Версия для печати темы

Автор: Simbian 5.4.2007, 6:53

Вот условие:
На пути движения машины 5 светофоров, на каждом из которых зелёный свет может гореть с вероятностью 0.4. Составить закон рапределения числа светофоров, пройденных машиной без остановки. Найти функцию распределения и математические характеристики. Вычислить вероятность Р(Х<=3).

а вот моё решение:
Р(Х=1)= 0.4^1-1*0.6=0.6
P(X=2)=0.4^2-1*0.6=0.24
P(X=3)=0.4^3-1*0.6=0.096
P(X=4)=0.4^4-1*0.6=0.0384
P(X=5)=0.4^4=0.0256
Закон распределения
X 1 2 3 4 5
Px 0.6; 0.24; 0.096; 0.0384; 0.0256;
Ф-ция распределения F(x)=P(X<x)

0,x<=1
0.6,1<x<=4
F(x)= 0.84,2<x<=3
0.936,3<x<=4
0.9744,4<x<=5
1,x>5

Мат-е характеристики:
M[x]= 1.4496

D[x]=2.0288

∂x(сигма)= корень из Dx = 1.4243595

P(X<=3) = P(X<3) + P(X=3) = F(3) + P(3) = 0.84 + 0. 0.096 = 0.936

Это решение сказали не правильное, т.е в самом начале не правильно рассчитана вероятность, от преподавателя точно добился что 1-я вероятность = 0.4, но как посчитать он даж не намекнул.

Пробовал вероятность считать по формуле Бернулли, но этот вариант ещё не проверили .
Помогите а то завтра консультация и мне капут


Если знаете как по другому найти вероятность, - если не затруднит то объясните в краце, мне главное вероятность верно посчитать дальше сам
Заранее огроомное спасибо - буду тоже помогать чем смогу

Автор: Руководитель проекта 5.4.2007, 8:24

Случайная величина X - количество светофоров пройденных без остановки. Возможные значения: 0, 1, ..., 5
P(X=0)=0.4
P(X=1)=0.6*0.4=0.24
P(X=2)=(0.6^2)*0.4
...
P(X=5)=0.6^5

Автор: Ботаник 5.4.2007, 11:37

Цитата(Simbian @ 5.4.2007, 11:23)

Автор: Simbian 5.4.2007, 11:58

To >>Руководитель проекта<< ?? поясните немного решение

Автор: Руководитель проекта 5.4.2007, 17:19

X=0 - не проехали ни одного светофора, т.е. первый же горел красным светом. Вероятность этого 1-0,4=0,6. X=1 - на первом зеленый сигнал, а на втором красный. И т.д.

Автор: A_nn 5.4.2007, 17:27

А ведь может быть, что первый был красный, а потом все зеленые - это разве не считается? Там же не говорится, что без остановок с начала движения, просто - без остановок...

Автор: Руководитель проекта 5.4.2007, 17:44

Цитата(A_nn @ 5.4.2007, 21:27)

Автор: Simbian 5.4.2007, 18:09

Т.е получается вот так?
P(X=0)=0.4
P(X=1)=0.6*0.4=0.24
P(X=2)=(0.6^2)*0.4
Р(Х=3)=(0.6^3)*0.4
Р(Х=4)=(0.6^4)*0.4
P(X=5)=0.6^5

ну так это окончательное нахождение вероятности? - так счас попробую остальное всё посчитать. но я подобным образом решал уже - и сказали не правильно

Автор: Руководитель проекта 5.4.2007, 19:28

В таком случае нужна более четкая формулировка задачи.

Автор: Simbian 6.4.2007, 4:48

На пути движения машины 5 светофоров, на каждом из которых зелёный свет может гореть с вероятностью 0.4. Составить закон рапределения числа светофоров, пройденных машиной без остановки. Найти функцию распределения и математические характеристики. Вычислить вероятность Р(Х<=3). - это всё что у меня есть из условий, была бы более чёткая я бы сам всё сделал.

Автор: Simbian 6.4.2007, 18:16

Нет как я и думал решение по методу Бернулли оказалось верным - всем спасибо- Извиняюсь, что развёл панику

Автор: Ботаник 6.4.2007, 18:26

Всегда пожалуйста! Было интересно следить за веткой.

Автор: chocolet1 23.11.2022, 22:37

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Автор: potapovsergei0 3.4.2024, 13:51

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