Deber de Variables Aleatorias Discretas

download Deber de Variables Aleatorias Discretas

of 17

Transcript of Deber de Variables Aleatorias Discretas

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    1/17

    Determine, con un nivel

    "0 9

    "# "$ &

    9 "'

    # "'

    "' ""

    9 "#

    ""

    9 9

    & 9

    ()*+-/!' 1

    # $

    2 &

    9

    "0 ""

    "' "1

    "# "$

    "2 "&

    " "9

    Clase Frecuencia

    1 '

    $ "0

    & "0

    9 '1

    "" '$

    "1 "$

    "$ "1

    "& "

    "9 "

    3 ma3or... 0

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    2/17

    de confanza de 90%, qué tipo de distribución siguen los datos. Use la prueba d

    "0 9 "1 "0

    "" 2 "' "0 $ "0 9 "0 "0 $

    "$ & $ 9 "# "'

    "1 & & & " $

    "# 9 "1 "# "0 "0

    "" $ "" ' "0 "$

    $ 9 "" "" & "0

    # 9 "1 "'

    "1 "0 "" 2 9 "0

    4 4 4+ 54+45'   0.0' 0.0' 0.0"" 0.009

    "0   0."0 0."' 0.020 0.020

    "0   0."0 0.'' 0."$ 0.02'

    '1   0.'1 0.#$ 0.'#" 0.'09

    '$   0.'$ 0.&0 0.'1 0.#2'

    "$   0."$ 0.$ 0."2# 0.22

    "1   0."1 0.9 0.01 0.9&

    "   0.0" 0.99 0.01' 0.9$

    "   0.0" ".00 0.0"0 0.990

    "00

    0

    "0

    '0

    10

    Histograma

    6recuencia

    Clase

    Frecuencia

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    3/17

      e Kolmogorov!mirnov.

    "2 "1 )(-+/ D+ 7)6()8 0.90

    9 "' a 0."1 "1 n "00

    "" "0 ma "

    9 "0 min '

    "0 "$ "2

    # "$ m "0

    "1 $ ".2

    "$ "$ 9.90

    "$ &

    :o; tiene una distribucion de poison:"; tien otra distribucion

    7 0.990

    K! 0."''

     

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    4/17

    INTERVALO O   P(x) E=n.P(x) (EO)!"#E

    0   0 0.0009&2$2 0.09&2$2'$ 0.09&2$2'$

    "   0 0.009&2$21 0.9&2$2'$ 0.9&2$2'$'   # 0.0#19#$1" #.19#$1"'$ 0.01$#'0"#

    1   2 0.""&"&$ "".&"&$ '.&90&$

    # " 0.'0$0&"1 '0.$0&"'$ 0.1022292#

    $ '& 0.'#2091&$ '#.2091&$ 0.'1''1'"#

    2 '' 0.'0$0&"1 '0.$0&"'$ 0."0$#

    & "' 0.""&"&$ "".&"&$ 0.002&$

    "0 0.0#19#$1" #.19#$1"'$ &."$002"

    9 " 0.009&2$21 0.9&2$2'$ 0.000$2'$

    "0 0 0.0009&2$2 0.09&2$2'$ 0.09&2$2'$

    "00 " "".0'9'02

    :o; el con

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    5/17

    N "0

    %   0.$

    &   0.$NIVEL 'E CONFIANA   0.90

    0."0

    m   ""

    C   "".0'9'02"$.9&"&9'

    mial

    u3en de acuerdo con la

    ""

       @AA B"CC';

        @A B"CC'

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    6/17

    INTERVALO O   P(x) (P(x)) (P(x)O)!"#P(x)

    "   "1 "2.222& 1.222& 0.02&

    '   "# "2.222& '.222& 0.#'2&1   " "2.222& ".1111 0."02&

    #   "# "2.222& '.222& 0.#'2&

    $ '" "2.222& #.1111 "."'2&

    2 '0 "2.222& 1.1111 0.222&

    "00

    Determine, con un nivel de confanza de 90%, si los datos se distribu3distribucion uni>orme discreta A"2C.

