Probabilidades.pdf

  • Uploaded by: Jefferson Cesar Mamani
  • 0
  • 0
  • July 2020
  • PDF

This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA


Overview

Download & View Probabilidades.pdf as PDF for free.

More details

  • Words: 9,062
  • Pages: 30
  

 

                

       !"#$%&' (   !" $&'( )  !"*$+&' '(,  !"-$+&( .  !" $/&'( 0  !" &$ %(12  

   13  !"#$&' (13  !"$&4!'$( 1  !"$&4!'$( 1,  !"5&' ( 1.  !" &'6(10  !"-$$&'(17  !"8&$ %( 31  !"9:!%%&( 33  !"%!%&(3  !";%%&'$( 3 -  < 

  3, 3,  

     3,  !"4!$3.  

   3.  !"$ / 30  - ;=  37

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

                #  %%   -#                  .                           #                      #                 #                      #

                                                                             /                 !  ##. #     "0         

               

         ,                                                                                      123                                                                         )                                    *             #                 

4

,                                5    (  ) +   6374            78,                 # ,  4.                                                                                         #     9 : $;               #  <       #                                     =                  #! $ "     ! ",         #    #>         ?   #       )  !#   0  "=           !2"!2"#*  #    5   ,  4.    $        @      ,   4.   )               #               

            (<   += 

   



:)  



A  



A  B# 



? #)  



 

                                                    ,   4.               ,      # #                  0                  $C.C1          *    $     

6

 #       D.1467EF    .@E   = =  C. C1*     =

=         ,    78 #   0    .7*  G<     H              *                #          I.I78     .47>       $ 47           ,   4.                           47 J ,  4.                  

  !"

  #

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

  )   #

   0  + 

) ) 1)

      #83

                   #        ,                  $                #   #   () +(+     !@"      $              *)            () + # #       ,         $$  )          $        !        $                #  $"       !  $  "

7

                    *        #               I.#    A    = =8.1    = =* K8     ) 8L.  ,18#  ( +    (+                    37M           ( +   (+   ( +  $0  )     #.6   ? ,  4.           , I18I837 I.6 J ,  4.            2   34    

!    5 !"

  6 7

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

 818  #1)1 

   0  + 

 #6

)

    #.6   *8E.

           #)    $    #       )       )                        ,       *        #     #)                 $ ,        #  =     B          J                    () +

E

!        ",*() +      N          $                            #)   BJ <    N            #              $                     #)                      = =  !"###  "  "F       !$  "          = = N  K8  =*)    ≥8  =* K8   0         3M      *    *#            .88                   /       $    .8       $       ,**   JI883×.88I3 N  I.8    D* ≤1F J ,  4.            9 : 5  3; 3<  =     > ;34 5     34     !"

 6  )

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

 )#    ) 1

   0  + 

 6  ?1

    *      8OP

     0# *                () +           #)                 #     $    *  Q           )   $5         *                         

3

                                       P8M  >     (             ) +   #          #)         I8P  ;      

  #)  *        N     #)    $               $        #                       )  ,       ( ?Q +                    =8.1    = =   ) 8L.       ) )# ( + # 8PG   7 (# +    H      (* #    + #     :)   I8P J ,  4.            @ 5   

!    5 !"

 1 7

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

  #    #

   0  + 

 )  #)

                 7     (# +             .!8OOO3"

         # $                #)                  *       2 )   $                  $             2)   )    #             #     AB!"    #)    I. *$     E   #AB!4.@E"

P

,                      #                              )          )      (       +       #   #          *         2       ,      $      $     #*  #  $        $0  !R  0: "     #     *#   # #,         )        #       #)                 #                       *                                                    )                    >     #                                     >       !( %  +"PO,                                          #             # *      =8.1     =   ) 8LL. >*) ≥8  0  .88% $  G<* *  .8 H 0            (* *  O + #      #   IOI88. J ,  4.            2  : A    34  5

!    5 !"

?    

   0  + 

 1? 

, .8  PO.* 

O

  !             )0    !.3P.2.P68"      .3.P5  9         #    ) *#  .8,#       $     A !" * #    ) N>#   2   ( + ≥18≤887( + ≥.88≤88.               )  #              (+            *                       8 !8.1"5*  #   *      #  . *)    #  *#    * #      #               ,  #                $       # )    # ,   (+                 Q                   Q    0# *         #       % I10      .888     $  !QI."813>       QI1467E   =813> 8.P>  88O>  884    88.    QI.8                   8  ,       $Q   Q     #      ,  4.=

       #               = . ,          N  !          #"                N   

.8

1         N      4 ,*    N      N) ,                     #                    !    #  $    *                  "  !*     * #  " ,               %        *               )   %  (  +   5     S   S            *      S   S      .8888      5  *                 N                         #               ;             *             ,           2    2N  )         ?        N          #         *               %  !  #         "        #   $0                                                    #     =8.1    =  % =      % K8

 ,*    #      16   641  0     *78G<      #   HJ                                                 = &    %%   '$% % %#

..

