Реферат: Обработка результатов эксперимента

МИНИСТЕРСТВООБРАЗОВАНИЯ РОССИЙСКОЙ ФЕДЕРАЦИИ

ВОЛГОГРАДСКИЙГОСУДАРСТВЕННЫЙ ТЕХНИЧЕСКИЙ УНИВЕРСИТЕТ

КАФЕДРА МАТЕМАТИКИ

                        

     

СЕМЕСТРОВАЯ РАБОТА ПО СТАТИСТИКЕ

<span Times New Roman",«serif»; mso-ansi-language:RU">«Обработка результатов эксперимента»

Вариант №999

                               

                             

                                  

                                      ВЫПОНИЛ:  студент группы АТ–312

   ЛитвиновАлександр Владимирович 

                                 ПРОВЕРИЛ: Африкян Арсен Джуванович

                               

ВОЛГОГРАД 2003

<span Courier New";letter-spacing:-1.0pt">Исследованияпрочности 250 образцов бетона на сжатие образуют совокупность независимых иравноточных измерений случайной величины Х (МПа):

<img src="/cache/referats/16220/image001.gif" v:shapes="_x0000_s1031"><span Courier New";letter-spacing:-1.0pt">

<span Courier New";mso-fareast-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:RU;mso-fareast-language: RU;mso-bidi-language:AR-SA">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">21,8

<span Courier New";letter-spacing:-1.0pt">24,7

<span Courier New";letter-spacing:-1.0pt">25,3

<span Courier New";letter-spacing:-1.0pt">19,8

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,2

<span Courier New";letter-spacing:-1.0pt">25,9

<span Courier New";letter-spacing:-1.0pt">24,0

<span Courier New";letter-spacing:-1.0pt">24,9

<span Courier New";letter-spacing:-1.0pt">24,1

<span Courier New";letter-spacing:-1.0pt">22,0

<span Courier New";letter-spacing:-1.0pt">22,9

<span Courier New";letter-spacing:-1.0pt">24,7

<span Courier New";letter-spacing:-1.0pt">24,1

<span Courier New";letter-spacing:-1.0pt">21,5

<span Courier New";letter-spacing:-1.0pt">21,6

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">21,8

<span Courier New";letter-spacing:-1.0pt">24,5

<span Courier New";letter-spacing:-1.0pt">24,6

<span Courier New";letter-spacing:-1.0pt">24,2

<span Courier New";letter-spacing:-1.0pt">19,3

<span Courier New";letter-spacing:-1.0pt">24,6

<span Courier New";letter-spacing:-1.0pt">24,9

<span Courier New";letter-spacing:-1.0pt">24,1

<span Courier New";letter-spacing:-1.0pt">22,8

<span Courier New";letter-spacing:-1.0pt">25,4

<span Courier New";letter-spacing:-1.0pt">22,0

<span Courier New";letter-spacing:-1.0pt">24,5

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">24,6

<span Courier New";letter-spacing:-1.0pt">24,7

<span Courier New";letter-spacing:-1.0pt">19,1

<span Courier New";letter-spacing:-1.0pt">24,8

<span Courier New";letter-spacing:-1.0pt">24,1

<span Courier New";letter-spacing:-1.0pt">24,0

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">22,8

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,2

<span Courier New";letter-spacing:-1.0pt">24,3

<span Courier New";letter-spacing:-1.0pt">24,4

<span Courier New";letter-spacing:-1.0pt">19,2

<span Courier New";letter-spacing:-1.0pt">25,7

<span Courier New";letter-spacing:-1.0pt">22,8

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">25,1

<span Courier New";letter-spacing:-1.0pt">25,5

<span Courier New";letter-spacing:-1.0pt">25,6

<span Courier New";letter-spacing:-1.0pt">22,3

<span Courier New";letter-spacing:-1.0pt">25,7

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,0

<span Courier New";letter-spacing:-1.0pt">23,5

<span Courier New";letter-spacing:-1.0pt">23,3

<span Courier New";letter-spacing:-1.0pt">23,4

<span Courier New";letter-spacing:-1.0pt">23,9

<span Courier New";letter-spacing:-1.0pt">25,7

<span Courier New";letter-spacing:-1.0pt">25,3

<span Courier New";letter-spacing:-1.0pt">25,8

<span Courier New";letter-spacing:-1.0pt">25,0

<span Courier New";letter-spacing:-1.0pt">20,1

<span Courier New";letter-spacing:-1.0pt">24,1

<span Courier New";letter-spacing:-1.0pt">20,0

<span Courier New";letter-spacing:-1.0pt">23,7

<span Courier New";letter-spacing:-1.0pt">23,8

<span Courier New";letter-spacing:-1.0pt">20,9

<span Courier New";letter-spacing:-1.0pt">20,1

<span Courier New";letter-spacing:-1.0pt">18,0

<span Courier New";letter-spacing:-1.0pt">20,7

<span Courier New";letter-spacing:-1.0pt">20,1

<span Courier New";letter-spacing:-1.0pt">20,5

<span Courier New";letter-spacing:-1.0pt">23,7

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<span Courier New";letter-spacing:-1.0pt">24,7

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<span Courier New";letter-spacing:-1.0pt">20,6

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">19,5

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<span Courier New";letter-spacing:-1.0pt">20,7

<span Courier New";letter-spacing:-1.0pt">23,7

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<span Courier New";letter-spacing:-1.0pt">20,3

<span Courier New";letter-spacing:-1.0pt">20,8

<span Courier New";letter-spacing:-1.0pt">20,0

<span Courier New";letter-spacing:-1.0pt">25,2

<span Courier New";letter-spacing:-1.0pt">25,6

<span Courier New";letter-spacing:-1.0pt">19,6

<span Courier New";letter-spacing:-1.0pt">20,3

<span Courier New";letter-spacing:-1.0pt">20,9

<span Courier New";letter-spacing:-1.0pt">20,6

<span Courier New";letter-spacing:-1.0pt">26,8

<span Courier New";letter-spacing:-1.0pt">21,0

<span Courier New";letter-spacing:-1.0pt">21,9

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">22,3

<span Courier New";letter-spacing:-1.0pt">21,1

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">21,1

<span Courier New";letter-spacing:-1.0pt">26,2

<span Courier New";letter-spacing:-1.0pt">26,6

<span Courier New";letter-spacing:-1.0pt">21,3

<span Courier New";letter-spacing:-1.0pt">21,0

<span Courier New";letter-spacing:-1.0pt">26,7

<span Courier New";letter-spacing:-1.0pt">26,3

<span Courier New";letter-spacing:-1.0pt">21,5

<span Courier New";letter-spacing:-1.0pt">24,7

<span Courier New";letter-spacing:-1.0pt">21,6

<span Courier New";letter-spacing:-1.0pt">23,9

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">24,3

<span Courier New";letter-spacing:-1.0pt">24,7

<span Courier New";letter-spacing:-1.0pt">24,0

<span Courier New";letter-spacing:-1.0pt">21,8

<span Courier New";letter-spacing:-1.0pt">20,8

<span Courier New";letter-spacing:-1.0pt">20,2

<span Courier New";letter-spacing:-1.0pt">21,1

<span Courier New";letter-spacing:-1.0pt">21,2

<span Courier New";letter-spacing:-1.0pt">21,6

<span Courier New";letter-spacing:-1.0pt">26,8

<span Courier New";letter-spacing:-1.0pt">26,1

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">21,3

<span Courier New";letter-spacing:-1.0pt">21,4

<span Courier New";letter-spacing:-1.0pt">22,8

<span Courier New";letter-spacing:-1.0pt">22,0

<span Courier New";letter-spacing:-1.0pt">21,9

<span Courier New";letter-spacing:-1.0pt">21,6

<span Courier New";letter-spacing:-1.0pt">27,2

<span Courier New";letter-spacing:-1.0pt">28,0

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">21,0

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">21,2

<span Courier New";letter-spacing:-1.0pt">21,6

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,5

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">22,8

<span Courier New";letter-spacing:-1.0pt">21,3

<span Courier New";letter-spacing:-1.0pt">21,8

<span Courier New";letter-spacing:-1.0pt">21,6

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,5

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">22,3

<span Courier New";letter-spacing:-1.0pt">22,0

<span Courier New";letter-spacing:-1.0pt">22,9

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">23,6

<span Courier New";letter-spacing:-1.0pt">22,3

<span Courier New";letter-spacing:-1.0pt">22,4

<span Courier New";letter-spacing:-1.0pt">22,9

<span Courier New";letter-spacing:-1.0pt">24,8

<span Courier New";letter-spacing:-1.0pt">24,0

<span Courier New";letter-spacing:-1.0pt">24,3

<span Courier New";letter-spacing:-1.0pt">24,4

<span Courier New";letter-spacing:-1.0pt">24,9

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,7

<span Courier New";letter-spacing:-1.0pt">21,9

<span Courier New";letter-spacing:-1.0pt">21,1

<span Courier New";letter-spacing:-1.0pt">22,4

<span Courier New";letter-spacing:-1.0pt">22,9

<span Courier New";letter-spacing:-1.0pt">19,9

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">21,7

<span Courier New";letter-spacing:-1.0pt">21,1

<span Courier New";letter-spacing:-1.0pt">21,1

<span Courier New";letter-spacing:-1.0pt">22,1

<span Courier New";letter-spacing:-1.0pt">22,5

<span Courier New";letter-spacing:-1.0pt">22,3

<span Courier New";letter-spacing:-1.0pt">22,8

<span Courier New";letter-spacing:-1.0pt">19,6

<span Courier New";letter-spacing:-1.0pt">22,0

<span Courier New";letter-spacing:-1.0pt">23,2

<span Courier New";letter-spacing:-1.0pt">23,6

<span Courier New";letter-spacing:-1.0pt">23,7

<span Courier New";letter-spacing:-1.0pt">23,3

<span Courier New";letter-spacing:-1.0pt">23,8

<span Courier New";letter-spacing:-1.0pt">22,3

<span Courier New";letter-spacing:-1.0pt">23,7

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">24,7

<span Courier New";letter-spacing:-1.0pt">25,6

<span Courier New";letter-spacing:-1.0pt">25,0

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,6

<span Courier New";letter-spacing:-1.0pt">23,7

<span Courier New";letter-spacing:-1.0pt">21,0

<span Courier New";letter-spacing:-1.0pt">21,3

<span Courier New";letter-spacing:-1.0pt">21,4

<span Courier New";letter-spacing:-1.0pt">21,9

<span Courier New";letter-spacing:-1.0pt">23,8

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,0

<span Courier New";letter-spacing:-1.0pt">23,3

<span Courier New";letter-spacing:-1.0pt">23,4

<span Courier New";letter-spacing:-1.0pt">22,4

<span Courier New";letter-spacing:-1.0pt">24,6

<span Courier New";letter-spacing:-1.0pt">22,9

<span Courier New";letter-spacing:-1.0pt">23,3

<span Courier New";letter-spacing:-1.0pt">23,8

<span Courier New";letter-spacing:-1.0pt">23,0

<span Courier New";letter-spacing:-1.0pt">23,3

<span Courier New";letter-spacing:-1.0pt">22,6

<span Courier New";letter-spacing:-1.0pt">23,9

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,9

<span Courier New";letter-spacing:-1.0pt">23,6

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,9

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,7

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">23,5

<span Courier New";letter-spacing:-1.0pt">23,6

<span Courier New";letter-spacing:-1.0pt">23,7

<span Courier New";letter-spacing:-1.0pt">23,8

<span Courier New";letter-spacing:-1.0pt">23,1

<span Courier New";letter-spacing:-1.0pt">24,6

<span Courier New"; letter-spacing:-1.0pt">24,7

<span Courier New"; letter-spacing:-1.0pt">24,3

<span Courier New"; letter-spacing:-1.0pt">24,8

<span Courier New"; letter-spacing:-1.0pt">23,2

<span Courier New"; letter-spacing:-1.0pt">22,6

<span Courier New"; letter-spacing:-1.0pt">22,7

<span Courier New"; letter-spacing:-1.0pt">23,2

<span Courier New"; letter-spacing:-1.0pt">23,6

<span Courier New"; letter-spacing:-1.0pt">20,4

<span Courier New"; letter-spacing:-1.0pt">23,7

<span Courier New"; letter-spacing:-1.0pt">23,4

<span Courier New"; letter-spacing:-1.0pt">19,3

<span Courier New"; letter-spacing:-1.0pt">23,9

<span Courier New"; letter-spacing:-1.0pt">23,6

<span Courier New"; letter-spacing:-1.0pt">23,1

<span Courier New"; letter-spacing:-1.0pt">23,5

<span Courier New"; letter-spacing:-1.0pt">20,7

<span Courier New"; letter-spacing:-1.0pt">20,6

<span Courier New"; letter-spacing:-1.0pt">23,6

<span Courier New"; letter-spacing:-1.0pt">23,6

<span Courier New";mso-fareast-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:RU;mso-fareast-language: RU;mso-bidi-language:AR-SA">

<span Courier New"; letter-spacing:-1.0pt"> 

<span Courier New";letter-spacing:-1.0pt">Требуется

<span Courier New";letter-spacing:-1.0pt">:

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">1.вычислить точечные оценки для математического ожидания, среднеквадратическогоотклонения, коэффициентов асимметрии и эксцесса;

<span Courier New";letter-spacing:-1.0pt">2.составить интервальный статистический ряд распределения относительных частот ипостроить гистограмму и полигон относительных частот;

<span Courier New";letter-spacing:-1.0pt">3. найтиэмпирическую функцию распределения и построить ее график и график кумуляты;

<span Courier New";letter-spacing:-1.0pt">4. исходяиз общих представлений о механизме образования СВ Х, а также по виду гистограммыи полигона относительных частот и вычисленным числовым характеристикам,выдвинуть гипотезу о виде распределения СВ Х; записать плотность распределениявероятностей и функцию распределения для выдвинутого гипотетического закона, заменяяпараметры закона вычисленными для них оценками;

<span Courier New";letter-spacing:-1.0pt">5. покритерию согласия χ2 Пирсона проверить соответствие выборочногораспределения гипотетическому закону для уровня значимости

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">q<span Courier New";letter-spacing:-1.0pt"> =0,05;

<span Courier New";letter-spacing:-1.0pt">6.вычислить интервальные оценки для математического ожидания и среднеквадратическогоотклонения, соответствующие доверительным вероятностям γ = 0,95 и γ =0,99.

<span Courier New";letter-spacing:-1.0pt">

<span Courier New"; letter-spacing:-1.0pt">Решение

<span Courier New"; letter-spacing:-1.0pt">:

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">Изучение непрерывныхслучайных величин начинается с группировки статистического материала, т. е.разбиения интервала наблюдаемых значений СВ Х на

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">k<span Courier New";letter-spacing:-1.0pt"> частичных интерваловравной длины и подсчета частот попадания наблюдаемых значений СВ Х в частичныеинтервалы. Количество выбираем равным 10 (<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">k= 10)<span Courier New";letter-spacing:-1.0pt">.

<span Courier New";letter-spacing:-1.0pt">Разобьем весь диапазонзначений на 10 интервалов (разрядов). Длину частичного интервала определим поформуле:

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image003.gif" v:shapes="_x0000_i1025">

<span Courier New";letter-spacing:-1.0pt">Шкала интервалов игруппировка исходных статистических данных сведены в таблицу. В результатеполучили статистический ряд распределения частот (<img src="/cache/referats/16220/image005.gif" v:shapes="_x0000_i1026">

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt">Интервалы наблюдаемых значений СВ Х, МПа

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[18;19

<span Courier New";letter-spacing:-1.0pt">)

<span Courier New";letter-spacing:-1.0pt">[19;20)

<span Courier New";letter-spacing: -1.0pt;mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[20;21)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[21;22)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[22;23)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[23;24)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[24;25)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[25;26)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[26;27)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[27;28]

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">Частота mi

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">1

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">9

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">20

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">41

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">56

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">60

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">38

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">16

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">7

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">2

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt">Для получениястатистического ряда частостей разделим частоты

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">mi<span Courier New";letter-spacing:-1.0pt"> на объем выборки n. Врезультате получим интервальный статистический ряд распределений частостей <img src="/cache/referats/16220/image007.gif" v:shapes="_x0000_i1027">

<span Courier New";letter-spacing:-1.0pt">Интервалы наблюдаемых значений СВ Х, МПа

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[18;19

<span Courier New";letter-spacing:-1.0pt">)

<span Courier New";letter-spacing:-1.0pt">[19;20)

<span Courier New";letter-spacing: -1.0pt;mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[20;21)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[21;22)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[22;23)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[23;24)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[24;25)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[25;26)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[26;27)

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">[27;28]

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">Часто

<span Courier New";letter-spacing: -1.0pt">с<span Courier New";letter-spacing: -1.0pt;mso-ansi-language:EN-US">т<span Courier New"; letter-spacing:-1.0pt">и<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US"> mi<span Courier New";letter-spacing:-1.0pt">/n<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,004

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,036

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,080

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,164

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,224

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,240

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,152

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,064

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,028

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,008

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">F* (x) (накопленны

<span Courier New"; letter-spacing:-1.0pt">е частости)

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">0,004

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,040

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,120

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,284

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,508

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,748

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,900

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,964

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0,992

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">1,000

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">Для построениягистограммы частостей на оси Ox откладываются частичные интервалы, на каждом изних строится прямоугольник, площадь которого равна частости данного частичногоинтервала. Если частости отнести к серединам частичных интервалов, тополученная замкнутая линия образует полигон частостей. На рисунке 1 изображенагистограмма и полигон частостей.

