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4. Suppose that spectators arrive to a baseball game according to a Poisson process with a rate o...
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...
Q4. Suppose that small aircrafts arrive at a certain airport, according to a poisson process, at...
Q4. Suppose that small aircrafts arrive at a certain airport, according to a poisson process, at the rate of 1 per day. (a) What is the probability that 4 small aircrafts arrive during a two-days period? b) What is the probability that no small aircraft arrives during a 1-day period? (c) What is the probability that in exactly four days of a week no small aircraft arrives? (d) In how many days of a month we should expect that small...
Suppose that mechanics arrive randomly at a tool crib according to a Poisson process with rate...
Suppose that mechanics arrive randomly at a tool crib according to a Poisson process with rate 1 = 10 per hour. It is known that the single tool clerk serves a mechanic in 4 minutes on the average, with a standard deviation of approximately 2 minutes. Suppose that mechanics make $15.00 per hour. Estimate the steady-state average cost per hour of mechanics waiting for tools.
Customers arrive at a bank according to a Poisson process having a rate of 2.42 customers...
Customers arrive at a bank according to a Poisson process having a rate of 2.42 customers per hour. Suppose we begin observing the bank at some point in time. What is the probability that 3 customers arrive in the first 1.8 hours? Customers arrive at a bank according to a Poisson process having a rate of 2.3 customers per hour. Suppose we begin observing the bank at some point in time. What is the expected value of the number of...
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α...
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t. (Round your answers to three decimal places.) (a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? What is the probability that at least 14 small aircraft arrive during a 1-hour period? What...
Parishioners arrive at church on Sunday morning according to a Poisson process at rate 2/minute starting...
Parishioners arrive at church on Sunday morning according to a Poisson process at rate 2/minute starting at 9:00am until 11:00am. Each parishioner wears a hat with probability 1/3, independent of other parishioners, and brings an umbrella with probability 1/4, independent of whether she wears a hat and independent of other parishioners. The cloakroom has umbrella stands and baskets for hats. The sermon begins at 11:00am. Once the sermon begins, each parishioner falls asleep after an exponentially distributed amount of time...
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour,
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter u= 8t. (Round youranswers to three decimal places.) (a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? What is the probability that at least 6 small aircraft arrive during a 1-hour period? What is...
Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate α...
Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate α = 8 per hour. Suppose that with probability 0.5 an arriving vehicle will have no equipment violations. (a) What is the probability that exactly eight arrive during the hour and all eight have no violations? (Round your answer to four decimal places.)(b) For any fixed y ≥ 8, what is the probability that y arrive during the hour, of which eight have no violations?(c)...
Messages arrive to a computer server according to a Poisson distribution with a mean rate of...
Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that 9 messages will arrive in 2 hours? (b) What is the probability that 10 messages arrive in 75 minutes?
A car wash has one automatic car wash machine. Cars arrive according to a Poisson process...
A car wash has one automatic car wash machine. Cars arrive according to a Poisson process at an average rate of 5 every 30 minutes. The car wash machine can serve customers according to a Poisson distribution with a mean of 0.25 cars per minute. What is the probability that there is no car waiting to be served?
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...
Q4. Suppose that small aircrafts arrive at a certain airport, according to a poisson process, at the rate of 1 per day. (a) What is the probability that 4 small aircrafts arrive during a two-days period? b) What is the probability that no small aircraft arrives during a 1-day period? (c) What is the probability that in exactly four days of a week no small aircraft arrives? (d) In how many days of a month we should expect that small...
Suppose that mechanics arrive randomly at a tool crib according to a Poisson process with rate 1 = 10 per hour. It is known that the single tool clerk serves a mechanic in 4 minutes on the average, with a standard deviation of approximately 2 minutes. Suppose that mechanics make $15.00 per hour. Estimate the steady-state average cost per hour of mechanics waiting for tools.
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t. (Round your answers to three decimal places.) (a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? What is the probability that at least 14 small aircraft arrive during a 1-hour period? What...
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter u= 8t. (Round youranswers to three decimal places.) (a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? What is the probability that at least 6 small aircraft arrive during a 1-hour period? What is...
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