The victims of a certain disease being treated at Wake Medical Center are classified annually as follows: cured, in temporary remission, sick, or dead from the disease. Once a patient is cured, he is permanently immune. Each year, those in remission get sick again with probability 0.12, are cured with probability 0.23, die with probability 0.05, and stay in remission with probability 0.6. Those who are sick are cured with probability 0.05, die with probability 0.2, go into remission with probability 0.4, and remain sick with probability 0.35. Find the transition matrix and do the calculations necessary to answer these questions.
(a) If a patient is now in remission, what is the probability he is still alive in 2 years? (Hint: In which of the states is the patient still alive?)
(b) If a patient is now in remission, what is the probability he dies within 3 years?
The victims of a certain disease being treated at Wake Medical Center are classified annually as...
The victims of a certain disease being treated at Wake Medical Center are classified annually as follows: cured, in temporary remission, sick, or dead from the disease. Once a victim is cured, he is permanently immune. Each year, those in remission get sick again with probability 1/4, are cured with probability 1/2, and stay in remission with probability 1/4. Those who are sick are cured, go into remission, or die from the disease with probability 1/3 each. Determine the probability...
sheer speed with which end-stage liver failure can consume a patient is what makes the disease so devastating.1,2 Unfortunately, Ms. S.’s family had never been informed about that reality. When they brought her in for a mere urinary tract infection, they were shocked that it took only days for her heart, lungs, and immune system to fail alongside her liver. Her family waited in hopeful anticipation for Ms. S.’s condition to take a turn for the better, and therefore repeatedly...
The sheer speed with which end-stage liver failure can consume a patient is what makes the disease so devastating.1,2 Unfortunately, Ms. S.’s family had never been informed about that reality. When they brought her in for a mere urinary tract infection, they were shocked that it took only days for her heart, lungs, and immune system to fail alongside her liver. Her family waited in hopeful anticipation for Ms. S.’s condition to take a turn for the better, and therefore...