<span Courier New";letter-spacing:-1.0pt">Значения эмпирическойфункции распределения выписаны в последней строке статистического рядараспределения частостей. Запишем значения эмпирической функции распределения ваналитическом виде:

<img src="/cache/referats/16220/image008.gif" v:shapes="_x0000_s1037"><span Courier New";letter-spacing:-1.0pt">                0,      если  

<span Courier New";letter-spacing:-1.0pt">        <span Courier New";letter-spacing:-1.0pt"> <span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 18;

<span Courier New";letter-spacing:-1.0pt">                0,004,  если  18 <

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 19;

<span Courier New";letter-spacing:-1.0pt">                0,04,   если  19 <

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 20;

<span Courier New";letter-spacing:-1.0pt">                0,12,   если  20 <

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 21;

<span Courier New";letter-spacing:-1.0pt">                0,284,  если 21 <

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 22;

<span Courier New";letter-spacing:-1.0pt"> 

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">F<span Courier New";letter-spacing:-1.0pt">*<span Courier New";letter-spacing:-1.0pt">(<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">x<span Courier New";letter-spacing:-1.0pt">)=<span Courier New";letter-spacing: -1.0pt">  <span Courier New";letter-spacing:-1.0pt">          <span Courier New"; letter-spacing:-1.0pt"> <span Courier New";letter-spacing:-1.0pt">      <span Courier New"; letter-spacing:-1.0pt">   0,508,  если 22 < <span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 23;

<span Courier New";letter-spacing:-1.0pt">                0,748, если  23 <

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">x<span Courier New";letter-spacing:-1.0pt">≤ 24;      

<span Courier New";letter-spacing:-1.0pt">                0,9,    если 24 <

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 25;

<span Courier New";letter-spacing:-1.0pt">                0,964,  если 25 <

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 26;

<span Courier New";letter-spacing:-1.0pt">                0,992,  если 26 <

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 27;

<span Courier New";letter-spacing:-1.0pt">                      

<span Courier New";letter-spacing:-1.0pt">     <span Courier New"; letter-spacing:-1.0pt">1, <span Courier New"; letter-spacing:-1.0pt">                                                                                                                                                     <span Courier New";letter-spacing:-1.0pt">если  27 < <span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">x<span Courier New";letter-spacing:-1.0pt"> ≤ 28;

<span Courier New";letter-spacing:-1.0pt">                      

<span Courier New";letter-spacing:-1.0pt">      <span Courier New"; letter-spacing:-1.0pt">1,     <span Courier New";letter-spacing:-1.0pt">                        <span Courier New"; letter-spacing:-1.0pt">если       <span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">x<span Courier New";letter-spacing: -1.0pt"> <span Courier New";letter-spacing:-1.0pt">≥28;

<span Courier New";letter-spacing:-1.0pt">

<span Courier New"; letter-spacing:-1.0pt">График эмпирической функции изображен на рисунке 2.

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<img src="/cache/referats/16220/image010.gif" v:shapes="_x0000_i1028">

<img src="/cache/referats/16220/image012.gif" align=«left» hspace=«12» v:shapes="_x0000_s1038">

<span Courier New"">

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt">В техслучаях, когда наблюдаемые значения случайной величины задаются многозначнымичислами и объем выборки достаточно велик (

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">n<span Courier New";letter-spacing:-1.0pt"> <span Courier New";letter-spacing:-1.0pt">> 25), вначалецелесообразно найти среднюю арифметическую по формуле <img src="/cache/referats/16220/image014.gif" v:shapes="_x0000_i1029"> а за тем перейти квычислению центральных моментов порядка <span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">k<span Courier New";letter-spacing:-1.0pt"> (<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">k<span Courier New";letter-spacing: -1.0pt"> <span Courier New";letter-spacing:-1.0pt">=2, 3, 4):

