8. Starting at time 0, customers arrive at a service counter in accordance with a Poisson process of rate A (customers per hour). Assume that each customer requires exactly 1 hour of service, and that the number of servers is unlimited. Fix t > 1. (a) Find the probability that there are no customers being served at time t. (b) Find the expected number of customers being served at time t.
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Hellow can I get help wth this question? I'm studying for my final and wanna know how to solve it.
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- Suppose taxicab arrivals from 3 to 5 p.m. are a Poisson process. If the cabs arrive at an average rate of 18 per hour, what is the probability that a person will have to wait up to 5 minutes for a cab?Consider the M/M/1 queueing system with arrival rate λ > 0 and service rate μ > 0. (a) Compute the expected number of arrivals during a service time (also called service period). (b) Compute the probability that no customers arrive during a service period.A company has 9000 arrivals of Internet traffic over a period of 18,050 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= (μ^x • e^−μ) / x! to find the probability of exactly 2 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
- If we are watching buses pass by in a Poisson process with buses arriving at the average rate of 10 per hour, then what is the probability (to three decimal place accuracy) that between 3:06pm and 3:24pm we see less than 5 buses?2- In a telephone exchange, the number of incoming calls is estimated to follow a Poissondistribution with a mean of 12 calls per hour.● Find the probability that the time between two consecutive calls is less than 5.minutes● For every 1,000 calls answered by the central, a salary incentive is granted to all theworkers of that company. How soon are workers expected to obtain saidcompensation?A company has 9000 arrivals of Internet traffic over a period of 20,740 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)=μx•e−μx! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
- A company has 8000 arrivals of Internet traffic over a period of 17,460 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= μx•e−μ x! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?Starting at time 0, amusement park attendees enter the park and arrive at a according to a Poisson process with rate equal to 48 per hour. (a) What is the expected number of attendees that arrive in the first two minutes? (b) What is the probability that 5 or more refugees arrive in the first two minutes? (c) If 10 attendees arrive in the first minute, what is the expected number of attendees that arrive in the first two minutes?Suppose that the number of customers arriving to a store follows the Poisson process with rate 1/λ per minute. Choose an option that is not correct. The expected number of customers arriving to the store between 9am and 11am is twice bigger than the expected number of customers arriving to the store between 10am and 11am. The number of customers arriving to the store between 9am and 10am is independent of the number of customers arriving to the store between 10am and 11am. The expected number of customers arriving to the store between 9am and 10am is 60λ. The number of customers arriving to the store between 9am and 10am follows the same distribution as the number of customers arriving to the store between 10am and 11am
- Suppose customers arrive to a 7–11 convenience store according to a Poisson process with rate 10 per hour. What are the probabilities of (a) no customers in an hour; (b) exactly 5 customers in an hour; (c) exactly 10 customers in two hours; and (d) at least two customers in half an hour?2a) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Find lambda λ? 2b) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Using Normal approximation, we will need to find the probability that the Sarah’s garden will contain less than 45 flowers. First graph and answer what is the continuity correction? 2c) Using the previous results for lambda and continuity correction, find z, then graph and use your table to find φ table value of z Write down your final answer for the probability that Sarah’s garden will contain less than 45 flowers as a decimal number with 4 decimal places.