J ,  4.            !          !"

7#) 

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

  ##?  186 

   0  + 

7#) 7#)

      8.4

            (<   += 

 



:



B



, 



#



T 2



# 



0 



A 



U0

                   *                                   V W              ,                 =                                                       

  

.1

<     U     %    XIU!%" #         V8.W,    # *        )     ( %)  '=

≤≤    =

=   =    0#         4P8.188 = .           1           5  ,                                   

  V4P8.188W       J ,  4.               

 #1   ) !% 

 

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

 68  

   0  +     

   6? 

         * 816  3O8   $  $  143 

 ?%!# !!/@%!" #!!% !"!#$))@.)$%!$5> .      E8  1       5  ,                                   

  V7737W      

.4

J ,  4.               

    !%

 6 8 

 *+,  ! $%-&'( )   . ! $%/&'(      0  +     

    8

     E8  * 837  E7

    " #                             <   ,  U  9 !.334"                                       )                                                           =  #      #          ,                       #!     "      T        )               !T 2 U"                            = !*"    !+ , " ( %)  '= 2∞LL∞

   = *=     2∞L*L∞ + , =       + , K8  0     #      .3O.#@   1P1#@ . <      .EO#@

.6

1 G<     .8M     H 4 J    ,    ,  4. =     #            ,          .J ,  4.           3  B:     B:  A >  !%

6? )1) 8?

 *+,  ! $%-&'(   . ! $%/&'(  C! $D%D-&'(

   8#??  6) )

,      .EO#@4EM 1J ,  4.           3  B:     6? B:  A >  )1)  *+,  ! $%-&'(  ?   . ! $%/&'(    C! $D%D-&'(  ) !%

  

5 1.716#@   .8M    

.7

  $   " #                                         *     + ,  #    #  *!"+ , !"       %        % #    #     #*    )               0'5      &'?C  ( %)  '= LL∞    = *= 2∞L*L∞ + , = + , K8  0#  N#     *# !     "     #     #           141        818  <*                  .1  N                                J ,  4.           E:  B:  F   B: G   !%

)#)  ) )

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

 6?)  

   0  +       

 #1) 7#?1)   ?6686

     .1N * 818             *#     =

.E

  $ %        #   $             #   ,  #                          )                    2      # $      # <  0   #   =           ⎛  ⎞ ⎟  #          #   ,        V8.W           A = ⎜ ⎝ 1 −  ⎠      ,       $                    # #  ( %)  '= 2∞LL∞    =

=   2∞L L∞ = K8

 ,            !M"                     #       #    .1<       N   7M    

.3

J ,  4.           E:   

!>  F   ) !%   *+,  ! $%-&'(   . ! $%/&'(  C! $D%D-&'(    0  +       

 11 1   )#17  #?  

      #    7M 8.1

   &                   V8.W   ,                 $                                           #            

                                              V8.W        I.I. A !.." ( %)  '= 8≤≤.    = = K8 = K8 .P

 ,      #    A !11" . G<   # 17M    H 1 G<          H J ,  4.           2   ,

G   ,G   !%

) )  )

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

 8#  

   0  +   

      

/           #     8P6          78M

          #  $ #  =        #    %                                 #         #       I × %  !"   - !"  0    :! "      # $      !  " ,          (  + $   $        !           )   (            #    #   +" ( %)  '= 8LL∞    =

=  K8 = K8

.O

 ,*  # )  #       4   <        ##           (    # #  + #    :!E1"

J ,  4.           @    

F  

G   !%

8 ) 

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

   67

   0  +   

 ####   8  886

       ##   8OP 

0    N           *#    #    :  I8P.I3P.*= . ,     1 N      8.

J ,  4.           @    

F  

G    *+,  ! $%-&'(   . ! $%/&'(

 1 61  ?  

!%

  

   0  +   

  ? #6 17 67

,      .8N

18

  '(                #)     ,                                 >   $            #,     #     $        #    )  .6             (   +,  #             N  .    )                      #                 8                             $                       #           >               #          %                        / )      #! " I %  I. ,                                                 ( %)  '= 8LL∞      % =  % K8  0        #       .ENG<                                   18  NH  0       7N  G       17NH      (  + #        % [email protected]8E17 J ,  4.           F          <   !%

  8) ) 

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

  )18

1.

    #    18N  * 83. /   (  +        17N  7 #     18N !%L17@%K7"I!%L18"I83.

  )*            :   I.@1 I@1       T 2  #   ,     #       B!8."   T 2                                              0                      $  $             #                    #               T 2       #  # ( %)  '= 8≤L∞    = =#  /  <     T 21#   . GY)      O1.H 1 GY)    .8M     H .J ,  4.           HC   @     !%

) ?)

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

 ?? 

,.M     O1. 1J ,  4.           HC   @      *+,  ! $%-&'(   . ! $%/&'(

)  ?  