    " ' 1 # $

    0

    $

    "0

    "$

    '0

    '$

    :istograma

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    7/17

    n   "00

    %   0.$

    &   0.$NIVEL 'E CONFIANA   0.90

    0."0

    m   2

    C   1.$2009.'121$29

    n de acuerdo con una

       @AA B"CC';

    2

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    8/17

    4AC 4AC 4

    0 0.00& 0.00& 1 0.0"$0" 0.01# 0.0#0 1 0.0"$0

    ' 0.0# 0."'$ "2 0.000

    1 0."#0 0.'2$ '0 0."000

    # 0."&$ 0.##0 1 0."900

    $ 0."&$ 0.2"2 1 0."900

    2 0."#2 0.&2' 1$ 0."&$0

    & 0."0# 0.2& "& 0.0$0

    0.02$ 0.91' "1 0.02$0

    9 0.012 0.92 "" 0.0$$0

    "0 0.0" 0.92 2 0.0100'00

    :! /+*( 4E+D( AC

    " 0.#''$ # #

    ' 0.10'9 # #

    1 0.0""& " 1

    # 0.22#$ 2 1.&$

    $ 0.#00 # 1.

    2 0.$$0 $ #

    & 0.$0"& $ #."#'$&"#'9

    0.'9$9 # #."'$

    9 0.' 2 #.1111111111

    "0 0."&'& 1 #.'

    "" 0.&20 2 #.1212121212

    "' 0.###0 $ #.#"2222222&

    "1 0.02$# ' #.'10&29'10

    "# 0.#9#1 $ #.'$&"#'$&

    "$ 0.&$2 & #.#22222222&

    "2 0."9 & #.2'$

    "& 0.02'2 ' #.#&0$'1$1

    " 0.&20 & #.2"""""""""

    "9 0.$&'& $ #.21"$&9#

    '0 0.1'&1 # #.2

    '" 0."$9" 1 #.$'109$'1

    '' 0.$##" $ #.$#$#$#$#$$

    '1 0.29 2 #.2029$2$''

    '# 0.2$0" 2 #.222222222&

    '$ 0.'21 # #.2#

    '2 0."'#" ' #.$1#2"$1$

    !imular el proceso de >abricacion de televisores, cu3o promedio es de $ tel!imular por '00 Foras. 7uantos televisores se >abricaran en '00 Foras 3 cu

    00.000

    0.0'0

    0.0#0

    0.020

    0.00

    0."00

    0."'0

    0."#0

    0."20

    0."0

    0.'00

    0.0200

    0.000

    0."000

    0."'00

    0."#00

    0."200

    0."000.'000

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    9/17

    '& 0.''"# 1 #.#"#"#"$

    ' 0.$'0# $ #.$

    '9 0.#'&2 # #.#'&$2'0&

    10 0.9""1 #.2

    1" 0.9&92 "0 #.&"91$##

    1' 0.#19 # #.&$

    11 0."$2" 1 #.29292929&1# 0.##1$ $ #.&0$'1$'9

    1$ 0.$&$2 $ #.&"#'$&"#1

    12 0.&"2 2 #.&$

    1& 0.#09& # #.&'9&'9&'9&

    1 0.'#02 1 #.2#'"0$'21

    19 0."10 1 #.2#"0'$2#"

    #0 0.$2&2 $ #.2$

    #" 0.10&9 # #.21#"#21#"$

    #' 0.9#1 9 #.&109$'1"

    #1 0.20 2 #.&2#"20$## 0.1912 # #.&$

    #$ 0.9$'2 9 #.#########

    #2 0.2$ 2 #.29$2$'"

