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4. On the weekends l sometimes take the #12 bus, which I have observed to arrive...
4. You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive...
4. You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 10:30. (a) What is the probability that you will have to wait longer than 10 minutes? (b) If at 10:10 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 2 minutes?
The time a bus will arrive is uniformly distributed from 8:00 AM until 8:20 AM. You...
The time a bus will arrive is uniformly distributed from 8:00 AM until 8:20 AM. You arrive at the bus stop at exactly 8:00 AM. What is the probability you will wait 12 minutes or more?
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,...
You are waiting at a bus stop and can take any one of two buses Bus...
You are waiting at a bus stop and can take any one of two buses Bus 1 or Bus 2. Bus 1 comes every 5 minutes and Bus 2 every 10 minutes. Further assume that the waiting times are memoryless in the sense that the amount of time since the previous bus arrived does not affect how much time to wait until the next bus comes and that the waiting times for each of the three buses are independent. (a)...
3. You are waiting at a bus stop and can take any one of two buses...
3. You are waiting at a bus stop and can take any one of two buses Bus 1 or Bus 2. Bus 1 comes every 5 minutes and Bus 2 every 10 minutes. Further assume that the waiting times are memoryless in the sense that the amount of time since the previous bus arrived does not affect how much time to wait until the next bus comes and that the waiting times for each of the three buses are independent....
You are waiting at the bus stop for a bus, which arrives every X minutes, where...
You are waiting at the bus stop for a bus, which arrives every X minutes, where X is a random variable with an exponential PDF, and a mean of 30 minutes. You have been already waiting for 10 minutes. What is the probability that you will wait for 20 more minutes, given that you have already been waiting for 10 minutes?
Suppose your wait time for shuttle bus follows an exponential distribution with u = 5. (a)...
Suppose your wait time for shuttle bus follows an exponential distribution with u = 5. (a) What is the probability that you have to wait longer than 10? (b) Given you already waited 10 minutes, what is the probability that you have to wait for another 10 more minutes? (c) Let X be exponentially distributed with parameter 1/u. Prove that P(X >a+b|X >a)=P(X >b)
The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0, 12]. You observe the wait time for the next 100 trains to arrive. Assume wait times are independent
The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0, 12]. You observe the wait time for the next 100 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2 decimal places) that the sum of the 100 wait times you observed is between 565 and 669? Part b) What is the approximate probability (to 2 decimal places) that the average of the...
Part 3: The Uniform Distribution Suppose that you need to take a bus that comes every...
Part 3: The Uniform Distribution
Suppose that you need to take a bus that comes every 30 minutes.
Assume that the amount of time you have to wait for this bus has a
uniform distribution between 0 and 30 minutes. The probability
density curve for this distribution is given below.
1) Is waiting time a discrete or continuous random variable?
2) What is the area of this entire rectangle?
3) What numbers are represented by a, b and c (note:...
4. You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 10:30. (a) What is the probability that you will have to wait longer than 10 minutes? (b) If at 10:10 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 2 minutes?
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,...
You are waiting at a bus stop and can take any one of two buses Bus 1 or Bus 2. Bus 1 comes every 5 minutes and Bus 2 every 10 minutes. Further assume that the waiting times are memoryless in the sense that the amount of time since the previous bus arrived does not affect how much time to wait until the next bus comes and that the waiting times for each of the three buses are independent. (a)...
3. You are waiting at a bus stop and can take any one of two buses Bus 1 or Bus 2. Bus 1 comes every 5 minutes and Bus 2 every 10 minutes. Further assume that the waiting times are memoryless in the sense that the amount of time since the previous bus arrived does not affect how much time to wait until the next bus comes and that the waiting times for each of the three buses are independent....
Suppose your wait time for shuttle bus follows an exponential distribution with u = 5. (a) What is the probability that you have to wait longer than 10? (b) Given you already waited 10 minutes, what is the probability that you have to wait for another 10 more minutes? (c) Let X be exponentially distributed with parameter 1/u. Prove that P(X >a+b|X >a)=P(X >b)
Part 3: The Uniform Distribution
Suppose that you need to take a bus that comes every 30 minutes.
Assume that the amount of time you have to wait for this bus has a
uniform distribution between 0 and 30 minutes. The probability
density curve for this distribution is given below.
1) Is waiting time a discrete or continuous random variable?
2) What is the area of this entire rectangle?
3) What numbers are represented by a, b and c (note:...
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