Question
Please answer the following questions...
We are interested in the movement of patients within a hospital. For purposes of our analysis, we shall consider the hospital to have three different types of rooms: general care, special care, and intensive care. Based on past data, 60% of arriving patients are initially admitted into the general care category, 30% in the special care category, and 10% in intensive care. A "general care" patient has a 55% chance of being released healthy the following day, a 30% of remaining in the general cane room, and a 15% of being moved to the special care facility. A "special care" patient has a 10% chance of being released the following day, a 20% chance of being moved to general care, a 10% chance of being upgraded to intensive care, and ai 5% chance of dying during the day. An "intensive care" patient is never releassi from the hospital directly from the intensive care unit (ICU), but is always ma to another facility first. The probabilities that the patient is moved to general can special care, or remains in intensive care are 5%, 30%, or 55%, respectively. Let be a Markov chain where X0 is the type of room that an admitted patient initially uses, and Xn is the room category of that patient at the end of day n. Give the Markov matrix for X. What is the probability that a patient admitted into the intensive care room eventually leaves the hospital healthy? What is the expected number of days that a patient, admitted into intensive care will spend in the ICU? What is the expected length of stay for a patient admitted into the hospital as a general care patient? During a typical day, 100 patients are admitted into the hospital. What is the average number of patients in the ICU?
Explanation / Answer
markov matrix state0=release,state1=General care,state2=special care,state3=intensive care marix= [0 0.6 0.3 0.1] [0.55 0.3 0.15 0] [0.15 0.2 0.55 0.1] [0 0.05 0.3 0.55]