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Консультация № 132490
16.04.2008, 20:14
0.00 руб.
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Здравствуйте!
Помогите пожалуйста с заданием и если можно с обьяснениями!
Вероятность отказа детали за время испытания на надежность равняется 0,2.
Найти математическое ожидание числа деталей, которые отказали, если испытанию подлежат 10 деталей!
И еще: напишыте пожалуйста кратко что такое мат. ожидание и формулу.
СПАСИБО БОЛЬШОЕ!
Помогите пожалуйста с заданием и если можно с обьяснениями!
Вероятность отказа детали за время испытания на надежность равняется 0,2.
Найти математическое ожидание числа деталей, которые отказали, если испытанию подлежат 10 деталей!
И еще: напишыте пожалуйста кратко что такое мат. ожидание и формулу.
СПАСИБО БОЛЬШОЕ!
Обсуждение
Неизвестный
17.04.2008, 00:20
общий
это ответ
Здравствуйте, SkyNET//!
введем события:
A-отказ детали
p=p(A)=0.2
B-не отказ детали
q=p(B)=1-p(A)=0.8
будем пользоваться формулой Бернулли:
P(X)=C(X,10)*p^X *q^(n-X)
где n-общее кол-во интересующих нас испытаний, оно равно по одному испытанию на деталь итого 10
P(0)=C(0,10)*0.2^0 *0.8^10=0.107
P(1)=0.268
P(2)=0.302
P(3)=0.201
P(4)=0.088
P(5)=0.026
P(6)=0.0055
P(7)=0.000786
P(8)=7.373*10^5
P(9)=4.096*10^-6
P(10)=1.024*10^-7
формула математического ожидания такова, что надо все умножить каждое возможное значение этой случайное величины на вероятность появления именно этого значения
то есть:
m=0*P(0)+1*(P1)+2*(P2)+3*(P3)+....+10*P(10)=2
расчет довольнатаки кропотливый, советую считать в какой-нить математическом пакете
введем события:
A-отказ детали
p=p(A)=0.2
B-не отказ детали
q=p(B)=1-p(A)=0.8
будем пользоваться формулой Бернулли:
P(X)=C(X,10)*p^X *q^(n-X)
где n-общее кол-во интересующих нас испытаний, оно равно по одному испытанию на деталь итого 10
P(0)=C(0,10)*0.2^0 *0.8^10=0.107
P(1)=0.268
P(2)=0.302
P(3)=0.201
P(4)=0.088
P(5)=0.026
P(6)=0.0055
P(7)=0.000786
P(8)=7.373*10^5
P(9)=4.096*10^-6
P(10)=1.024*10^-7
формула математического ожидания такова, что надо все умножить каждое возможное значение этой случайное величины на вероятность появления именно этого значения
то есть:
m=0*P(0)+1*(P1)+2*(P2)+3*(P3)+....+10*P(10)=2
расчет довольнатаки кропотливый, советую считать в какой-нить математическом пакете
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