28
Profesora: Leticia Cañedo Suárez. ESCOM-IPN

Probabilidad y estadistica Notas Cap1

Embed Size (px)

DESCRIPTION

Probabilidad y estadistica Notas Cap1Ejemplos y explicaciones del primer capitulo

Citation preview

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    ! "! !#$$%!%"&'#'%!(#$$%!%(#'#(&'#( ! %##() ('# ( ## #*#+!,() !# "! (%'*#( !#( # '#($-(% #(.

    '#/!#$$%!%(!*!(*'*-'% (0"('"%!#(12*#(0"(" (#(1#'"%'#( ## %#('*$%3 #!#*$4#(#(#!'#%#(. !"# $5%('&% %!5%(' %!#(6"+#(4(!7#89::+%'#)#!("(''#*'*-'% # ! '#/ ! #$$%!% ( %% %# # !#(*'*-'% #(1 (( !%( ( !;

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    8

    %%> !!$ '/!"#$&! 5%*'# ( ! #! %2 # #6"'#"! !#( #(%$!(("!'#(!5%*'#.

    %%%> 0"#!/!( "!0"%("$ #6"'#!( %#*"('!.1'&!.B.# '"!4"*#8& (."$ - %% 0"!*# ,5%% 0"!*# "4.!$ '/!"#$&CD ) 5) 5 )5 ) 55)55 )5 5)555E0"! #( (CD 5) 5 )5 E

    !*#(" CD ) 5) 5 )5 ) 55)55 )5 5E!#*-(" "4CD ) 5) 5 )5 E

    .B.# '"&A/ "!#!!+"%'( %2 '(,"&"!'! A)!%40"%#(+"%1'."$ -%% 0"!&A/ "!#&"!'! A)&"!'!%40"%,%% 0"(%+"1'.!$ '/!"#$&CD))E0"!!&A/ "!#(%+"1'CDE!&A/ "!#('%CDEC 8.B.# '"!%+!4'('/ "!#("# (#*"1 '")(%( %# "#!!#(,( !(%1% #*#1 '"#(##$"#.!$ '/!"#$&CD)))))))E0"!5 '*'#('/ "!#($"#(CD))E

    !#*-("'/ "!#1 '"#(#CD)))EF.B.# '"!4"*#A('#$'" "4;5>#'( (; >.!$ '/!"#$&CD5) 5) 5) E0"!*#(#( (CD 5) E

    8

    5

    5

    5

    %+*-$#!!#$!*F.

    G*#!4*%'#

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    F

    9.B"'"'#*2&%! ( (*$! #"+G*#"'#( (#!".("3(!(*$!#)(%( %# "'#,( "'!G*#'#'!1 '#(."$ -(!G*#'#'!"'#((#!".!$ '/!"#$&CD:)))...)E0"!!'$6#(%* $!CD:E

    '""G*#1 '#(*,#!9:H!'#'!"'#(

    +++

    ++=

    %* #E)...)I>;)I>D;

    #E)...)I)ID

    !'&'"/0" #( '#!( %#*"('!(! #6"'#'##(!#(!*'#(0"#('-.#' #*# ) # . E,JDK =

    ! / "!#('!&'#,!'(#*$! #*!*'#)! '-+"!#(!( %#*"('! .

    %%> "#! - ! 0"! ( ! #6"'# !*'#( 0" ' !#( #(

    &'#(!*%(*#'%*#,(( %$ E,JD =

    ! / "!#!%40"%('!&'#,!! A!&'#)!'(#*$(!%'( %2*$#(&'#(,! '-+"!#(!( %#*"('!.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    9

    %%%> #(&'#((#.&/2"!# !1/"!(%#(%'( ')( % =

    %&> / -!0"! (! #6"'#!*'#(0"('- "!0"% !#(#(&'#(#*$#(,(#' E#JD =

    #(!,(0"(-+,"!#!+#(' "(#(#!(!!*(,(L#+

    %> KK>K; = ! #*!*'#!"%2(!%'( %2!#( #*!*'#(.%%> KK>K; = ! #*!*'#!%'( %2(!"%2!#( #*!*'#(.

    34#/" !"$.B#$$%!%"&'#(%'' #*#!1 " %!'%& #!0"(#$'/( ("!'#(%!# (#( %'%"+G*#& () #% %#((%*%!(.#6*!#(%( !4"*#& (,5 '*' !4*%'#( !*# #!

    A %%$('/0"!#$$%!%#$' ('-#

    .

    &*! $.B('-$(! # '#("!'#(%+"!*'(/*%!()( %(("*0" "#!#(("!'#('%!*%(*##'"%# "%.!6*!#!*#'*#(#(#(%$!( ("!'#() # "4) # !# ''# (% ! #$$%!% 0" # " " ( !#$$%!%0"# "" "4 '*$%3() "*!%# %'(#%(0"&*#(*-(!'./)1" 0$.B'%0"& #!+# ## %*%'#!(#(#$!&'#,$(('5% %!(#(%+"#$$%!% #&%'.+%5%M,# (%#(0"# (%'*#( ## '!!!#(!*'#(!( %#*"('!*-($% (%'*#(($ "'#((#.(/0"*#("# #(#$*3'##( #'#.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    >;>...;>;>;;

    >>;>...;>;>;;>>...;>;;

    +=

    >Q;

    Q

    =

    ++%, -') $ -("+!##$6'#(%('%'#(##%*#'!#. #*$% %2%1%#'(2!#(%! #'%#(%1'.1'&.B#(%#"&*'!( "'#!'()$) )('%0"

    %> M,F #*$% %#(%('%'('#*#"(#!!'!&4)$) ).%%> M, M,F #*$% %#(%('%'('#*#8!'(!&4$ C $C$ C$ C $C $)

    $C$C$C$C$C$)$ C$ C $C $C$ C $) C C C C C .

    %&> 2!#*( !(F!'(!&4$ .

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    R

    $(&0"'/*#(*"' %#('#*##(!'(!&4)##0"#(!'(" *$%!#& ()!#%*#'!##(#'#((!#*%(*#!;$>0"!;$>)#(!'(#(#*%'#()0"%'#!('% %#(#(0"*#( #;

    >;

    >;

    >; +=

    +=

    +=+

    8.BS "-'(*("1#*%8(#(%(%('(+"% "!!(!(#'(T >%"'*%# #6"'#(#() "!!((%+(+"%!#'T

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    U

    &/ ->%#A,('% %2!+") "!0"%!()(" #*#FQCF*(%1'()#'# "('(F*( !( 8 (#( 0" 0"% ('6"'( ( " #*# 8Q C CFF*(%1'( #*#!(S "-'(*("*#'(9'"0"(("$4!'!'T&/ ->1%6"#$6'# "!0"%"#(% %2! % "!#,A/( #*# !#( >; #$6'#((''(.$>FQCF;8>;>;>CF*(*#'!(9'"0"((.9.BS"-'#(G*#(%1'(8/+%'#("1#*( #!#(G*#(8)F)R)U,V(%((0"(*,#(0"9::,0"#(%'!#(/+%'#(T&/ -0"!G*#(*,#0"9::$ #*4 #R)U#V, #*##("'%)!(%+"%'/+%'#"( "!0"%!#(FG*#(0"0",!' /+%'# "!0"%!#(8G*#((''(.;8>;F>;8>C8

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    V

    &/ -0"!G*#($'*% #:# #)( %(2!#A,#(# %#(#;8>;>CFG*#(( #'(/+%'#(#'%#(.R.BS"-'#(G*#( '!12% #(%1'((%'/+%'#( ("1#* (% !%*/+%'##"( #T&/ -#A,('% %2(#$!('% %#((/0"!G*#%#(V;:>; #!((%+"%'(#%(%> >;: %%> >; =

