Question

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?

Answer #1

the bus arrives at the stop at some time uniformly distribution between 9:55 and 10:10

An interval of 15 minutes

Someone arrive at 10 o' clock

probability that you will be board the bus within 2 minutes of your arrivals =

probability that you will be board the bus within 2 minutes of your arrivals =

**probability that you will be board the bus within 2
minutes of your arrivals = 0.1333**

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...

A passenger arrives at a bus stop at 10am and waits for a bus
that arrives at a time uniformly distributed between 10am and
10:30am. (a) What is the probability that the passenger waits more
than 10 minutes? (b) What is the expected wait time? (c) What is
the variance in wait time?

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.

4.) SWA university provides bus service to students while they
are on campus. A bus arrives at the North main Street and College
Drive stop every 30 minutes between 6am and 11am during weekdays.
Students arrive at the bus stop at random times. A time that a
student waits is uniformly distributed from 0 to 30 minutes.
What is the probability a student will wait between 10 and 20
minutes?
Please show work using Excel.

I arrive at a bus stop at a time that is normally distributed
with mean 07:59 and SD 1.5 minutes. My bus arrives at the stop at
an independent normally distributed time with mean 08:03 a.m. and
SD 2 minutes. The bus remains at the stop for 1 minute and then
leaves.
What is the chance that I miss the bus?

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.

The actual arrival time of the scheduled 10:20 a.m. bus
at the alpine and Broadway stop is a uniformly distributed random
variable ranging from 10:18 to 10:23. (a) What is the average
arrival time of the 10:20 a.m. bus? (b) The standard deviation? (c)
What is the probability that the bus is early? (d) What is the
probability that the bus arrives between 10:19 and 10:21
a.m.?

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...

A passenger arrives at a bus stop(poisson distribution, lamda
= 1min) and waits for a bus. Every bus runs at 10 mins Intervals
and all people who have waited for the bus board the bus. If a
passenger waits 1 min, it costs 1,000 dollars. So, if a passenger
waits 2mins, it costs 2,000 dollars.
(1)What's the expected cost per min?
It's renewal reward process.

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

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