Question
In: Statistics and Probability
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 6 small aircraft arrive during a 1-hour period?
What is the probability that at least 11 small aircraft arrive during a 1-hour period?
(b)
What is the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period?
expected value standard deviation
(c)
What is the probability that at least 23 small aircraft arrive during a 2.5-hour period?
What is the probability that at most 15 small aircraft arrive during a 2.5-hour period?
Solutions
orchestra answered 1 year agoRelated Solutions
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.
What is the probability that at least 7 small aircraft arrive
during a 1-hour period?
What is the probability that at least 11 small aircraft arrive
during a 1-hour period?
What is the probability that at least 23...
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 8 small aircraft arrive
during a 1-hour period?
What is the probability that at least 8 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
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 λ = 8t.
(a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? At least 6? At least 10?
(b) What are the expected value and standard deviation of the number of small aircraft that arrive during...
Small aircraft arrive at a private airport according to a given Poisson process at a rate...
Small aircraft arrive at a private airport according to a given
Poisson process at a rate of 6 per hour.
What is the probability that exactly 5 small aircraft arrive in
the first hour (after opening) and exactly 7 arrive in the hour
after that?
What is the probability that fewer than 5 small aircraft arrive
in the first hour and at least 10 arrive in the hour after
that?
What is the probability that exactly 5 small aircraft arrive...
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.
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 7 small aircraft arrive during a 1-hour period? What is the probability that at least 7 small aircraft arrive during a 1-hour period? What is the probability that at...
1.Suppose small aircraft arrive at a certain airport at a rate of 8 per hour. What...
1.Suppose small aircraft arrive at a
certain airport at a rate of 8 per hour. What is the probability
that at least 13 small aircrafts arrive during a given hour?
2.A particular telephone number is
used to receive both voice calls and fax messages. Suppose that 30%
of the incoming calls involve fax messages. Consider a sample of 20
incoming calls, what is the probability that at most 6 of the calls
involve a fax message.
Customers arrive in a certain shop according to an approximate Poisson process on the average of...
Customers arrive in a certain shop according to an approximate
Poisson process on the average of two every 6 minutes.
(a) Using the Poisson distribution calculate the probability of
two or more customers arrive in a 2-minute period.
(b) Consider X denote number of customers and X follows binomial
distribution with parameters n= 100. Using the binomial
distribution calculate the probability oftwo or more customers
arrive in a 2-minute period.
(c) Let Y denote the waiting time in minutes until...
People arrive at a party according to a Poisson process of rate 30 per hour and...
People arrive at a party according to a Poisson process of rate
30 per hour and remain for an independent exponential time of mean
2 hours. Let X(t) be the number of people at the party at time t
(in hours) after it started. Compute E[X(t)] and determine how long
it takes to have on average more than 40 people at the party.
Emails arrive in an inbox according to a Poisson process with rate λ (so the number...
Emails arrive in an inbox according to a Poisson process with
rate λ (so the number of emails in a time interval of length t is
distributed as Pois(λt), and the numbers of emails arriving in
disjoint time intervals are independent). Let X, Y, Z be the
numbers of emails that arrive from 9 am to noon, noon to 6 pm, and
6 pm to midnight (respectively) on a certain day. (a) Find the
joint PMF of X, Y, Z....
Suppose that people arrive at a bus stop in accordance with a Poisson process with rate...
Suppose that people arrive at a bus stop in accordance with a
Poisson process with rate λ. The bus departs at time
t.
1. Suppose everyone arrives will wait until the bus comes, i.e.,
everyone arrives during [0, t] will get on the bus. What is the
probability that the bus departs with n people aboard?
2. Let X be the total amount of waiting time of all those who
get on the bus at time t. Find E[X]. (Hint:...
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