    %%%>% ...))) (#&'#(*"'"*'5 !",'('# (

    ==

    =

    >;

    %&>% ...)) ("( " %"*$!&'#(*"'"*'5 !",'()'# (

    =

    =

    =

    >;

    #'$.B ) , '( &'#( "!(0"% " ( %# *"('! (# %# "5%*'#)'# (%> ( ) := %%> >;>K; = %%%> >;>;>;>; += %&> >;>;>;>;>;>;>;>; +++=

    &>

    +++=

    =

    =< =;>;>;

    &%>% '# ( >;>; '!"#$ -%> =

    == #>;>;

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    :

    >;>;>;>; =+= :>;>;>; ==

    %%> K = # =K

    >K;>;>K;>; +== >;>;>K; =

    >;>K; = %%%>$(&0" = K , ( )( ) =K

    K= , ( )( ) = K '# ( ( ) >;K>; += ;>

    >K;>;>; += ;>

    *$%3 KK = ,!#('(&'#((#*"'"*'5 !",'(

    >K;>;>K;>; ++= ;8>(6# >K; ;>, >K; ;>,("('%'",#;8>

    >;>;>;>;>;>; ++=

    >;>;>;>; += %&>#(%*#(!"%2, #*#"(#!#&'#,"'%!%4*#(%%>!(& (0"( (%#.

    W>X;>;>;W>X; += >W;>X;>;>;>;>; ++= >W;>;>;X>;>;>;>; +++=

    >;>;>;>;>;>;>; +++= &>%'."+ %'%!%4!*3'##%" %2*'*-'% .&%>$(&0"(% '# ( K= # = K

    >K;>;>; += #*# :>K;

    '%0"(% :>K; = >;>; =

    (% :>K; > >;>; ;Y ., -#$$%!%!&'#1%%#!( %#*"('!('-#

    >;Y

    >;Y>;

    =

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    1'&!

    .B #$$%!% 0" Z" "$ ! "(# #$$%!% (8

    , ! #$$%!% 0"

    "$! "(#('/('% (V

    F.% !#$$%!%#$*$#( "(#((

    F

    .S"-! ( !

    #$$%!%0"Z"...>"$ "#*#("#('#( "(#(T$>"$#$$%!%T >"$!(#(*'%(T&/ -!#(&'#(Z""$! "(##$$%!%.

    Z""$! "(#('/('% .

    '#(8

    >; = )

    V

    F>; = ,

    F

    >; =

    >8;>;>;>; =+=+=

    $>8

    8

    >;>K; ===

    >8K;>KK; ====

    .B #('", "#* 0" ! , ! # " # !#$! !1 " % 0" (('!9)! "!# " #"1 " %8& (("%#!8)!F#!

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    $>U

    U>F; ==

    >V

    UU

    8>9;#9; =+=+=

    $(&0"'*$%3"%*#(4#!*(%+"%'"#*#(0" !#$$%!%# " %!8)!F,!'*#(0"

    V

    F

    U

    UUF;>;>; =

    ==++=++=

    8.B('-!%4#!%( %21%!'#('!&%(%2("3(!(*$!.%'%1% '( '%#( 1 '#( #*# /'% #() *,#( , *#( , " *( &/#( # ## !#( !(%1% )#*( '%&*'.!%4!#('#( #!#((%+"%'(("!'#(

    '#(0"(2!#'%1 '#( /'% #(H.

    '#(0"(2!#'%1 '#(*,#(9H.

    '#(0"(2!#'%1 '#(*#(RH.

    '#(0"(2!#'%1 '#( /'% #(,*,#(8H.

    '#(0"(2!#'%1 '#( /'% #(,*#(FH.

    '#(0"(2!#'%1 '#(*,#(,*#(8H.

