Suppose you live in an off campus apartment, and the time it takes you to reach...
Suppose you live in an off campus apartment, and the time it takes you to reach class from your apartment, if you are walking, is 25 minutes. You can also use a bus. Buses arrive at the bus stop according to a Poisson process with a constant rate of 6 per hour. Suppose walking from your apartment to bus stop takes 8 minutes. The length of the bus ride from the bus stop to the union station is 5 minutes, and walking from union station to class takes 7 minutes. What is the probability the bus will get you to union station faster than walking? In the following, let T be an exponential random variable denoting the time until the next bus arrival, and assume time units are in minutes. Please state if this is Poisson , Exponential Random Variable, or Erlang Random Variable. and use the correct notation and formula.
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Suppose you live in an off campus apartment, and the time it
takes you to reach...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
C. In Regular Bus City, there is a shuttle bus that goes between Stop A and Stop B, with no stops...
Question D
C. In Regular Bus City, there is a shuttle bus that goes between Stop A and Stop B, with no stops in between. The bus is perfectly punctual and arrives at Stop A at precise five minute intervals (6:00, 6:05, 6:10, 6:15, etc.) day and night, at which point it immediately picks up all passengers waiting. Citizens of Regular Bus City arrive at Stop A at Poisson random times, with an average of 5 passengers arriving every minute,...
Suppose the time between buses at a particular stop is a positively skewed random variable with...
Suppose the time between buses at a particular stop is a positively skewed random variable with an average of 59 minutes and standard deviation of 6 minutes. Suppose the time between buses at this stop is measured for a randomly selected week, resulting in a random sample of n = 38 times. The average of this sample, X , is a random variable that comes from a specific probability distribution. (a)Which of the following is true about the distribution of...
3. Let th e random variable Ti denote the time you must wait to place your order in a fast-food restaurant, let Tz denote the time that it takes to place your order after you reach the counter, le...
3. Let th e random variable Ti denote the time you must wait to place your order in a fast-food restaurant, let Tz denote the time that it takes to place your order after you reach the counter, let s denote the time that it takes to receive vour food after you've placed your order, and let T enote the time that it takes to east vour food after you've received it. Assume that all of these random variables are...
Poisson Processes. Suppose you have two independent Poisson processes (N1(t), 12 0} and {N2(t), t...
Poisson Processes. Suppose you have two independent Poisson processes (N1(t), 12 0} and {N2(t), t 0), where Ni(t) has rate λ and N2(t) has rate μ. Label the arrivals from N(t) as "type1" and arrivals from N2(t) as "type 2." Let Z be a random variable that represents the time until the next arrival of either type. What is the distribution of Z? (Justify your answer.)
Poisson Processes. Suppose you have two independent Poisson processes (N1(t), 12 0} and {N2(t),...
Consider a simple queuing system in which customers arrive randomly such that the time between successive...
Consider a simple queuing system in which customers arrive randomly such that the time between successive arrivals is exponentially distributed with a rate parameter l = 2.8 per minute. The service time, that is the time it takes to serve each customer is also Exponentially distributed with a rate parameter m = 3 per minute. Create a Matlab simulation to model the above queuing system by randomly sampling time between arrivals and service times from the Exponential Distribution. If a...
1. Suppose you're back at home and you need to schedule an appointment with your internet provide...
1. Suppose you're back at home and you need to schedule an appointment with your internet provider to have someone come over and fix it. You have to be at home to let the person in. If you miss the serviceperson, you have (a) Although you're given an exact time (3:00pm), the company tells you that the serviceperson could show up Let X - the arrival time (in minutes) of tife serviceperson relative to the scheduled time. Then based on...
Can you solve 12 Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note...
Can you solve 12
Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note that it is wrong to reason like this: Alice expects to arrive at 12:30, Bob expects to arrive at 1:00: thus, we expeet that Bob will wait 30 mimutes for Alice.) (b). We want to compute the probability that Bob has to wait for Alice, which is P(Y < X), which we do by integrating the joint density, f(r,y), over the region where <...
Suppose you and your friend Alanis live, together with n − 2 other people, at a...
Suppose you and your friend Alanis live, together with n − 2 other people, at a popular off-campus cooperative apartment, the Upson Collective. Over the next n nights, each of you is supposed to cook dinner for the co-op exactly once, so that someone cooks on each of the nights. Of course, everyone has scheduling conflicts with some of the nights (e.g., exams, concerts, etc.), so deciding who should cook on which night becomes a tricky task. For concreteness, let’s...
Art 250 Choose the best answer of both hands at the same time is A. flow process chart simultaneo...
art 250 Choose the best answer of both hands at the same time is A. flow process chart simultaneous-motion (SIMO) chart 2 The best chart used to analyze the Body is called B. Operations charts D. None of the above 3. In a stopwatch time study, the average time it takes a given worker to perform a task a certain number of times is the: A. Observed time B. Normal time C. Standard time D. Performance rating time Labor Standards...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
Question D
C. In Regular Bus City, there is a shuttle bus that goes between Stop A and Stop B, with no stops in between. The bus is perfectly punctual and arrives at Stop A at precise five minute intervals (6:00, 6:05, 6:10, 6:15, etc.) day and night, at which point it immediately picks up all passengers waiting. Citizens of Regular Bus City arrive at Stop A at Poisson random times, with an average of 5 passengers arriving every minute,...
Suppose the time between buses at a particular stop is a positively skewed random variable with an average of 59 minutes and standard deviation of 6 minutes. Suppose the time between buses at this stop is measured for a randomly selected week, resulting in a random sample of n = 38 times. The average of this sample, X , is a random variable that comes from a specific probability distribution. (a)Which of the following is true about the distribution of...
3. Let th e random variable Ti denote the time you must wait to place your order in a fast-food restaurant, let Tz denote the time that it takes to place your order after you reach the counter, let s denote the time that it takes to receive vour food after you've placed your order, and let T enote the time that it takes to east vour food after you've received it. Assume that all of these random variables are...
Poisson Processes. Suppose you have two independent Poisson processes (N1(t), 12 0} and {N2(t), t 0), where Ni(t) has rate λ and N2(t) has rate μ. Label the arrivals from N(t) as "type1" and arrivals from N2(t) as "type 2." Let Z be a random variable that represents the time until the next arrival of either type. What is the distribution of Z? (Justify your answer.)
Poisson Processes. Suppose you have two independent Poisson processes (N1(t), 12 0} and {N2(t),...
1. Suppose you're back at home and you need to schedule an appointment with your internet provider to have someone come over and fix it. You have to be at home to let the person in. If you miss the serviceperson, you have (a) Although you're given an exact time (3:00pm), the company tells you that the serviceperson could show up Let X - the arrival time (in minutes) of tife serviceperson relative to the scheduled time. Then based on...
Can you solve 12
Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note that it is wrong to reason like this: Alice expects to arrive at 12:30, Bob expects to arrive at 1:00: thus, we expeet that Bob will wait 30 mimutes for Alice.) (b). We want to compute the probability that Bob has to wait for Alice, which is P(Y < X), which we do by integrating the joint density, f(r,y), over the region where <...
art 250 Choose the best answer of both hands at the same time is A. flow process chart simultaneous-motion (SIMO) chart 2 The best chart used to analyze the Body is called B. Operations charts D. None of the above 3. In a stopwatch time study, the average time it takes a given worker to perform a task a certain number of times is the: A. Observed time B. Normal time C. Standard time D. Performance rating time Labor Standards...
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