TOPIC: MARKOV CHAINS A book club has 3 mailing lists: A special list M of the most senior active members. Another list R containing the regular members, and A list of regular members and names of individuals who have shown interest in club activities in the past. For each new publication, it is necessary to decide which list should be used to mail the sale announcements. sale. If after the last mailing there was a request for too few copies, the secretary uses list R with probability of ¼ and P with a probability of ¾. If after the last mailing there was a satisfactory response, the secretary uses the R list and the P list with equal probabilities. If, after the preceding shipment, there was an excessive number of orders or over demand, the secretary uses list M with probability 1/3 and list P with probability ¾. list M with probability 1/3 and R with probability 2/3. If list M is used, there will be poor sales or satisfactory sales with equal probabilities; if list R is used, there will be poor sales with equal probabilities. R, there will be poor sales with probability ¼ and satisfactory sales with probability ¾; if list P is used, there will be satisfactory sales with probability 1/3 and over demand with probability 2/3. In what proportion of the times are the sales sparse, satisfactory and over demand respectively?

TOPIC: MARKOV CHAINS

A book club has 3 mailing lists:

• A special list M of the most senior active members.
• Another list R containing the regular members, and
• A list of regular members and names of individuals who have shown interest in club activities in the past.

For each new publication, it is necessary to decide which list should be used to mail the sale announcements.
sale.
If after the last mailing there was a request for too few copies, the secretary uses list R with probability
of ¼ and P with a probability of ¾.
If after the last mailing there was a satisfactory response, the secretary uses the R list and the P list with equal
probabilities.
If, after the preceding shipment, there was an excessive number of orders or over demand, the secretary uses list M with probability 1/3 and list P with probability ¾.
list M with probability 1/3 and R with probability 2/3.
If list M is used, there will be poor sales or satisfactory sales with equal probabilities; if list R is used, there will be poor sales with equal probabilities.
R, there will be poor sales with probability ¼ and satisfactory sales with probability ¾; if list P is used,
there will be satisfactory sales with probability 1/3 and over demand with probability 2/3.
In what proportion of the times are the sales sparse, satisfactory and over demand respectively?