    '#(0"'%!#('('%#(1 '#(H.>S["3# '6!#('#(#'%1 '#(T

    #('#( #1 '#( /'% #(#*,#(;#*$#(>$*"1 '"("&*'.$>S["3# '6 #(#(' '+#/T&/ -M "%+*@,#*" A# "%# #!!$N(2!#O.>R9H#'%1 '#(.$>UH!#('#($*"1 '"("&*'.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    8

    F.B#(%!#(&'#(,'!(0"8

    >; = ,

    >; = .'*%!&!# >K;

    " !( (%+"%'( #% %#( > , (# %(6"'#() $> ('- #'%# , >

    U

    >; = .

    &/ -

    >%!#(&'#((#%(6"'#( =K '# (

    >;>K; ==

    $>% '# (;>K; =

    ===

    >%!#( #6"'#((%'( ')'# (U

    8

    U

    F

    U

    >;>;>K; =

    ===

    9.B"'#!#'( #!#(G*#())8,F( #!# "$#!()(*4 !,(( "#"S"-!(!#$$%!%0"(!+6"('#(#T&/ -%*# (%'# #' "'(*"(!%!(F$#!%'() #*#('-"*(('## " FQF = *(!( "!((2!#"((*((%+"!#(#)#!#''#

    =>F)8));F

    ; ==

    R.B%+%#"1-$% *% # % "%'#(%( %#-"!#'#$!((%!% %#'' #'!(1 '#(."20"A, "'# % "%'#( %'+#(1 '"#(#(" %%'0" #'%:#$!(.(%( %2((! %##$!(!4.! "!!#$$%!%0">%+"!!('+1 '#(.$>#!#*#("!(#'+1 '#(.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    F

    &/ ->M,F1 '"#((,U;9QFQ

    >;9;QF

    QFQ

    Q;

    >;>J;

    = #

    .:>; >

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    9

    )!#0$ ->% :>; = '# (!#$$%!% #% %#!#('-1%%.> #$$%!% #% %#! "*! !( #%( 0"A*#( &%('# ! #$$%!% "&'##A#!( %#*"('!0"'((A" %#!&'#.(/#6*!#('%0"

    %> >JK;>J; =+

    %%> ( ) ( ) ( ) ( ) += '!"#$ -

    %> >;

    >;

    >;

    >K;

    >;

    >K;>;

    >;

    >K;

    >;

    >;>K;>; ==

    =

    +=+=+

    %%>>;

    >;>;>;

    >;

    >;

    >;

    W>X;>;

    +=

    =

    =

    >;>;>;>;

    >;

    >;

    >;

    >;

    >;

    +=+=

    1'&!.B ( ! #$! %2 +(#( ! %*+ %2 ! ) ( !(%1% (+G (" #% %2(5#,('## " %2 #*#(*"('!'$!(%+"%'.

    *!# (*!# #'!

    ( "!%# FS"-!(!#$$%!%0"!%&%'##'+*!#(%(($0"("A#*$T&/ -!#(&'#(!!+%#("A#*$)!!+%#("*"6)!!+%#'%*!#, !!+%#('-(*!#.$(&0"A,#(*((#!&!#$!* 8# "# !$ #/ .B#(%(' #'!#$$%!%!&'#%'3($(!( %#*"('!" %## #% %2.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    !( %#*"('!" %#( #*#G% *'!#(+(#(*!#(.!#( "!(*%'(!#(A#*$()('( %#*"('!" %#A,F

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    R

    &/ -

    # $ # % !#(&'#(!*#(##)#",#".'#(

    >;>; == ##

    >J; =# , >J; =#

    $(&0"!&'#N!*#(##O("& #*#!"%2!#(&'#(N(##!"O,N(##!"O)!# "!('*#(*%'!5(%2

    ## = ( % >;>;>; ## +=

    >;>J;>;>J; #### +=

    '%!%4*#(!A A#0" ( ) ( )( )

    J#

    ## = (6# ( ) ( ) ( ) J ### =

    '# (

    >;>J;>;>J;

    >;>J;

    >;

    >;>J;

