Question

The number of buses arriving at the bus stop for T minutes is defined as a random variable B. The average (expected value) of random variable B is T / 5.

(1)A value indicating the average number of occurrences per unit time in the Poisson distribution. What is the average rate of arrival per second?

(2)find PMF of B

(3)Find the probability of 3 buses arriving in 2 minutes

(4)Find the probability that the bus will not arrive in 10 minutes

(5)Find the probability of at least one bus arriving in T minutes

Answer #1

1. average number of occurrences per unit time = B/T

= (T/5) / T

= 1/5 = 0.2

2.

P(B buses in T time) = e^(-0.2*T) * (0.2*T)^B / (B!)

3.

P(B buses in T time) = e^(-0.2*T) * (0.2*T)^B / (B!)

P(3 buses in 2 min) = e^(-0.2*2) * (0.2*2)^3 / (3!)

= **0.0072**

4.

P(B buses in T time) = e^(-0.2*T) * (0.2*T)^B / (B!)

P(0 buses in 10 min) = e^(-0.2*10) * (0.2*10)^0 / (0!)

= **0.1353**

5.

probability of at least one bus arriving in T minutes

P(B >=1 buses in T time) = 1 - P(0 buses in T min)

= 1 - e^(-0.2*T) * (0.2*T)^0 / (0!)

**probability of at least one bus arriving in T
minutes**

**= 1 - e^(-0.2*T) * (0.2*T)^0 / (0!)**

**(please UPVOTE)**

Suppose that buses are scheduled to arrive at a bus stop at noon
but are always X minutes late, where X is an exponential random
variable. Suppose that you arrive at the bus stop precisely at
noon.
(a) Compute the probability that you have to wait for more than
five minutes for the bus to arrive.
(b) Suppose that you have already waiting for 10 minutes.
Compute the probability that you have to wait an additional five
minutes or more.

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...

Central Limit Theorem
The arrival of Blue Loop buses to the Penn State library stop
can be modeled as a Poisson process. Buses are scheduled to arrive
every 15 minutes. You and your friends are making observations at
the library stop during different times of the day. You and your
friends observe 53 Blue Loops arrivals, and you record the
inter-arrival times (i.e. the time between the arrival of the
nth and the (n+1)st bus in minutes.
1. What is...

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

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...

The number of cars arriving at a
petrol station in a period of t minutes may be assumed to
have a Poisson distribution with mean
720t.
Use this information to
answer questions 31-32.
Find the probability that exactly 12 cars will arrive in one
and half hours.
Find the probability that more than 24 cars will arrive in an
hour.

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.

Problem
3. Alice is waiting for a bus at a bus stop. She needs to
take a bus number 10 or 12, and she takes the first suitable bus
that arrives. The arrival time of bus 10 is exponential with
λ10 = 6/19, and the arrival time of
bust 12 is exponential with λ12 =
3/19. Moreover, arrival times of 10 and 12 are
independent.
What is the probability that Alice will take bus number 10
instead of bus number...

1. Suppose the number of messages arriving on a communication
line seems to be describable by a Poisson Random Variable with an
average arrival rate of 10 messages/second. Determine the
following:
a. The probability that no messages arrive in a one second
period.
b. The probability that 1 message arrives in a one second
period.
c. The probability that 2 messages arrives in a one second
period.
d. The probability that 3 messages arrives in a one second
period.
e.The...

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?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 24 minutes ago

asked 28 minutes ago

asked 42 minutes ago

asked 45 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago