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Консультация № 182566
20.03.2011, 20:37
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Здравствуйте, уважаемые эксперты! Прошу вашей помощи в решении данной задачи:
Дана матрица Р вероятностей перехода цепи Маркова. Распределение по состояниям в момент t=0 определяется вектором q .
Найти:
1. Распределение по состояниям в момент t=2.
2. Вероятность того, что в моменты t=0, 1, 2 состояниями цепи будут соответственно 2,1,3 состояния.
3. Стационарное (предельное) распределение вероятностей.
0.6 0.1 0.3
P = ( 0.2 0.2 0.6 )
0.6 0.3 0.1
q = {0.1 0.4 0.5}
Оч нуждаюсь в вашей помощи.Заранее спасибо
Дана матрица Р вероятностей перехода цепи Маркова. Распределение по состояниям в момент t=0 определяется вектором q .
Найти:
1. Распределение по состояниям в момент t=2.
2. Вероятность того, что в моменты t=0, 1, 2 состояниями цепи будут соответственно 2,1,3 состояния.
3. Стационарное (предельное) распределение вероятностей.
0.6 0.1 0.3
P = ( 0.2 0.2 0.6 )
0.6 0.3 0.1
q = {0.1 0.4 0.5}
Оч нуждаюсь в вашей помощи.Заранее спасибо
Обсуждение
21.03.2011, 02:18
общий
это ответ
Здравствуйте, Минковский Георгий Андреевич!
Для однородной марковской цепи
или
В частности
откуда P{S(0)=2} = 0.4, P{S(1)=1} = 0.44, P{S(2)=3} = 0.308.
Стационарное (предельное) распределение вероятностей определяется условием
или
где
В данном случае
или
Определитель системы равен 0, поэтому она имеет бесконечно много решений. В общем виде их можно записать как q = {9t; 3t; 5t}. Исходя из условия q[sub]1[/sub]+q[sub]2[/sub]+q[sub]3[/sub]=1 имеем t = 1/17 и q = {9/17; 3/17; 5/17}.
Для однородной марковской цепи
или
В частности
откуда P{S(0)=2} = 0.4, P{S(1)=1} = 0.44, P{S(2)=3} = 0.308.
Стационарное (предельное) распределение вероятностей определяется условием
или
где
В данном случае
или
Определитель системы равен 0, поэтому она имеет бесконечно много решений. В общем виде их можно записать как q = {9t; 3t; 5t}. Исходя из условия q[sub]1[/sub]+q[sub]2[/sub]+q[sub]3[/sub]=1 имеем t = 1/17 и q = {9/17; 3/17; 5/17}.
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