Question

While doing his undergraduate in California, professor Pham likes to visit Disney- land and California Adventure parks (they are next to each other). These parks are so popular that visitors may stay there for many days. Thus a guest at Disneyland on any day has a 0.4 chance of staying at Disneyland, 0.5 chance of going to California Adventure and 0.1 chance of leaving the parks. A guest at California Adventure on any day has a 0.3 chance of staying at California Adventure, 0.5 chance of going to Disneyland and 0.2 chance of leaving the parks. New guests arriving at the parks each day according to a Poisson(10,000) distribution. A new guest has a 0.4 chance of going to Disneyland and 0.6 chance of going to California Adventure on their first day. Find the long term distribution of the number of guests at Disneyland and California Adventure at the end of each day.

Answer 1