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">Интервалы

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt">наблюдаемых значений СВ Х, МПа

<span Courier New";letter-spacing:-1.0pt">Середины интервалов

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">xi<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt">Частоты

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">mi<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image016.gif" v:shapes="_x0000_i1030">

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image018.gif" v:shapes="_x0000_i1031">

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image020.gif" v:shapes="_x0000_i1032">

<span Courier New";letter-spacing: -1.0pt"><img src="/cache/referats/16220/image022.gif" v:shapes="_x0000_i1033">

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[18;19)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">18,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">1

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-4,44

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">19,71

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-87,53

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">388,63

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[19;20)

<span Courier New";letter-spacing: -1.0pt">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">19,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">9

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-30,96

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">106,50

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-366,37

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">1260,31

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[20;21)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">20,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">20

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-48,80

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">119,07

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-290,54

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">708,91

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[21;22)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">21,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">41

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-59,04

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">85,02

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-122,43

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">176,29

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[22;23)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">22,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">56

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-24,64

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">10,84

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">-4,77

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">2,10

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[23;24)

<span Courier New";letter-spacing: -1.0pt">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">23,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">60

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">33,60

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">18,82

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">10,54

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">5,90

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[24;25)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">24,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">38

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">59,28

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">92,48

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">144,26

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">225,05

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[25;26)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">25,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">16

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">40,96

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">104,86

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">268,44

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">687,19

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[26;27)

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">26,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">7

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">24,92

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">88,72

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">315,83

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">1124,34

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">[27;28]

<span Courier New";letter-spacing: -1.0pt">

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">27,5

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">2

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">9,12

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">41,59

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">189,64

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">864,75

<span Courier New";letter-spacing:-1.0pt">Итого

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">250

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">0

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">687,61

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">57,07

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">5443,47

<span Courier New";letter-spacing:-1.0pt">

<span Courier New";letter-spacing:-1.0pt">Следовательно,

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image024.gif" v:shapes="_x0000_i1034">

<span Courier New";letter-spacing:-1.0pt">Дляпредварительного выбора закона распределения вычислим вначале средниеквадратические ошибки определения асимметрии

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image026.gif" v:shapes="_x0000_i1035">

<span Courier New";letter-spacing:-1.0pt">иэксцесса

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image028.gif" v:shapes="_x0000_i1036">

<span Courier New";letter-spacing:-1.0pt">Критерием«нормальности» распределения прочности бетона на сжатие является равенство нулюасимметрии и эксцесса. Из приведенных расчетов видно, что выборочныекоэффициенты асимметрии <img src="/cache/referats/16220/image030.gif" v:shapes="_x0000_i1037"> и эксцесса Эотличаются от нуля не более чем на удвоенные средние квадратические ошибки ихопределения, что соответствует нормальному распределению. Вид полигона игистограммы частостей также напоминает нормальную кривую (кривую Гаусса).

<span Courier New";letter-spacing:-1.0pt">Можнопредположить, прочность бетона на сжатие (СВ Х) изменяется под влияниембольшого числа факторов, примерно равнозначных по силе. Поэтому, исходя из«технологии» образования СВ Х, т. е. механизма образования отклонений прочностиот некоторого номинального значения, можно предположить, что распределение прочностибетона на сжатие является нормальным.

<span Courier New";letter-spacing:-1.0pt">Плотностьвероятности нормального распределения имеет вид

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image032.gif" v:shapes="_x0000_i1038">

<span Courier New";letter-spacing:-1.0pt">Найдёмточечные оценки параметров

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">a<span Courier New";letter-spacing:-1.0pt"> <span Courier New";letter-spacing:-1.0pt">и σ нормального распределения методом моментов:

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image034.gif" v:shapes="_x0000_i1039">

<span Courier New";letter-spacing:-1.0pt">Следовательно,плотность вероятности предполагаемого нормального распределения имеет вид

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image036.gif" v:shapes="_x0000_i1040">

<span Courier New";letter-spacing:-1.0pt">Функцияраспределения предполагаемого нормального распределения имеет вид

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image038.gif" v:shapes="_x0000_i1041">

<span Courier New";letter-spacing:-1.0pt">Используянормированную функцию Лапласа <img src="/cache/referats/16220/image040.gif" v:shapes="_x0000_i1042">