    ####

    ##

    ##

    +==

    =

    +

    =

    8

    F.B" (#( A#(# ( ! !% " ("# ! &0" ( ($ ( #1%$! V:H "# !(#( "!$!,VVH "#!(#(%# '.#'(!$()!:H!#( "!$!(( #(% %# ' "# ( "( ! ("# , ! H !#( %# '( ( 6"4+ "!$!. % !(#( A#(# ( ( #+%2 "+"#! "! (2!# 9HA #*'%# !+" &4 " %* , ! ("#%% 0"!(#( "!$!.S"-!(!#$$%!%0"(%# 'T&/ -!#(&'#( "!$!) K %# ')"(% %# ''#*#!("# K" (% "!$!'#*#!("#.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    U

    '#( .:>J; =" V.:>JK; = " :.:>KJK; ="

    :9.:>; = V9.:>K; =

    =

    +=

    +==

    >:9.:;V.:>V9.:;:.:

    >V9.:;:.:

    >;>JK;>K;>KJK;

    >K;>KJK;

    >K;

    >KK;>KJK;

    ""

    "

    "

    "" :.RF

    9.B #" "%&('%+ %2'!! %'(3#(.#$$%!%0"" %'#1!!('" '"!(%'%1%0" # '*'(:.V,!#$$%!%0"" %'0"#($"1!!('" '"!(%'%1%0"1#*% # ' #*#" %'#1!!('" '"!(:..%!9H!#( %'(3#(($1!!(('" '"!()'*%!#$$%!%0"" %'3#0"(A%'%1% # #*#$%#"1!!('" '"!!%A,# "%##"1!!(''%#.&/ -!#(&'#( %'#1!!('" '"!,(%'%1% #*#1!!('" '"!.'#(

    V.:>J; = .:>KJ; =

    9.:>; = R9.:>K; = '# (

    =

    +=

    +==

    >R9.:;.:>9.:;V.:

    >9.:;V.:

    >K;>KJ;>;>J;

    >;>J;

    >;

    >;>J;

    :.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    V

    !&'#%'3("&( #*#!"%2#(&'#(%(6"'#(\ K =

    ( ) ( ) K = ( ) ( ) K += ( ) ( ) ( ) ( )KK +=

    &&

    &

    &&

    +

    =

    >;

    &

    &

    &&

    +

    =

    >;

    >;

    +=

    &&

    &&

    >;

    ++=

    &&

    &&& ( )

    >;

    +=

    &&

    &&

    R.B"('0"(%),(#'(&'#('!(0" :>; , >J;>J; = '# (

    >J;>J; = .&/ -'%0" >J;>J; = "(#!1%% %2#$$%!% #% %#!

    >J;>;

    >;

    >;

    >;>J;

    ===

    >;

    >;

    >;

    >;

    =

    >J;>J; =

    :%1'&!.B#(%" 6 #F$#!%'('%0"'(!!F.( "!!(!4,(#$(&!G*#!'%0"'.#!#(&'#(,1%%#( #'%" %2.

    = D))8)FE

    = D)E

    >; =

    = D)8E

    >; =

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    :

    = DEF

    >; =

    '# ( ===

    F

    >;

    >;>J;

    $(&0" >J;>; = .B!#(&%6#(0"!!+"#"'#0"7#)@%6#+# %#(&%2%T >M,&%6#&%2%#0"!#A #+# %#(T&/ -!#(&'#(

    '&%6#!/%*#''.&%6&%2%.&%6#!/ #* %!.&%6#+# %#(.

    '#(; =' 9.:>J; =' 8.:>; = J; = .:>; = V.:>J; =

    >(#"&%6#+# %#( "!0"%!('(#!/(),#"&%6#(#*-(#!/(!&4#!#''#(#&'#(%(6"'#(,('%0"

    >;>;>;>; ' ++= >;>J;>;>J;>;>J; '' ++=

    :.9R:.V;:.>:.:.9;:. =++= $(&0" >J;>; ' ) >J;>; , >J;>; $> === >8.:;;>J;>; :.U

    > ====V

    ;

    >;>J;

    :.89U

    $(&'*$%30" >;>J; .