    #& 0.2&2# 2 #.912"&0'"1

    # 0.2'$ 2 #.9"2222222&

    #9 0.$#' $ #.9"12&1#29

    $0 0.1'#0 # #.9

    $" 0.9&01 "0 $

    $' 0.#"10 # #.90&29'10

    $1 0.$0"# $ #.9""1'0&$$

    $# 0.2'2 2 $

    $$ 0.2' $.0$#$#$#$#$

    $2 0.$2& $ $.0$1$&"#'2

    $& 0.1"#0 # $.01$0&&"91

    $ 0.#""2 # $.0"&'#"1&91

    $9 0.&&29 & $.0$0#$&2

    20 0.#&& $ $.0$

    2" 0.21## 2 $.02$$&1&&0$

    2' 0.9 $.""'901''$

    21 0.&921 & $."#'$&"#'9

    2# 0.$0$ $ $."#02'$

    2$ 0.2''' 2 $."$1#2"$1

    22 0.$1'$ $ $."$"$"$"$"$

    2& 0.9190 9 $.'09$$''19

    2 0.2"&9 2 $.''0$'1$1

    29 0.&$10 2 $.'1"#0$

    &0 0.$$&0 $ $.''$&"#'2

    &" 0.0&00 ' $."109$9"$

    00.0000

    0.0'00

    0.0#00

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    10/17

    &' 0.2"$9 $ $."0$$$$$$2

    &1 0.9#21 9 $.'1'&2&"'1

    0.192 # $.'"2'"2'"2'

    &$ 0.0$ & $.'#

    &2 0.#&"0 $ $.'12#'"0$1

    && 0.&&1 & $.'$9'$9&

    & 0.92&& 9 $.10&29'10&&&9 0.'0"2 1 $.'&#"0"'&

    0 0.1&1& # $.'2'$

    " 0.$1'" $ $.'$9'$9'$91

    ' 0."00& ' $.'"9$"'"9$"

    1 0.'210 1 $."9'&&"0#1

    # 0.1&'1 # $."&$&"#'2

    $ 0.&$2# 2 $."'1$'9#"

    2 0.1&9 # $."#"20#&

    & 0.$'01 $ $."&'#"1&91"

    0.&0'$ 2 $."""""9 0.19& # $."2$191'$

    90 0.9'& "0 $.''''''''''

    9" 0.29#2 2 $.'10&29'10

    9' 0.99& "0 $.''2029$&

    91 0.1"'& # $.'2"&'0#1

    9# 0.'#"9 1 $.'##20$""

    9$ 0."'"# ' $.'"0$'21"$

    92 0.110 # $."9&9"2222&

    9& 0.000# 0 $."##1'9929

    9 0.90$ $."&1#291&

    99 0.'$$# 1 $."$"$"$"$"$

    "00 0.9"'1 $."

    "0" 0.22$ 2 $."""""9

    "0' 0.'$$$ 1 $."22222222&

    "01 0.0'9 " $."'2'"1$9''

    "0# 0.#1#9 # $.""$1#2"$#

    "0$ 0.$#&2 $ $.""#'$&"#1

    "02 0.$"2 $ $.""1'0&$#&'

    "0& 0.21 $."#0"29"$9

    "0 0.22$9 2 $."#"#"#"

    "09 0.'00 1 $."'##012&

    ""0 0.19$ # $."""""'

    """ 0.&9# $."##"##"##"

    ""' 0.$'0" $ $."#'$&"#'9

    ""1 0.#'&1 # $."1'p'

    ""# 0."""2 ' $."0$'21"$&9

    ""$ 0.$90 & $."'"&19"10#

    ""2 0.$#2" $ $."'0292$$'

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    11/17

    ""& 0.2"$$ $ $.""92$""9&

    "" 0.2##1 2 $."'&""2##"

    ""9 0.919$ 9 $."$92212$$

    "'0 0.#091 # $."$

    "'" 0.0$"& ' $."'19229#'"

    "'' 0.#19 & $."191##'2'1

    "'1 0.#"99 # $."100"100"'# 0.&2$0 & $."#$"2"'901

    "'$ 0.#'9 $ $."##

    "'2 0."##& 1 $."'29#"'&

    "'& 0.9"29 $."#9202'99'

    "' 0.#1& & $."2#02'$

    "'9 0.' # $."$$01&$9&

    "10 0.##$ & $."29'10&29'

    "1" 0.02&2 ' $."#$01"2&9

    "1' 0.#1"$ # $."12121212#

    "11 0.$201 $ $."1$111#$9"1# 0.2'& 2 $."#"&9"0##

    "1$ 0.#" # $."111111111

    "12 0.#""9 # $."'$

    "1& 0.#209 $ $."'#0&$9"'