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image042.gif" v:shapes="_x0000_i1043">

<span Courier New";letter-spacing:-1.0pt">Проведемпроверку гипотезы о нормальном распределении СВ Х (прочности бетона на сжатие)с помощью критерия согласия <img src="/cache/referats/16220/image044.gif" v:shapes="_x0000_i1044">дляэтого интервалы наблюдаемых значений нормируют, т.е. выражают их в единицахсреднего квадратического отклонения

<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">s<span Courier New";letter-spacing:-1.0pt">:<img src="/cache/referats/16220/image046.gif" v:shapes="_x0000_i1045"><img src="/cache/referats/16220/image048.gif" v:shapes="_x0000_i1046"><img src="/cache/referats/16220/image050.gif" v:shapes="_x0000_i1047"><img src="/cache/referats/16220/image052.gif" v:shapes="_x0000_i1048">х<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">i<span Courier New"; letter-spacing:-1.0pt">-1<span Courier New";letter-spacing:-1.0pt">; х<span Courier New";letter-spacing:-1.0pt;mso-ansi-language:EN-US">i<span Courier New";letter-spacing:-1.0pt">) по формуле

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image054.gif" v:shapes="_x0000_i1049">

<span Courier New";letter-spacing:-1.0pt">где

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image056.gif" v:shapes="_x0000_i1050">

<span Courier New";letter-spacing:-1.0pt">Например,вероятность того, что СВ Х (прочность бетона на сжатие) попадает в первый частичныйинтервал (<img src="/cache/referats/16220/image050.gif" v:shapes="_x0000_i1051">

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US"><img src="/cache/referats/16220/image058.gif" v:shapes="_x0000_i1052">

<span Courier New";letter-spacing:-1.0pt">Аналогично

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US"><img src="/cache/referats/16220/image060.gif" v:shapes="_x0000_i1053">

<span Courier New";letter-spacing: -1.0pt">

<span Courier New";letter-spacing:-1.0pt">и т. д.После этого вычисляют теоретические (модельные) частоты нормальногораспределения <img src="/cache/referats/16220/image062.gif" v:shapes="_x0000_i1054"> и наблюдаемое значениекритерия <img src="/cache/referats/16220/image044.gif" v:shapes="_x0000_i1055">

<span Courier New";letter-spacing:-1.0pt"><img src="/cache/referats/16220/image064.gif" v:shapes="_x0000_i1056">

<span Courier New";letter-spacing:-1.0pt">Затем потаблицам квантилей распределения <img src="/cache/referats/16220/image044.gif" v:shapes="_x0000_i1057"> по уровню значимости

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">q<span Courier New";letter-spacing:-1.0pt"> = 0,05 и числустепеней свободы ‚ <img src="/cache/referats/16220/image066.gif" v:shapes="_x0000_i1058"><span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">k<span Courier New";letter-spacing:-1.0pt">— число интервалов; <span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">r<span Courier New";letter-spacing:-1.0pt"> <span Courier New";letter-spacing:-1.0pt">— число параметров предполагаемогораспределения СВ Х) находят критическое значение <img src="/cache/referats/16220/image068.gif" v:shapes="_x0000_i1059">

<span Courier New";letter-spacing:-1.0pt">Если <img src="/cache/referats/16220/image070.gif" v:shapes="_x0000_i1060">

<span Courier New";letter-spacing:-1.0pt">Впротивном случае, т. е. если <img src="/cache/referats/16220/image072.gif" v:shapes="_x0000_i1061">

<span Courier New";letter-spacing:-1.0pt">Вычисления,необходимые для определения наблюдаемого значения выборочной статистики <img src="/cache/referats/16220/image044.gif" v:shapes="_x0000_i1062"> приведем в таблице:

<span Courier New";letter-spacing:-1.0pt">Интервалы наблюдаемых значений СВ Х, МПа

<span Courier New";letter-spacing:-1.0pt">Частоты

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">mi<span Courier New";letter-spacing:-1.0pt;mso-ansi-language: EN-US">

<span Courier New";letter-spacing:-1.0pt">Нормированные интервалы

<span Courier New";letter-spacing:-1.0pt; mso-ansi-language:EN-US">          [ui, ui-1]

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">pi

<span Courier New"; letter-spacing:-1.0pt;mso-ansi-language:EN-US">npi

<span Courier New";letter-spacing:-1.0pt;mso-ansi-lan

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