An insurance company classifies its customers into three categories: 1. Good Risk 2. Acceptable Risk 3....
An insurance company classifies its customers into
three categories:
1. Good Risk
2. Acceptable Risk
3. Bad Risk
Customers independently transition between categories at the end of
each year according to
a Markov process with the following transition matrix:
P =
0.6 0.3 0.1
0.5 0.0 0.5
0.4 0.4 0.2
Find the long-run proportion of time in Good Risk, and
the expected number of steps needed
to return to Good Risk.
Homework Answers
long-run proportion is given by P^n when n tend to infinity
pi_1 = 0.531
hence 53.1 %
Add Answer to:
An insurance company classifies its customers into
three categories:
1. Good Risk
2. Acceptable Risk
3....
The same scenario is used for the remainder of the questions. A psychiatrist clinic classifies its...
The same scenario is used for the remainder of the
questions.
A psychiatrist clinic classifies its accounts receivable into
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State 1. Paid
State 2. Bad debt
State 3. 0-30 days
State 4. 31-90 days
The clinic currently has $8000 accounts receivable in the 0-30 days
state and $2000 in the 31-90 days state. Based on historical
transition from week to week of accounts receivable, the following
matrix of transition probabilities has been developed for the
clinic...
An insurance company classifies its customers into 3 categories: below average, average, and above average. No...
An insurance company classifies its customers into 3 categories: below average, average, and above average. No one moves more than one state at a time. For example, a customer cannot move from below average to above average or from above average to below average in a given period. After a given period, we notice that: 40% of those in the below average category become average 30% of those in the average category become above average 10% of those in the...
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix...
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix and initial distribution π = (0.2, 0.5, 0.3). Calculate P(X1 = 2) and P(X3 = 2|X0 = 0) 0.3 0.1 0.6 p0.4 0.4 0.2 0.1 0.7 0.2
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2} has...
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2} has transition probability matrix 0.1 0.3 0.6 p = 0.5 0.2 0.3 0.4 0.2 0.4 If P(X0 = 0) = P(X0 = 1) = 0.4 and P(X0 = 2) = 0.2, find the distribution of X2 and evaluate P[X2 < X4].
2. (15 points) The state of a process changes daily according to a three-state Markov chain....
2. (15 points) The state of a process changes daily according to a three-state Markov chain. If the process is in state i during one day, then it is in state j the following day with probability Piy, where Poo 0.2, Po0.4, Po2 0.4, P 0.25, P 0.7, P12 0.05, and P20 0.3, P21 = 02, P22 = 0.5. Every day a message is sent. If the state of the Markov chain that day is i then the message sent...
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3. A spider hunts a fly moving between the positions 1 and 2 according to a Markov Chain P= 0.3 0.7 The fly, independently of the spider, moves between 1 and 2 according to a second Markov with transition matrix 0.0.3 Chain whose transition matrix is 0.4 0.6 0.6 0.4 The hunt finishes the first time both the spider and the fly are on the same position, (a) Describe the hunt with a suitable 3 states Markov Chain; (b) Assuming...
3. A spider hunts a fly moving between the positions 1 and 2 according to a...
3. A spider hunts a fly moving between the positions 1 and 2 according to a Markov Chain with transition matrix 0.7 0.3 The fly, independently of the spider, moves between 1 and 2 according to a second Markov Chain whose transition matrix is 0.4 0.6 0.6 0.4 -(04) The hunt finishes the first time both the spider and the fly are on the same position, (a) Describe the hunt with a suitable 3 states Markov Chain (b) Assuming that...
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, ...
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, p4,4=0.4 p5,1=0.3, p5,2=0.2, p5,4=0.3, p5,5 = 0.2 (a) Let T denote the transition matrix. Compute T3. Find the probability that if you start in state #3 you will be in state #5 after 3 steps. (b) Compute the matrix N = (I - Q)-1. Find the expected value for the number of...
Question 4 (2 points) An automobile insurance company divides customers into three categories: good risks, medium...
Question 4 (2 points) An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 12,573 customers, 6,524 are good risks, 1,190 are medium risks, and the rest are poor risks. As part of an audit, one customer is chosen at random. What is the probability that the customer is not a poor risk? Write only a number as your answer. Round to two decimal places (for example: 0.43)....
#10) An automobile insurance company divides customers into three categories: good risks, medium risks, and poor...
#10) An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that 70% of the customers are good risks, 20% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.00s of filing an accident claim a medium risk customer has probability 0.01 and a poor risk customer has probability 0.02s chosen at random. [Let GR denote good risks, MR denote...
The same scenario is used for the remainder of the
questions.
A psychiatrist clinic classifies its accounts receivable into
the following four states
State 1. Paid
State 2. Bad debt
State 3. 0-30 days
State 4. 31-90 days
The clinic currently has $8000 accounts receivable in the 0-30 days
state and $2000 in the 31-90 days state. Based on historical
transition from week to week of accounts receivable, the following
matrix of transition probabilities has been developed for the
clinic...
2. (15 points) The state of a process changes daily according to a three-state Markov chain. If the process is in state i during one day, then it is in state j the following day with probability Piy, where Poo 0.2, Po0.4, Po2 0.4, P 0.25, P 0.7, P12 0.05, and P20 0.3, P21 = 02, P22 = 0.5. Every day a message is sent. If the state of the Markov chain that day is i then the message sent...
3. A spider hunts a fly moving between the positions 1 and 2 according to a Markov Chain P= 0.3 0.7 The fly, independently of the spider, moves between 1 and 2 according to a second Markov with transition matrix 0.0.3 Chain whose transition matrix is 0.4 0.6 0.6 0.4 The hunt finishes the first time both the spider and the fly are on the same position, (a) Describe the hunt with a suitable 3 states Markov Chain; (b) Assuming...
3. A spider hunts a fly moving between the positions 1 and 2 according to a Markov Chain with transition matrix 0.7 0.3 The fly, independently of the spider, moves between 1 and 2 according to a second Markov Chain whose transition matrix is 0.4 0.6 0.6 0.4 -(04) The hunt finishes the first time both the spider and the fly are on the same position, (a) Describe the hunt with a suitable 3 states Markov Chain (b) Assuming that...
Question 4 (2 points) An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 12,573 customers, 6,524 are good risks, 1,190 are medium risks, and the rest are poor risks. As part of an audit, one customer is chosen at random. What is the probability that the customer is not a poor risk? Write only a number as your answer. Round to two decimal places (for example: 0.43)....
#10) An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that 70% of the customers are good risks, 20% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.00s of filing an accident claim a medium risk customer has probability 0.01 and a poor risk customer has probability 0.02s chosen at random. [Let GR denote good risks, MR denote...
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