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    #!#(#(6*!#(&%#(A*#(&%('#0"A, (#(#!# " %"&'##!'!# " %!#'#) #*#!6*!#)!#$$%!%% #% %#!;$(!( %#*"('!#%+%! > , ! #$$%!% #% %#! ; $( ! ( %# *"('! " %#> (# %+"!(X >J;>J;>; == W)(%# "### ")!#$$%!%#(!')( %#( "#('## "(% 0" , (#%%'(.% *$%# ! # " % "# !' ! # " % ! #'#) #*#( ( 0" A, " %'!!#( #*## "!6*!#),(' (#!#$$%!%% #% %#!,!#$$%!% #% %#!(#%1'(., -#(&'#(,(# "!(% >J;>; = ,(( %$ .( %)!# " %#%1!",!# " %)(##(!#$$%!%# *$%.

    )!#0$ -% ==>;

    >;>J;>;0"($*#(

    >;>;>; = ( %)(%

    ,(#&'#(%%'('# (!#$$%!%!%'( %2!!#((!#" '#!(#$$%!%(%%&%"!(.]!*'(*#(0"(%#(&'#((#%(6"'#(#5 !",'('# ((#%%'()#('##(&) #(%!(%+"%'1'&8)CD))8)FE

    CD)E

    >; =

    CD8)FE

    >; =

    = :>; = >;>;F

    = #(&'#(,(#%(6"'#()##%%'(.

    "$9 % 0" !#( &'#() , (# *"'"*' %%'( (% ( "*! '#( !( #% %#((%+"%'(%> >;>;>; = %%> >;>;>; = %%%> >;>;>; = %&> >;>;>;>; = F.B! "# ( : ( : !!#.#(%!( %##$$%!%"%1#*(#$! "#,(,!#(&'#(

    )9.::J>)D; = E: ):J>)D; = E9.:: S#%%'(,T

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    &/ -

    IF

    I

    )9.::J>)D; = E9.::

    >;>;F

    U

    >; =

    ==

    9.B% '# (S KK T&/ -

    '# ( >;>;>; = #!(,(L#+('%0" >K;>KK; =

    >;>;>;>W;>;>;X>; +=+== >W;>X;>K;>;>;>;>W;X =+=

    >K;>K;>W;>XK;>K;>;>K; === KK

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    8

    $*#(0" >;>;>;>; += >K;>;>;>W;>X;>; +=+=

    '# ( ==

    =

    =

    ;>;

    :.88

    U.B "2 0" ) , (# &'#( *"'"*' %%'( , 0" :>; . "(' 0"

    >;>J; = &/ -

    >;>;

    >;>;

    >;

    >;>J;

    ===

    V.B"2 0" ( !4 8*#( %3'% ( , 1 '*' $! ( " (#! &4. !

    &'#0" ! =3(%**# ."('0" !#(&'#( ) ) 8 (#*"'"*'

    %%'(.&/ -!( %#*"('!!5%*'#(

    CD555)5 ) 5 ) 5)55 )5 5) 55) E

    CD 5 ) 5) 55) E

    >; =

    CD5 ) 5)5 5) E

    >; =

    8 CD5 ) 5 )55 ) E

    >; 8 =

    CD 5) E F

    >; =

    8 CD 5 ) E F

    >; 8 =

    8 CD5 ) E F

    >; 8 =

    8 CD E U

    >; 8 =

    '%0" >;>;>; = = ))8.

