Question

The time between successive arrivals of calls to emergency
service is random variable which

follows exponential distribution. It was observed that on average
calls arrive to emergency

service every four minutes (1 / λ = 4min) and average number of
calls in one minute is λ = 0.25 calls/ 1 min

The probability that the time between successive calls is less than 2 minutes is ______

A call just arrived to emergency service. The probability that next call will arrive to emergency service no sooner than in 3 minutes is __________.

The probability that the time between successive calls is between 6 and 8 minutes is ______

Answer #1

The time between arrivals at a toll booth follows an
exponential distribution with a mean time between arrivals of 2
minutes.
What is the probability that the time between two successive
arrivals will be less than 3 minutes?
What is the probability that the time will be between 3 and 1
minutes?

The
time between telephone calls to a cable televisiom service call
center follows an exponential distribution with a mean of 1.5
minutes.
a. What is the probability that the time between the next two
calls will be 48 seconds or less?
b. What is the probability that the between the next two calls
will be greater than 118.5 seconds?

Let X = the time between two successive arrivals at the drive-up
window of a local bank. If X has an exponential distribution with λ
= 1/3 , compute the following:
a. If no one comes to the drive-up window in the next 15 minutes
(starting now), what is the chance that no one will show up during
the next 20 minutes (starting now)?
b. Find the probability that two people arrive in the next
minute.
c. How many people...

Let X be the time between successive arrivals to an intersection
in a rural area. Suppose cars arrive to the intersection via a
Poisson process at a rate of 1 every 5 minutes.
(a) What distribution does X have?
(b) What is the mean time between arrivals?
(c) What is the probability that more than 7 minutes will pass
between arrivals to the intersection?

Suppose that the time between successive occurrences of an event
follows an exponential distribution with mean number of occurrences
per minute given by λ = 5. Assume that an event occurs. (A) Derive
the probability that more than 2 minutes elapses before the
occurrence of the next event. Derive the probability that more than
4 minutes elapses before the occurrence of the next event. (B) Use
to previous results to show: Given that 2 minutes have already
elapsed, what is...

Let X = the time between two successive arrivals at the drive-up
window of a local bank.
Suppose that X has an exponential distribution with an average
time between arrivals of 4
minutes.
a. A car has just left the window. What is probability that it
will take more than 4 minutes before the next drive-up to the
window?
b. A car has just left the window. What is the probability that
it will take more than 5 minutes before...

Let X = the time between two successive arrivals at the drive-up
window of a local bank. If X has an exponential distribution with
λ=1, compute the following:
a) The expected time between two successive arrivals
b) The standard deviation of the time between success
arrivals
c) Calculate the probability P (X≤3)
d) Calculate the probability P(2≤X≤5)

Customers arrive at
random times, with an exponential distribution for the time between
arrivals. Currently the mean time between customers is 6.34
minutes. a. Since the last customer arrived, 3 minutes have gone
by. Find the mean time until the next customer arrives.
b. Since the last
customer arrived, 10 minutes have gone by. Find the mean time until
the next customer arrives.

The time between customer arrivals at a furniture store has an
approximate exponential distribution with mean θ = 9.9 minutes.
[Round to 4 decimal places where necessary.]
If a customer just arrived, find the probability that the next
customer will arrive in the next 9.4 minutes.
Tries 0/5
If a customer just arrived, find the probability that the next
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Tries 0/5
If after the previous customer, no customer arrived in next...

The exponential distribution is frequently applied
to the waiting times between successes in a Poisson
process. If the number of calls received per hour
by a telephone answering service is a Poisson random
variable with parameter λ = 6, we know that the time,
in hours, between successive calls has an exponential
distribution with parameter β =1/6. What is the probability
of waiting more than 15 minutes between any
two successive calls?

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