    "1 0.0"'# " $.09#'0'92

    "19 0.01' ' $.0&"9#'##2

    "#0 0.0#2' ' $.0$

    "#" 0.&90 & $.021'9&&'

    "#' 0.0$10 ' $.0#''$1$'""

    "#1 0." $.02'91&02'9

    "## 0.9"" $.011111111

    "#$ 0.9&1$ "0 $.""&'#"1&91

    "#2 0.090 ' $.09$90#""

    "#& 0.&1#2 2 $."0'0#0"21

    "# 0.001" 0 $.02&$2&$2&2

    "#9 0.9$$' 9 $.0919$9&1"$

    "$0 0.&$$& 2 $."

    "$" 0.&9#1 & $.""'$'&"$

    "$' 0.91&2 9 $."1"$&9#&

    "$1 0.91' 9 $."211929'

    "$# 0.$92 & $."&$1'#2&$1

    "$$ 0.210 2 $."02#$"2"1

    "$2 0.2# 2 $."$9$9

    "$& 0.$""0 $ $."#&"11&$

    "$ 0.1" # $."&&'"$"99

    "$9 0.#'&& # $."29""1'0

    "20 0.&10 $."&$

    "2" 0.&0'& 2 $."9'$#2$19

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    12/17

    "2' 0.$$9" $ $."9"1$0'#&

    "21 0.2$0# 2 $."921"90"#

    "2# 0."1# 1 $."'9'2'91

    "2$ 0.$#$" $ $."""""

    "22 0.#"$$ # $."&9$'

    "2& 0.9$20 9 $."9&20#&90#

    "2 0.&& 2 $.'0'109$'#"29 0.&2 & $.'"10"&&$"$

    "&0 0."$# 1 $.'

    "&" 0.2#&& 2 $.'0#2&12'2

    "&' 0.$## $ $.'01#1&'"

    "&1 0.1#' # $."92$1"&9"9

    " 0.'02$ 1 $."1900#2

    "&$ 0.9220 9 $.'0$&"#'$&

    "&2 0.0002 0 $."&2"121212

    "&& 0.99#2 "0 $.'011910$

    "& 0."191 1 $."9"0""'12"&9 0.#&9 $ $."99##"1#"

    "0 0.&"20 2 $."9########

    "" 0."0'2 ' $."&2&9$$0"

    "' 0."'02 ' $."$91#02$91

    "1 0.#09# # $."$100$#2#$

    "# 0.220 & $."210#1#&1

    "$ 0.1$11 # $."$2&$2&$2

    "2 0."&$ 1 $."#$"2"'901

    "& 0.'&'1 # $."1901'

    " 0.&12 $."$#'$$1"9"

    "9 0."9"1 1 $."#'$&"#'9

    "90 0.#21 $ $."#'"0$'21'

    "9" 0.00 ' $."'$2$##$01

    "9' 0.''2$ 1 $.""#$11111

    "91 0.9"' $."'9$112&

    "9# 0.&00 2 $."1#0'02"2

    "9$ 0.$#09 $ $."111111111

    "92 0.291# 2 $."1&&$$"0'

    "9& 0.$$$ $ $."1&0$$1&2

    "9 0.$2 $ $."12121212#

    "99 0.&2"' 2 $."#0&01$"&2

    '00 0.&$1$ 2 $."#$

    "0'9

    numero de televisores en '00 Foras

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    13/17

    4 media $.0000

    0.0"$00.0100

    0.""00

    0.'"00

    0.#000

    0.$900

    0.&2$0

    0.$00

    0.9"$0

    0.9&00

    ".0000

    visiores por Fora 3 cu3a distribucion es 4oisson.l es el promedio de >abricacion por Fora.

    C(

    " ' 1 # $ 2 & 9 "0

    Ds de poison con datos Fistoricos

    Ds de poison con datos simulados

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    14/17

    " ' 1 # $ 2 & 9 "0

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    15/17

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    16/17

  • 8/16/2019 Deber de Variables Aleatorias Discretas

    17/17