Question

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.

Answer #1

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...

You arrive at a bus stop at 10 o’clock knowing that the bus
arrives at the stop at some time uniformly distribution between
9:55 and 10:10. What is the probability that you will be board the
bus within 2 minutes of your arrivals?

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...

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...

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?

You arrive at the train station between 7:20 am and
7:30 am, uniformly. The train arrives every 8 minutes starting from
7:00 am. Let Y be the waiting time. Please compute the pdf of
Y.

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...

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