All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
probability and stochastic modeling

Questions and Answers of Probability And Stochastic Modeling

Mark and Kevin play a series of games of cards. During each game each player bets $1, and whoever wins the game gets the $2. Sometimes a game ends in a tie in which case neither player loses his
A bag contains four red balls, three blue balls, and three green balls. Jim plays a game in which he bets $1 to draw a ball from the bag. If he draws a red ball, he wins $1; otherwise he loses $1.
Consider an m-server queueing system that operates in the following manner. There are two types of customers: type 1 and type 2. Type 1 customers 214 Markov Processes for Stochastic Modeling arrive
Consider a queueing system in which the server is subject to breakdown and repair. When it is operational, the time until it fails is exponentially distributed with mean 1/η.When it breaks down, the
Consider an MMBP(2)/Geo/1 queueing system, which is a single-server queueing system with a second-order Markov-modulated Bernoulli arrival process with external arrival parameters α and β and
Consider the superposition of two identical interrupted Poisson processes with internal rates α and β and external arrival rate λ. Obtain the infinitesimal generator and arrival rate matrix for
Give the state-transition-rate diagram for the BMAP(2)/M/1 queue with internal rates α12 and α21, external arrival rates λ1 and λ2, and service rateμ. Specify the infinitesimal generator, Q, if
Consider Problem 6.11. Assume that the time she spends with each of her children is exponentially distributed with the same means as specified.Obtain the transition probability functions {φij (t)}
In her retirement days, a mother of three grown-up children splits her time living with her three children who live in three different states. It has been found that her choice of where to spend her
A component is replaced every T time units and upon its failure. The lifetimes of successive components are independent and identically distributed random variables with PDF fX(x). A cost c1>0 is
Customers arrive at a taxi depot according to a Poisson process with rate λ.The dispatcher sends for a taxi when there are N customers waiting at the station. It takes M units of time for a taxi to
A machine can be in one of three states: good, fair, and broken. When it is in a good condition, it will remain in this state for a time that is exponentially distributed with mean 1/μ1 before going
Consider a Markov renewal process with the semi-Markov kernel Q given by Q =0.6(1 − e−5t) 0.4− 0.4e−2t 0.5− 0.2e−3t − 0.3e−5t 0.5− 0.5e−2t − te−2ta. Determine the
Larry is a student who cannot seem to make up his mind whether to live in the city or in the suburb. Every time he lives in the city, he moves to the suburb after one semester. Half of the time he
A high school student has two favorite brands of bag pack labeled X and Y.She continuously chooses between these brands in the following manner.Given that she currently has brand X, the probability
A machine has three components labeled 1, 2, and 3, whose times between failure are exponentially distributed with mean 1/λ1, 1/λ2, and 1/λ3, respectively. The machine needs all three components
Victor is a student who is conducting experiments with a series of lightbulbs.He started with 10 identical lightbulbs, each of which has an exponentially distributed lifetime with a mean of 200
The Merrimack Airlines company runs a commuter air service between Manchester, New Hampshire, and Cape Cod, Massachusetts. Because the company is a small one, there is no set schedule for their
Consider a machine that is subject to failure and repair. The time to repair the machine when it breaks down is exponentially distributed with mean 1/μ. The time the machine runs before breaking
Consider a queueing system in which customers arrive according to a Poisson process with rate λ. The time to serve a customer is a third-order Erlang random variable with parameter μ. What is the
Consider a queueing system in which the interarrival times of customers are the third-order Erlang random variable with parameter λ. The time to serve a customer is exponentially distributed with
Consider a finite-capacity G/M/1 queueing that allows at most 3 customers in the system including the customer receiving service. The time to serve a customer is exponentially distributed with mean
Consider an M/G/1 queueing system where service is rendered in the following manner. Before a customer is served, a biased coin whose probability of heads is p is flipped. If it comes up heads, the
Consider an M/M/2 queueing system with hysteresis. Specifically, the system operates as follows. Customers arrive according to a Poisson process with rate λ customers per second. There are two
Consider an M/M/1 queueing system with mean arrival rate λ and mean service time 1/μ. The system provides bulk service in the following manner.When the server completes any service, the system
Consider an M/M/1 queueing system with mean arrival rate λ and mean service time 1/μ that operates in the following manner. When the number of customers in the system is greater than three, a newly
Consider an M/M/1/5 queueing system with mean arrival rate λ and mean service time 1/μ that operates in the following manner. When any customer is in queue, the time until he defects (i.e., leaves
