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QUESTION 7 Buses arrive and depart from a college every 20 minutes. The probability density function...
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...
A bus comes by every 15 minutes. The times from when a person arives at the...
A bus comes by every 15 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 15 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 5 minutes is d. Suppose that the person has...
A bus comes by every 14 minutes. The times from when a person arives at the...
A bus comes by every 14 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 14 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. c. The probability that the person will wait more than 4 minutes is _____ d. Suppose that the person has already been waiting for 0.5 minutes. Find the probability that the...
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....
A bus comes by every 13 minutes. The times from when a person arives at the...
A bus comes by every 13 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 13 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is ? c. The probability that the person will wait more than 7 minutes is ? d. Suppose that the...
A person arrives at a bus stop each morning. The waiting time, in minutes, for a...
A person arrives at a bus stop each morning. The waiting time, in minutes, for a bus to arrive is uniformly distributed on the interval (0,15). a. What is the probability that the waiting time is less than 5 minutes? b. Suppose the waiting times on different mornings are independent. What is the probability that the waiting time is less than 5 minutes on exactly 4 of 10 mornings?
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
2. The University of Southwest Arizona provides bus transportation services to students while they are on...
2. The University of Southwest Arizona provides bus transportation services to students while they are on campus. A bus arrives at the North Main Street and College Drive stop every 30 minutes, between 6 in the morning and 11 at night during the week. Students arrive at the stop at random times. The time a student waits has a uniform distribution of 0 to 30 minutes. A. Draw a graph of the distribution. B. Show that the area of this...
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...
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....
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
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