Question

Buses arrive at a certain stop according to a Poisson process
with rate λ. If you take the bus from that stop then it takes a
time R, measured from the time at which you enter the bus, to
arrive home. If you walk from the bus stop then it takes a time W
to arrive home. Suppose your policy when arriving at the bus stop
is to wait up to time s, and if a bus has not yet arrived by that
time then you walk home.

Find the value of s which maximizes the expected time from
when you arrive at the bus stop until you reach home.

Answer #1

suppose starting at 8am buses arrive at a bus stop according to
the poisson process at a rate of one every 15 mins. if the 1st bus
has not arrived by 815am what is the probability it will arrive
before 830 am.
B. find the probability that the 3rd bus arrives after 9am. note
we do not assume the condition that the 1st bus has not arrived by
815 am as stated above

Suppose that at a particular bus stop, Brown buses arrive
according to a Poisson process with a constant rate of 3
per hour. The travel time on the Brown bus to your class
is 7 minutes. (The Brown bus drops you off at your
class.). When you approach the bus stop, you see that
you have just missed a Blue bus. Class starts in 20 minutes and it
is exam day so you want to get to class as soon as...

Suppose buses arrive at 10:10 and 10:30 and you arrive at the
bus stop randomly between 10:00 and 10:30
Let A be the amount of time in minutes between when you arrive.
please Find CDF(Cumulative Distribution Functio)
and PDF (probability density function) for A.

Alice takes the bus to school. The bus is scheduled to arrive at
a bus stop at 9:30am. In reality, the time the bus arrives is
uniformly distributed between 9:28am and 9:40am. Let ? be the
number of minutes it takes, starting from 9:28 am, for the bus to
arrive to the bus stop. Then ? is uniformly distributed between 0
and 12 minutes.
(a) If Alice arrives at the bus stop at exactly 9:33 am, what is
the probability...

Suppose that buses are coming into a station at an average rate
4 per hour according to a Poisson process. We start to account the
buses from 1:00 (pm).
(a) What is the probability that no buses arrive between
1:00pm-2:00pm?
(b) What is the probability that three buses arrive between
1:00pm-3:00pm?
(c) What is the probability that the third bus takes more that 3
hours to arrive?
(d) What is the expected time the third bus arrive to the
station?

Suppose passengers arrive at a MARTA station between 10am-5pm
following a Poisson process with rate λ= 60 per hour. For notation,
let N(t) be the number of passengers arrived in the first t hours,
S0= 0 , Sn be the arrival time of the nth passenger, Xn be the
interrarrival time between the (n−1)st and nth passenger.
a. What is the probability that ten passengers arrive between
2pm and 4pm given that no customer
arrive in the first half hour?...

People arrive according to a Poisson process with rate λ, with
each person independently being equally likely to be either a man
or a woman. If a woman (man) arrives when there is at least one man
(woman) waiting, then the woman (man) departs with one of the
waiting men (women). If there is no member of the opposite sex
waiting upon a person’s arrival, then that person waits. Let X(t)
denote the number waiting at time t. Argue that...

Customers arrive at a two-server system according to a Poisson
process having rate λ = 5. An arrival finding server 1 free will
begin service with that server. An arrival finding server 1 busy
and server 2 free will enter service with server 2. An arrival
finding both servers busy goes away. Once a customer is served by
either server, he departs the system. The service times at server i
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µ2...

Customers depart from a bookstore according to a Poisson process
with a rate λ per hour. Each customer buys a book with probability
p, independent of everything else.
a. Find the distribution of the time until the first sale of a
book
b. Find the probability that no books are sold during a
particular hour
c. Find the expected number of customers who buy a book during a
particular hour

Customers arrive at bank according to a Poisson process with
rate 20 customers per hour. The bank lobby has enough space for 10
customers. When the lobby is full, an arriving customers goes to
another branch and is lost. The bank manager assigns one teller to
customer service as long as the number of customers in the lobby is
3 or less. She assigns two tellers if the number is more than 3 but
less than 8. Otherwise she assigns...

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