12.43 Consider the following transition probability matrix:0.6 0.2 0.2P= 0.3 0.4 0.30.0 0.3 0.7a. Give the state-transition diagram.b. Given that the process is currently in state 1, what is the probabilitythat it will be in state 2 at the end of the third transition?c. Given that the process is currently in state 1, what is the probabilitythat the first time it enters state 3 is the fourth transition?

transition probability matrix is given:

Answered: Consider the following transition…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 25 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered. 1. A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. 2. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. 3. A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money…
Pacific salmon populations have discrete breeding cycles in which they return from the ocean to streams to reproduce and then die. This occurs every one to five years, depending on the species. (a) Suppose that each fish must first survive predation by bears while swimming upstream, and predation occurs with probability d. After swimming upstream, each fish produces b offspring before dying. The stream is then stocked with m additional newly hatched fish before all fish then swim out to sea. What is the discrete-time recursion for the population dynamics, assuming that there is no mortality while at sea? You should count the population immediately before the upstream journey. nt + 1 = (b) Suppose that, instead of preying on fish while they swim upstream, bears do so only while the fish are swimming downstream. What is the discrete-time recursion for the population dynamics? (Again assume there is no mortality while at sea.) nt+1 (c) Which of the recursions obtained in parts (a) and (b)…
A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 25 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered. 1. A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. 2. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. 3. A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money…
Let S = {E1, E2, E3} be the sample space of an experiment and let A = {E1}, B = {E2}, and C = events from S. The probabilities of the sample points are assigned as follows: P(E,) = 0.35, P(E2) = 0.30, and P(E3) = 0.35. Find P(BC). {E2, E3} be Select one: O a. 0.65 O b. 0.70 O c. 0.35 O d. 0.30
Q. No. 5:Discuss the components of time series. b)There are five flights daily from Pittsburgh via US Airways into the Bradford Regional Airport in Bradford, Pennsylvania. Suppose the probability that any flight arrives late is 0.20. What is the probability that none of the flights are late today? What is the probability that exactly one of the flights is late today?
Pacific salmon populations have discrete breeding cycles in which they return from the ocean to streams to reproduce and then die. This occurs every one to five years, depending on the species. (a) Suppose that each fish must first survive predation by bears while swimming upstream, and predation occurs with probability d. After swimming upstream, each fish produces b offspring before dying. The stream is then stocked with m additional newly hatched fish before all fish then swim out to sea. What is the discrete-time recursion for the population dynamics, assuming that there is no mortality while at sea? You should count the population immediately before the upstream journey. nt + 1 = (b) Suppose that, instead of preying on fish while they swim upstream, bears do so only while the fish are swimming downstream. What is the discrete-time recursion for the population dynamics? (Again assume there is no mortality while at sea.) nt+1 = (c) Which of the recursions obtained in parts (a) and…
2. A Florida coastal community experiences a population increase during the winter months with seasonal residents arriving from northern states and Canada. The post office counter has three work stations. The service rate of each postal clerk is 0.75 customer per minute. The anticipated arrival rate is 1.2 customers per minute. Assume that customer arrivals follow a Poisson probability distribution, with an arrival and that service times follow an exponential probability distribution. Determine the following operating characteristics for the system:
Is there a unique way of filling in the missing probabilities in the transition diagram shown to the right? If so, complete the transition diagram and write the corresponding transition matrix. If not, explain why. 0.3 OA. Yes. The probability of transition from A to A is probability of transition from C to B is. (Type integers or decimals.) 0.4 0.5 0.7 B 0,2 0.1 Is there a unique way of filling in the missing probabilities in the transition diagram? If so, identify the missing probabilities. If not, explain why. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. the probability of transition from B to C is and the OB. No. It is possible to find the probability of transition from A to A, but the probability of transition from B to C is needed to find the probability of transition from C to B (and vice versa). OC. No. At least one of the missing probabilities is needed to find the other two. OD. No. It is possible to find the probability…
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 7 customers per hour and an average service rate of 12 customers per hour. The probability of 2 customers in the system is : a. 0.1418 b. 0.6597 C. 0.4167 d. 0.8582
Suppose the weather moves between three states 1,2,3. It stays in state 1 for an exponentially distributed number of days with mean 3, then goes to state 2. It stays in state 2 for an exponentially distributed number of days with mean 4, then goes to state 3. It stays in state 3 for an exponentially distributed number of days with mean 1, then goes to state 1. Compute the long-term probability that the weather is in state 1. Write your answer as a decimal.
A system consists of four components connected as shown below in the following diagram.Assume ?, ?, ?, and ? function independently. If the probability that ?,?, ?, and ? fail are 0.10, 0.05, 0.10, and 0.20 respectively. What is the probability that the system functions?b) A process manufactures ball bearing whose diameters are normally distributed with mean 2.505?? and standard deviation 0.008??. Specifications call for the diameter to be in the interval 2.5 ± 0.01 cm. what proportion of the ball bearings will meet the specification

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