Customers arrive at a checkout counter in a grocery store according to a Poisson process with an average rate of 10 customers per hour. There are two clerks at the counter, and the time either clerk
Students arrive at a checkout counter in the college cafeteria according to a Poisson process with an average rate of 15 students per hour. There are three cashiers at the counter, and they provide
Consider a birth-and-death process representing a multi-server finite population system with the following birth-and-death rates:λk = (4 − k)λ k = 0, 1, 2, 3, 4μk = kμ k = 1, 2, 3, 4a. Find the
A cyber cafe has six PCs that customers can use for Internet access. These customers arrive according to a Poisson process with an average rate of six per hour. Customers who arrive when all six PCs
A machine has four identical components that fail independently. When a component is operational, the time until it fails is exponentially distributed with a mean of 10 hours. There is one resident
A small PBX serving a startup company can only support five lines for communication with the outside world. Thus, any employee who wants to place an outside call when all five lines are busy is
minutes.a. How much capacity should the facility have to achieve this goal?b. With the capacity obtained in part (a), what is the probability that an arriving customer is lost?
A company is considering how much capacity K to provide in its new service facility. When the facility is completed, customers are expected to arrive at the facility according to a Poisson process
A clerk provides exponentially distributed service to customers who arrive according to a Poisson process with an average rate of 15 per hour. If the service facility has an infinite capacity, what
People arrive at a library to borrow books according to a Poisson process with a mean rate of 15 people per hour. There are two attendants at the library, and the time to serve each person by either
People arrive at a phone booth according to a Poisson process with a mean rate of five people per hour. The duration of calls made at the phone booth is exponentially distributed with a mean of 4
A shop has five identical machines that break down independently of each other. The time until a machine breaks down is exponentially distributed with a mean of 10 hours. There are two repairmen who
Cars arrive at a car wash according to a Poisson process with a mean rate of 8 cars per hour. The policy at the car wash is that the next car cannot pass through the wash procedure until the car in
People arrive to buy tickets at a movie theater according to a Poisson process with an average rate of 12 customers per hour. The time it takes to complete the sale of a ticket to each person is
Cars arrive at a parking lot according to a Poisson process with rate λ.There are only four parking spaces, and any car that arrives when all the spaces are occupied is lost. The parking duration of
Consider a system consisting of two birth and death processes labeled system 1 and system 2. Customers arrive at system 1 according to a Poisson process with rate λ1, and customers arrive at system
Trucks bring crates of goods to a warehouse that has a single attendant.It is the responsibility of each truck driver to offload his truck, and the time that it takes to offload a truck is
An assembly line consists of two stations in tandem. Each station can hold only one item at a time. When an item is completed in station 1, it moves into station 2 if the latter is empty; otherwise
Consider a collection of particles that act independently in giving rise to succeeding generations of particles. Suppose that each particle, from the time it appears, waits a length of time that is
A taxicab company has a small fleet of three taxis that operate from the company’s station. The time it takes a taxi to take a customer to his or her location and return to the station is
A service facility can hold up to six customers who arrive according to a Poisson process with a rate of λ customers per hour. Customers who arrive when the facility is full are lost and never make
A switchboard has two outgoing lines serving four customers who never call each other. When a customer is not talking on the phone, he or she generates calls according to a Poisson process with rate
Lazy Chris has three identical lightbulbs in his living room that he keeps on all the time. Because of his laziness, Chris does not replace a lightbulb when it fails. (Maybe Chris does not even
A small company has two PCs A and B. The time to failure for PC A is exponentially distributed with a mean of 1/λA hours, and the time to failure for PC B is exponentially distributed with a mean of
Customers arrive at Mike’s barber shop according to a Poisson process with rate λ customers per hour. Unfortunately Mike, the barber, has only five chairs in his shop for customers to wait when
A small company has two identical PCs that are running at the same time.The time until either PC fails is exponentially distributed with a mean of 1/λ. When a PC fails, a technician starts repairing
On a given day Mark is either cheerful, so-so, or glum. Given that he is cheerful on a given day, then he will be cheerful the next day with probability 0.6, so-so with probability 0.2, and glum with
Consider the following transition probability matrix:a. What is Pn?b. Obtain φ13(5), the mean occupancy time of state 3 up to five transitions given that the process started from state 1.
