 0) (%2$' .).&.$/, '(%40% $4/.&$* (/ 5*8/ '( 4*8$8./.'$'(%6 S( '(2$//$*$ 0) ((34/ 4$*$ 3$1* &34*()%.?)6 L$ 4*8$8./.'$' '( 0( 4$%$' 3$$)$ (%2 )08/$' %. %$8(3% 0( 71 (%25 )08/$' &**(%4)'( ()2)&(% ()2)&(% $ ()&)2*$* P;: ) _ :" )=6 P$*$ &$/&0/$* (%2$ 4*8$8./.'$' ($3.)$3% /% 4%.8/(% (%2$'% '(/ '$ '( 3$$)$ 1 /$% >*3$% '( &?3 //(9$* $ : ) ;)08/$'=, ; )08/$'=, (3% (%2 () (/ %.90.()2( 5*8/ ')'( % ;%/($'=
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
MODELO MATEMATICO: CADENA FINITA E% 0)$ &$'()$ '( M$*+ 4$*$ /$ 0( (.%2( %?/ 0) )Q3(* >.).2 + '( (%2$'% 4%.8/(% %",6%+ 1 () &0$/0.(* .)%2$)2( '( 2.(34 /$ &$'()$ (%25 () 0) '( (%2% + (%2$'%6 P$*$ (%2( &$% %( &)%.'(*$ &$)2.'$'(% .).&.$/(% 4$*$ '(2(*3.)$* /$% &$)2.'$'(% 0( 0('$) $>(&2$'$% 4* /% (%2$'% $8%*8()2(%, (/ 32' '( %/0&.?) (% (/ %.90.()2(
P",o >: 5"-#' d -#"2,'3'42 S( '(2$//$ /% (%2$'% () 4*&(% 1 /% (%2$'% $8%*8()2(%6
P",o : %( &/&$ %38/% $ /$% 3$2*.&(% >*3$'$% '(%40% '( %(4$*$*/% 4* 0)$ /)($ (*2.&$/ 1 7*.)2$/6
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
NF@ F.L C3 %( &)%.'(*? &$)2.'$'(% .).&.$/(% () /% (%2$'% '( 4*&(%, %/ 0('$ 30/2.4/.&$* (% 4* /$ )0($ 3$2*. 3$2*. >0)'$3()2$/ 1 '( (%( 3' *(%0/2$ *(%0/2$ )0(%2*$% &$)2.'$'(% &$)2.'$'(% '(%($'$%6 '(%($'$%6
MODELO MATEMATICO: CADENA FINITA EJEMPLO PRCTICO
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
9; "!!"# !" o9"9'!'d"d o9"9'!'d"d d "3&-"3'42 "3&-"3'42 )* -'2 -'2 3"d" 3"d" o&#"do# o&#"do# 2 ! &#'odo .
RESOLUCION $= M$2* M$2*. . '( 2*$) 2*$)%. %.&. &.?) ?)66
E> E E
CLARO ENTEL MOVISTAR CLARO !6K !6 !6 ENTEL !6 !6# !6 MOVISTAR !6 !6 !6
L$ %03$ '( /$% 4*8$8./.'$'(% '( &$'$ (%2$' () (%2( &$% 4(*$'* '(8() %(* .90$/(% $ "
9; "!!"# "!!"# !" o9"9'! o9"9'!'d"d 'd"d )* -'2 -'2 3"d" 3"d" o&#"do# o&#"do# 2 2 ! &#'odo &#'odo .
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Co5o &od5o, %# !" %"#'"3'42 2 ! &#'odo "! , 5*8 5=2'5" 3",' '2,'H2'7'3"2-
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
S 1 + S 2+ S 3=1 X;= S 1 , S2 y S 3
"!!"5o, !o, %"!o#, d: S': S 1=
∆ S1
S 2=
∆S
∆ S2 ∆S
S3 =
∆ S3 ∆S
So!o , #,o!%#6 3o2 !", 3*"3'o2, ; ; 8 ; 3o2 ! METODO DE CRAMER.
