the time between phone calls received by a telephonist is
exponentially distributed with a mean of...
the time between phone calls received by a telephonist is
exponentially distributed with a mean of 10 minutes.what is the
probability that there are no more than four calls within one
hour?
The time T between requests to a web server is exponentially
distributed with mean 0.5 seconds.
(a) What is the value of the parameter in this exponential
distribution? Give the p.d.f. and c.d.f. of T? [2]
(b) Use the c.d.f. of T to find the median request time and
interpret it. [3]
(c) What is the probability that the request time is between
0.25 and 1.5 seconds? [1](
d) Find the 60th percentile of the request time and interpret
it....
The distance between flaws on a long cable is exponentially
distributed with a mean of 12 m.
a) Find the probability that the distance between two flaws is
greater than 15 m.
b) Find the probability that the distance between two flaws is
greater than 25 m given that it is greater than 10 m.
c) Find the probability that the distance between two flaws is
greater than 20 m given that it is greater than 10 m.
given an exponentially distributed population with a mean of
385.06 what is the probability of the average of 138 randomly
selected items being less than 53018.8
Suppose the life time of a certain brand of light bulbs is
exponentially distributed with an average of 1000 hours.
a. What’s the probability that a new light bulb won’t be able
to reach this amount of time?
b. What’s the probability that a new light bulb will have a
life between 1000 and 2000 hours?
c. Given that a light bulb has been working for 1000 hours,
what’s the probability that it can work for another 2000 hours or...
Suppose the amount of time to finish assembling a component is
exponentially distributed with an average of 2 minutes.
(a) What is the probability that it takes more than 5 minutes to
assemble a component? (b) If 100 components are randomly selected,
what is the probability that the average amount of time to assemble
these100 components is more than 2.3 minutes?
The amount of a loss is exponentially distributed with mean 90.
An insurance pays 90% of the amount of a loss in excess of an
ordinary deductible of 20. The maximum payment is 117 per loss.
Determine the expected payment, given that a payment has been
made.
A critical component on a submarine has an operating lifetime
that is exponentially distributed with mean 0.50 years. As soon as
a component fails, it is replaced by a new one having statistically
identical properties. What is the smallest number of spare
components that the submarine should stock if it is leaving for a
one-year tour and wishes the probability of having an inoperable
unit caused by failures exceeding the spare inventory to be less
than 0.02?
Please show that...
A random variable X is exponentially distributed with a
mean of 0.21.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X?
(Round your answer to 2 decimal places.)
b. Compute P(X > 0.36).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
Car battery
The mileage of a car battery is exponentially distributed with a
mean value of 10000 km.
(a) What is the probability of a 5000 km trip without
replacement of the battery?
(b) What is the maximum length of travel that can be terminated
with 90% probability without replacing the battery?
(c) Determine the median, the mean and the variance of the
mileage of the battery
Suppose hard drive A has a lifetime that is exponentially
distributed with mean of 6 years and hard drive B has a lifetime
that is exponentially distributed with a mean of 2 years. What is
the probability that drive B lasts at least 3 times longer than
drive A?