The New England fall weather can be classified as sunny, cloudy, or rainy.A student conducted a detailed study of the weather conditions and came up with the following conclusion: Given that it is
A taxi driver conducts his business in three different towns 1, 2, and 3. On any given day, when he is in town 1, the probability that the next passenger he picks up is going to a place in town 1 is
Consider the following social mobility problem. Studies indicate that people in a society can be classified as belonging to the upper class (state 1), middle class (state 2), and lower class (state
A symmetric random walk {Sn:n = 0, 1, 2,...} starts at the position S0 = k and ends when the walk first reaches either the origin or the position m, where 0
Let X1, X2,... be independent and identically distributed Bernoulli random variables with values ±1 that have equal probability of 1/2. Let K1 and K2 be positive integers, and define N as follows:N
Let X1, X2,... be independent and identically distributed Bernoulli random variables with values ±1 that have equal probability of 1/2. Show that the partial sums Sn =n k=1 Xk k n = 1, 2,...form a
Let the random variable Sn be defined as follows:Sn =⎧⎨⎩0 n = 0n k=1 Xk n ≥ 1 where Xk is the kth outcome of a Bernoulli trial such that P[Xk = 1] = p and P[Xk = −1] = q = 1 − p, and the
A one-way street has a fork in it, and cars arriving at the fork can either bear right or left. A car arriving at the fork will bear right with probability 0.6 and will bear left with probability
Cars arrive from the northbound section of an intersection in a Poisson manner at the rate of λN cars per minute and from the eastbound section in a Poisson manner at the rate of λE cars per
Suzie has two identical personal computers, which she never uses at the same time. She uses one PC at a time, and the other is a backup. If the one she is currently using fails, she turns it off,
A five-motor machine can operate properly if at least three of the five motors are functioning. If the lifetime X of each motor has the PDF fX(x) = λe−λx, x≥0,λ>0, and if the lifetimes of the
Joe replaced two lightbulbs, one of which is rated 60 watts with an exponentially distributed lifetime whose mean is 200 hours, and the other is rated 100 watts with an exponentially distributed
Bob has a pet that requires the light in his apartment to always be on. To achieve this, Bob keeps three lightbulbs on with the hope that at least one bulb will be operational when he is not at the
Chris is conducting an experiment to test the mean lifetimes of two sets of electric bulbs labeled A and B. The manufacturer claims that the mean lifetime of bulbs in set A is 200 hours, while the
Customers arrive at a bank according to a Poisson process with an average rate of six customers per hour. Each arriving customer is either a man with probability p or a woman with probability 1−p.
Students arrive at the professor’s office for extra help according to a Poisson process with an average rate of four students per hour. The professor does not start the tutorial until at least
Three customers A, B, and C simultaneously arrive at a bank with two tellers on duty. The two tellers were idle when the three customers arrived, and A goes directly to one teller, B goes to the
Joe is a student who is conducting experiments with a series of lightbulbs.He started with 10 identical lightbulbs, each of which has an exponentially distributed lifetime with a mean of 200 hours.