    , =

    =

    8

    8 >;>;

    '# (!#('(&'#((#*"'"*'%%'(.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    F

    (#!1%% %2#$$%!% #% %#!('%0"

    >;

    >;>J;

    = >;>J;>; = ,'*$%3

    >;

    >;>J;

    = >;>J;>; =

    ('#( ## #*##*#,!*"!'%!% %2#$$%!%(,("! #*#)+++ ","-"" .#++++#+"

    -"++++,/0+++",

    "-"".#+++#+"-"++++

    -+1#&&"#'$&$'/&" & $ - >;>J;>;>J;>; == (''#*("+!%4!*(%+"%'

    >J;>J;>J;>;>; 8 =

    '!"#$ -

    >;

    >;

    >;

    >;

    >;

    >;

    >;

    >;>;>;

    8

    =

    1'&:.B#$$%!%0" ! !%0" ,#(?"(#0" !!+ ("'%(' (:..:>;8.:;J;>J;>;>; 2222 :.:U

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    9

    ;%, - % ((( (# &'#(*"'"*' 5 !",'() ( % = ) '!(

    0"

    =

    = (% 0"D ((( E("'% %2.

    "2 0" '*#( " '% %2 D ((( E ) " &'# #(%$! ; :>; > > , 0" (

    ## !(#$$%!%( >J; , >; C))...).S2*# #'*#( >; T

    $(&0"

    ==

    =

    ==

    # = = ))...))#''("'% %2.'# (

    ==

    =

    =

    >;>;

    >;>J;>;

    =

    =

    ('("!'#( ## #*##)$) & $""$&.%A#'*#(%'3( >J; # *#("(#!1%% %2#$$%!% #% %#!)!

    ,!*"!'%!% %2,!#$$%!%'#'!.(/\

    >;

    >;>J;

    =

    =

    =

    >;>J;

    >;>J;>J;

    ('("!'#( ## #*##'$$2!.

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    ; = V.:>K; =

    J; = ' .:>KJ; = '

    >#$$%!%'#'!&'#'('-#

    >;>J;>;

    =

    =

    $(&0"!'% %2('#$!*( #*##(&'#()0"(#!'/ "!#(1 '"#(###1 '"#(#)'# (C, = ) K = ,!&'#%'3((0"A,(##"%( %2 #*!')( % ' = ."('%'",#! " %2!#$$%!%'#'!!&'#%'3('*#(0"

    =+=+==

    =

    >V.:;.:>.:;K;>KJ;>;>J;>;>J;>;

    ' '''

    :.F

    $>(#!#*,(

    ==

    +=

    F.:

    >.:;K;>KJ;>;>J;

    >;>J;>J;

    ' '

    '' :.9

    .B %'+%2!/((($#5% %(((0"!#$$%!%!+%""!'#*-(F:7#( # - (:.:.%!#$$%!%0""# '#%+#('%0"1#* # ' 0" " (# '% - ( :.RU , ! #$$%!% 0" %+#('%0" 1#*% # '0""(#'% - (%#!#'%(:.:S"-!(!#$$%!%0"%+#('%0"0""(#'% - T$>%!%+2('% #!# '#(0"! %''% - .S"-!(!#$$%!%0"1 '#'+!1*T > ^S"-!!#$$%!%0"#!'+T

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    R

    &/ -!#(&'#('% - , %+#('% # - .'#( :.:>; = VU.:>K; =

    RU.:>J; = :KJ; =

    >#$$%!%'#'!!&'# .

    =+=+= >VU.:;::.:;RU.:>K;>KJ;>;>J;>; :.:RFF

    $> ===:RFF.:

    >:.:;RU.:

    >;

    >;>J;>J;

    :.:V ===:RFF.:

    >VU.:;:;

    >K;>KJ;>JK;

    :.RV

    *$%3 == >J;>JK; =:.:V

  • Profesora: Leticia Caedo Surez. ESCOM-IPN

    U

    9F8 #### +++=

    ( ) ( ) ( ) ( ) ( )9

    9

    ####

    ==

    ==

    ( )9

    =#

    ( )9

    =# ( ) F

    =#

    ( )9

    88 =# ( ) F

    8 =#

    ( )9

    FF =# ( ) F

    8F =#

    ( ) 9 =# ( ) 8 =#

    9

    >:;9

    F:>:; ==+++=

    +++=

    $> ( ) ( ) ( )( ) :8

    888 ==

    ###