Question

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 5 small aircraft arrive during a 1-hour period?

What is the probability that at least 5 small aircraft arrive during a 1-hour period?

What is the probability that at least 14 small aircraft arrive during a 1-hour period?

(b) What is the probability that at least 23 small aircraft arrive during a 2.5-hour period?

What is the probability that at most 19 small aircraft arrive during a 2.5-hour period?

Answer #1

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...

Suppose small aircraft arrive at a certain airport according to
a Poisson process at a rate α=8 per hour.
(a) What is the probability that exactly 6 small aircraft arrive
during a 1-hour period? (2 pts)
(b) What are the expected value and standard deviation of the
number of small aircraft that arrive during a 90 minute period? (3
pts)
(c) What is the probability that at least 5 aircraft arrive
during a 2.5 hour period? (5 pts)

Suppose small aircraft arrive at a certain airport according to
a Poisson process with a mean rate of 8
per hour.
a. Let be the waiting time until the 4th aircraft arrives.
Identify the distribution of T, including any parameters, and
find
P(T ≤ 1)
b. Let Y be the number of aircraft that arrive during a one-half
hour period. Identify the distribution of Y, including any
parameters, and find P(Y ≥ 3)

At an airport domestic flight arrive according to a Poisson
distribution with rate 5 per hour, and international flights arrive
according to a Poisson distribution with rate 1 per hour. What is
the probability that the time between third and fourth flight
arrivals is more than 15 minutes?

Vehicles arrive at a small bridge according to a Poisson process
with arrival rate l = 900 veh/hr. a. What are the mean and the
variance of the number of arrivals during a 30 minutes interval? b.
What is the probability of 0 cars arriving during a 4 second
interval? c. A pedestrian arrives at a crossing point just after a
car passed by. If the pedestrian needs 4 sec to cross the street,
what is the probability that a...

On Fridays at KK airport in Lusaka, airplanes arrive at an
average of 3 for the one hour period 13 00 hours to 14 00 hours. If
these arrivals are distributed according to the Poisson probability
distribution, what are the probability that either one or two
airplanes will arrive between 13.00 hours and 14 00 hours next
Friday?

Starting at time 0, a red bulb flashes according to a Poisson
process with rate ?=1 . Similarly, starting at time 0, a blue bulb
flashes according to a Poisson process with rate ?=2 , but only
until a nonnegative random time ? , at which point the blue bulb
“dies." We assume that the two Poisson processes and the random
variable ? are (mutually) independent. Suppose that ? is equal to
either 1 or 2, with equal probability. Write...

Starting at time 0, a red bulb flashes according to a Poisson
process with rate ?=1. Similarly, starting at time 0, a blue bulb
flashes according to a Poisson process with rate ?=2, but only
until a nonnegative random time ?, at which point the blue bulb
“dies." We assume that the two Poisson processes and the random
variable ? are (mutually) independent.
Suppose that ? is equal to either 1 or 2, with equal
probability. Write down an expression...

B. Customers arrive at a restaurant according to a Poisson
process. On the average, a customer arrives every half hour.
(a) What is the probability that, 1 hour after opening, there at
least one customer has arrived?
(b) What is the probability that at least 2 customers have
arrived?

Customers arrive at a bank according to a Poisson process with
rate 10 per hour.
Given that two customers arrived in the ﬁrst 5 minutes, what is
the probability that
(a) both arrived in the ﬁrst 2 minutes.
(b) at least one arrived in the ﬁrst 2 minutes.

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