Customers arrive at the neighborhood bookstore according to a Poisson process with an average rate of 10 customers per hour. Independent of other customers, each arriving customer buys a book with
An insurance company pays out claims on its life insurance policies in accordance with a Poisson process with an average rate of five claims per week. If the amount of money paid on each policy is
Suppose X(t) is a Gaussian random process with a mean E[X(t)] = 0 and autocorrelation function RXX(τ) = e−|τ|. Assume that the random variable A is defined as follows:A = B 0X(t)dt where B is a
Suppose X(t) is a Gaussian random process with a mean E[X(t)] = 0 and autocorrelation function RXX(τ) = e−|τ|. Assume that the random variable A is defined as follows:A = 1 0X(t)dt Determine the
Cars arrive at a gas station according to a Poisson process at an average rate of 12 cars per hour. The station has only one attendant. If the attendant decides to take a two-minute coffee break when
Students arrive for a lab experiment according to a Poisson process with a rate of 12 students per hour. However, the lab attendant opens the door to the lab when at least four students are waiting
A Girl Scout troop sells cookies from house to house. One of the parents of the girls figured out that the probability that they sell a set of packs of cookies at any house they visit is 0.4, where
A lady invites 12 people for dinner at her house. Unfortunately the dining table can only seat six people. Her plan is that if six or fewer guests come, then they will be seated at the table (i.e.,
A sequence of Bernoulli trials consists of choosing components at random from a batch of components. A selected component is classified as either defective or nondefective. A nondefective component
The probability that a patient recovers from a rare blood disease is 0.3.If 15 people are known to have contracted this disease, find the following probabilities:a. At least 10 survive.b. From three
A sequence of Bernoulli trials consists of choosing seven components at random from a batch of components. A selected component is classified as either defective or nondefective. A nondefective
15.5 Passengers arrive at a train station according to a Poisson process with a rate of 25 customers per hour. It has been found that 60% of the passengers are females. What is the probability that
15.4 A restaurant has two entrances A and B. Customers arrive at the restaurant through entrance A according to a Poisson process with a rate of five customers per hour, and customers arrive through
15.3 Let fX1; X2; ...g be a sequence of independent and identically distributed random variables with PDF fXðxÞ, and let N be an integer-valued random variable with PMF pNðnÞ, where N and the Xi
15.2 A hard-core point process is produced from a Poisson process of rate λ by deleting any point within distance v0 of another point, regardless of whether that point has itself already been
15.1 Two classes of customers arrive at Paul’s barber shop: class 1 and class 2. Class 1 customers arrive according to a Poisson process with rate λ1 customers per hour, and class 2 customers
14.6 Consider a system that can be modeled by an array of six states labeled 1; 2; ...; 6. Every state makes a transition to itself with probability p and makes a transition to the next higher state
14.5 Consider a system that can be modeled by an array of six states labeled 1; 2; ...; 6. Apart from state 4, which makes a transition to itself with probability p, every other state is visited only
14.4 Consider three coins labeled 1, 2, and 3. When coin 1 is tossed, the probability that it comes up heads is 0.75 and the probability that it comes up tails is 0.25. Similarly, when coin 2 is
14.3 Construct the PHMM for the following variable length sequences DOR, DM, DAP, VGBLM. (Hint: Use the following alignment to identify the match, insert, and delete states.) D O 2 2 R D 222 M D A 2
14.2 Consider the HMM shown in Figure 14.19 that has three hidden states 1, 2, and 3, and emits two output symbols: U and V. When it is in state 1, it is equally likely to emit either symbol. When it
14.1 Consider an HMM with two states 1 and 2 and emits two symbols: A and B. The statetransition diagram is shown in Figure 14.18.a. Use the Viterbi algorithm to obtain the most likely state
13.5 Consider a salesman who has offices in two towns called town 1 and town 2. He can be in one of these towns on any particular day but cannot split his time on any day between the two. On any day
13.4 Solve Problem 13.3, assuming a discount factor of 0.9.
13.3 A farmer is considering the optimal course of action for his farm each year. The two options are to fertilize the farm and not to fertilize the farm. Optimality is defined such that the farmer
13.2 The price of a certain stock is fluctuating among $10, $20, and $30 from month to month. Market analysis indicates that given that the stock is at $10 in the current month, then in the following
13.1 A recent college graduate is presented with N job offers, one after another. After looking at an offer, she must either accept it and thus terminate the process or reject it. A rejected offer

Showing 3200 - 3300 of 6914

First
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved