given an exponentially distributed population with a mean of
385.06 what is the probability of the...
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
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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.)
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.
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.
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?
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...
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
Given a normally distributed population with a mean of 100 and
a variance of 400, find the following probabilities for a sample
mean for 16 individuals. (X for a, b, c is X bar)
a) P(X≥100)
b) P(X≤110)
c) P(96≤X≤108)
Lifetime of certain device is exponentially distributed random
variable T( λ ). Probability that T > 10 is e-3: P{ T> 10} =
e-3 The system consists of 6 devices of such type and is in working
condition if all of its components are in working condition. a)
Find expectation μx and standard deviation σx for given
distribution. b) Find the probability that the system will not fail
I) in the next 3 years? II) in the next 8 years?...
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?