Slide - Definição dos Tempos Médios 2021 2

Aula 06/12/2021 Tempos Médios p_ij 1 2 3 4 1 1.0 0 0 0 2 0.3 0.4 0.3 0 3 0 0.3 0.4 0.3 4 0 0 0 1.0 Exemplo 1 Social mobility. Let X_n be a family’s social class in the nth generation, which we assume is either 1 = lower, 2 = middle, or 3 = upper. In our simple version of sociology, changes of status are a Markov chain with the following transition probability: 1 2 3 1 0.7 0.2 0.1 2 0.3 0.5 0.2 3 0.2 0.4 0.4 Para todos os estados i recorrentes. Para todos os estados transientes. Exemplo 2 Para todos os estados i recorrentes. Para todos os estados transientes. Exemplo 3 Tempo Médio de Primeira visita ao um estado recorrente “s” • O estado “s” passa a ser um estado absorvente. • Muda-se a matriz de transição. Exemplo 2 Brand preference. Suppose there are three types of laundry detergent, 1, 2, and 3, and let X_n be the brand chosen on the nth purchase. Customers who try these brands are satisfied and choose the same thing again with probabilities 0.8, 0.6, and 0.4 respectively. When they change they pick one of the other two brands at random. The transition probability is 1 2 3 1 0.8 0.1 0.1 2 0.2 0.6 0.2 3 0.3 0.3 0.4