!%

78 )

11

, 6E871      =O8M)  $     .8M 

    #       0      $ T 2      ,         N                   N0                   #  # 5  #       0     8  $.! " ( %)  '= 2∞LL∞    = =#  K8       0     #    . <    B!8."       887

3 <     0             /#    I .8I788                                        *I8+ , I. .J ,  4.           3  B:     B:  A >   *+,  ! $%-&'(   . ! $%/&'(  C! $D%D-&'(

    ?     

!%





   0  + 

  

,    #               ,   4.=       $          0  .8#  # $788#   

14

1J ,  4.            B  @     !%

 877?

 *+,  ! $%-&'(   . ! $%/&'(  C! $D%D-&'(

 ?#7   #

           B  @     !%

 877?

 *+,  ! $%-&'(   . ! $%/&'(  C! $D%D-&'(

 ?7?6     8

0                 #               0            B

  +  #  ;                    T 2   #   ,       #    U0  ?   U         )     $ N   ( %)  '= 8≤L∞    = =#  K8 =#   K8

 ,                               #         U   .8  #              .1 #           . <   7M     1 G<      648H 4 J        

16

.J ,  4.           G B    @       @     )  *+,  ! $%-&'(  ?   . ! $%/&'(    !%



,      887137

1J ,  4.           G B    @       @     ) !% 7#  *+,  ! $%-&'(   . ! $%/&'(

 ?? 

   0  +   

)  6)  816

     64888.

4                                      =

17

        ,   4.            #                                              5            (<   +           ,          *      $             !              # "                                                              #      ,           ##       *       ,    )       )    9*      #   #   *  %       )            ,      )    #       *          )           #                      V8.W,##   ..       $       *                      #*    #    )    # ) 9 <,  )   $             ,                ,  )   9   <            #          )       )     ,    # #=       $       

$                             ,       #   )  

             (:     + = 

   



:)  



A  



A  B# 



9  



 



? #)  

1E

<                             !(<   +"        

  "  : $          K1#       0    #         0#       

    0 I*  ! I."   2

       2   #        1 ! I."     &) = #)         #  P=6=60  P        !%.%1%4"= %.IBZ    %1IBZ  # %4IBZ     #       IP>.I[email protected]I87>1I[email protected]I817 4I[email protected]I817   *  N                )       N      ,  )  2  $#               #    =  I8.1! I."    = =* K8  =*K8  

 =    8L 1! -."



 = 1 

= 1

            (:     += 

 



:



B



, 



B   



T 2



#



0 



# 



U0



A  13

<         !(<   +"        

       U   :    #%'%           <                    #                    #           *   $+ ,           %I!%. %1"           *I!*1 *2"        + , I!+ , 1+ , 2"         %.%1 0      %. %1             I8 ( %)  '= 2∞L1L∞ 2∞L2L∞    = *I!*1*2"=   2∞L*1L∞2∞L*2L∞ + , I!+ , 1+ , 2"=    + , 1K8+ , 2K8     1≤ ≤. 5               B                                         #               0#                                #        µIE7Q#   σI.7Q#0#          #      µI.EP    σI818      837<                                                                !'9
3                              !   "      3*(I@ 1

 < *     3*(  48Q#@1 !    "

1P

J ,  4. @  >         3   A B: ; 0      8 81 B: 0    A      ) ;      >  6 0      8 81   +  > )) )) ))   7 <  =    ,    0      > CCCCCCCCCCCCCCCCCCCCCCCCC 6) 6) 67) 1)17?? 1?7 ?1)7 7))8 871# 1)6) I

<.888       3*( 48 Q#@1OM   <  $       $                      #              N 

  1 -# 5B 4%, %5 6 6  6   6, A =0 #2&#> .O44!/  #)=9 B7%   686$   $B[XQ= < >.O7E"

3 9  #UTJ $299

% 3   % %9 =,  5<>.OO3  9      % %  $  :   9

%  9) =  5 2R '  >.OPE 6 N*% $; % #1#7%   9 =5 $  / >.OO4 7 - $ 9 % ,$< 

 %) )*%  ) =05=RA0 <>.OO3

, ) T9*; % 9

%  (  % + %A=0 #>.OO3 3 ?   J    <   9                        = =@@[[[ @  @9\  

1O

P A ## 5, )<  >   ,=5 #< / 9 $ %  < 

#&6<   =T R ]0>.OOP1OE123 O -5R-<: %  ,=5 #< / 9 $ %  < 

#&.<   =T R ]0>.OOP4723 .8 #  T    >    ,=  5 #    <   /    9 $ %   < 

#&6<   =T R ]0>.OOP44OP24681 ..    ? * 6    6%     ,    ,     ,   % ,    6  + %+$ ? ,+ > ,

( ,@ * 6 $<  #9= ?   >.O7..6.2E

48

More Documents from "Jefferson Cesar Mamani"