[
0.20
∆ S = 0.20
−0.50 0.20
]
0.30 0.20
−0.60
0.20
−0.50 0.20
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
[ ( 0.20 x 0 x 1 ) + ( 0 x −0.60 x 1 )+ ( 0.30 x 0.20 x 1 ) ]−¿ [ ( 1 x 0 x 0.30 ) + ( 1 x – 0.60 x 0.20 ) + ( 1 x 0.20 x 0 ) ]=¿ ?.>
[
0.20
∆ S3= 0.20 1
]
−0.50
0 0.20
−0.50
0.20 1
0 0.20 1 1
0.2 1
[ ( 0.20 x 0.20 x 1 ) + (−0.50 x 0 x 1 )+ ( 0 x 0.20 x 1 ) ]−¿ [(
) (
) (
)]
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
ENTEL
0.25
CONCLUSIÓNES
S( 7$ *($/.$' 0) (%20'. 3$*&.$) '( (()2% .)>.).2%6
S( 7$) ($/0$' /% *(%0/2$'% &) 2*( 3(2'% ;M2' R(&0*%., M2' (%2$' E%2$&.)$*.=
L% '$2% (%&9.'% 4$*$ /$ 23$ '( '(&.%.) 7$) %.' %(/(&&.)$'%, 23$)' &3 *(>()*()&.$ /% '$2% '( /$ 3$2*. (%2$&.)$*.$6
L$ (34*(%$ '( 2(/(>).$ 3./ &) 3$1* $&(42$&.) () (/ 3(*&$' 4(*0$) (/
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
C.(*2 $ "!b '( /% o9##o, $%&.()'() $ o&#"#'o, 1 $0) "!b %( /(% 4.'( 0( $8$)')() /$ (34*(%$6 D0*$)2( 0) $ &0$/0.(*$, #b '( /% o&#"#'o, $%&.()'() $ ,*&#%',o#, 1 0) "b
o&#"#'o,, $)2(% '( %(* %( /(% 4.'( $8$)')$* /$ (34*(%$6 L% o9##o, '(8 '(8() () $%&() $%&()'(* '(* $ o&#"#'o ,*&#%',o#,. L% 2*$8$$'*(% 0( ) %( '(%(34($) $'(&0$'$3()2( $35% '(%&.()'() '( %0 &$2(9*$, 4(*3$)(&() () %0 ).(/ %( /(% 4.'( 0( $8$)')() /$ (34*(%$6
S &'d d-#5'2"#: $= C05/ (% /$ 4*8$8./.'$' '( 0( 0) o9##o //(90( $ ,*&#%',o#. 8= C05/ (% /$ 4*8$8./.'$' 4*8$8./.'$' '( 0( 0) o9##o //(90( $ *()0)&.$*6 *()0)&.$*6 &= C05/ (% /$ 4*8$8./.'$' '( 0( 0) o&#"#'o %( &).(*2$ () ,*&#%',o#. '= C05/ (% /$ 4*8$8./.'$' '( 0( 0) o&#"#'o *()0)&.(6
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Fx J
5 0 0.1 0.05
2.78 5.56 0.13
0.14 0.24
0.86 0.72
0
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
•
L$ 4*8$8./.'$' '( 0( 0) 8*(* //(90( $ %(* '(%4('.' (% '(/ Kb6
•
L$ 4*8$8./.'$' '( 0( 0) 4(*$*. //(90( $ %(* %04(*.%* (% '(/ b6
•
L$ 4*8$8./.'$' '( 0( 0) 4(*$*. //(90( $ %(* '(%4('.' (% '(/ b6
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world's largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
•
TAHA, H$3'1 A6 I)(%2.9$&.?) '( O4(*$&.)(%, U)$ I)2*'0&&.?)6 "6 E'.&.)(% A/>$3(9$, S6A6 M.&6 D6F6 M.&6
•
MONTAÑO, MONTAÑO, A90%2)6 I).&.$&.?) $/ M2' '(/ C$3.) C*2.&6 "6 E'.2*.$/ T*.//$%, S6A6 M.&6 D6F6 M.&6