Question

Car accidents at a certain intersection are randomly distributed in time according to a Poisson process, with 7 accidents per week on average. If there were 3 accidents in a 2-week period, what is the probability there were 2 accidents in the first 1 of these 2 weeks? (4 decimal accuracy please)

Answer #1

Car accidents at a certain intersection are randomly distributed
in time according to a Poisson process, with 5 accidents per week
on average. What is the probability that there are 1 accidents in
the first 1 week period and 1 more in the second 1 week period.? (4
decimal accuracy please)

The number of accidents that occur at a busy intersection is
Poisson distributed with a mean of 3.9 per week. Find the
probability of the following events.
A. No accidents occur in one week. Probability =
B. 3 or more accidents occur in a week. Probability =
C. One accident occurs today. Probability =

The number of traffic accidents at a certain intersection is
thought to be well modeled by a Poisson process with a mean of 3.5
accidents per year
If no accidents have occurred within the last six months, what
is the probability that an accident will occur within the next
year?

The probability that there is no accident at a certain busy
intersection is 91% on any given day, independently of the other
days.
(a)
[2 marks] Find the probability that there will be no accidents
at this intersection during the next 4 days.
(b)
[2 marks] Find the probability that in next 4 weeks there will
be exactly 4 days with accidents.
(c)
[2 marks] Today was accident free. Find the probability that
there is no accident during the next...

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 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...

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 X is equal to either 1 or 2, with equal
probability. Write down an expression...

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...

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 that minor defects are distributed over the length of a
cable according to a Poisson process with rate 9 per meter and,
independently, major defects are distributed over the same cable
according to a Poisson process with rate 1 per meter. a. If exactly
1 minor defect has been found in the first 1 meter of the cable,
what is the probability it is within the first 20 cm b. If exactly
2 defects have been found in the...

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