3. The victims of a certain disease are classified into three states: cured, dead from thedisease, or sick. Once a person is cured, he is permanently immune. Each year, 70%of those sick are cured, 10% die from the disease and 20% remain ill.(a) Create a transition diagram that describes this scenario.(b) Create a stochastic matrix that describes this scenario. Is this scenario ergodicor absorbing? Explain.(c) Rewrite the matrix in standard form.(d) Find N, R and B.(e) On average, if a person begins as healthy, how long will a person remain ill beforebeing cured or passing away?(f) Determine the probability that a person will be cured if they begin as ill.(g) Determine the probability that a person will die if they begin as healthy.

As per the rule of Bartleby we can answer 3 subparts at a time, please repost other subparts mentioning the number of the required subparts. Given three states cured, dead from the disease or sick. The probabilities of transitions from one state to the other is given as follows. If a person is cured he is permanently immune, i.e. the probability of transition of the cured person to other states is zero. Each year 70% of the sick are cured and 10% die from disease and 20% remain ill. If a person is dead then obviously the probabilities of transition of the dead person to other states are zero. (a) To create a transition diagram that describes the scenario. (b) To create a stochastic matrix that describe the scenario. To explain if the scenario is ergodic or absorbing. (c) To rewrite the matrix in standard form.(a) The transition probability diagram from one state to another state is given as follows (b) Suppose xn,yn,zn denotes the portion of population that is cured, sick and dead respectively in n-th year. Then xk+1=xk+0.7yk+0zkyk+1=0xk+0.2yk+0zkzk+1=0xk+0.1yk+zk So the transition matrix can be written in matrix form as Xk+1=xk+1yk+1zk+1=10.7000.2000.11xkykzk=10.7000.2000.11Xk So the transition matrix is A=10.7000.2000.11 A Markov chain is called an ergodic chain if it is possible to transform from every state to every other state in a finite steps. Here it is not possible to move from cured state to any other state for a person or for a dead person to move to other states. So obviously it is not ergodic. The transition probability matrix for an absorbing Markov chain will have at least a column in which all elements are zeros except one that is equal to 1. As the transition matrix has two such columns so it is absorbing.(c) To write the matrix A=10.7000.2000.11 in standard form. Perform the transformation in standard form. CSD10.70C00.20S00.11D→CDS100.7C010.1D000.2S So the standard matrix is A'=100.7010.1000.2.