The time until failure for an electronic switch has an
exponential distribution with an average time to failure of 4
years, so that λ =
1
4
= 0.25. (Round your answers to four decimal places.)
(a)
What is the probability that this type of switch fails before
year 3?
(b)
What is the probability that this type of switch will fail after
5 years?
(c)
If two such switches are used in an appliance, what is the
probability that...
The lifetime of a certain type of batteries follows an
exponential distribution with the mean of 12 hours.
a) What is the probability that a battery will last more than 14
hours? (Answer: 0.3114)
b) Once a battery is depleted, it is replaced with a new battery
of the same type. Assumingindependence between lifetimes of
batteries, what is the probability that exactly 2 batteries will be
depleted within 20 hours? (Answer: 0.2623)
c) What is the probability that it takes...
5) The lifetime of a certain type of batteries follows an
exponential distribution with the mean of 12 hours.
a) What is the probability that a battery will last more than
14 hours?
b) Once a battery is depleted, it is replaced with a new
battery of the same type. Assuming independence between lifetimes
of batteries, what is the probability that exactly 2 batteries will
be depleted within 20 hours?
c) What is the probability that it takes less than...
(Exponential Distribution) The life, in years, of a certain type
of electrical switch has an exponential distribution with an
average life of ?? = 2 years. i) What is the probability that a
given switch is still functioning after 5 years? ii) If 100 of
these switches are installed in different systems, what is the
probability that at most 30 fail during the first year?(also
Binomial Distribution
Suppose the time to failure follows an exponential distribution
with parameter λ. Based on type II censoring determine the
likelihood and the maximum likelihood estimator for λ. Assume that
n = 3 and the experiment ends after 2 failures.
The life, in years, of a certain type of electrical switch has
an exponential distribution with an average life 2 years. If 100 of
these switches are installed in different systems, what is the
probability that at most 2 fail during the first year?
The waiting time until a courier is received is followed by an
exponential distribution with an expected waiting time of 5 days.
Find the probability that the mean waiting time for the delivery
time of 50 couriers exceeds 6 days
b. There are 200 questions to an FRCS exam. Suppose the
probability of having through question correct is 0.6, no matter
other questions. If the cutoff for a grade B is 80%, what is the
likelihood of a "B"
The amount of time until a laptop
breaks down follows a an exponential distribution which has the
following distribution
F(x)
= 1 – exp(-
?x), if x ≥ 0
0
, otherwise
The parameter ?=1, the population mean and standard deviations
are equal to 1/?. A sample size of n = 32 was generated from the
above population distribution for k = 10,000 times. One of these
samples is presented in the table below.
2.5689
0.7311
1.6212
0.0021
1.3902
0.0057...
The amount of time until a laptop
breaks down follows a an exponential distribution which has the
following distribution
F(x)
= 1 – exp(-
?x), if x ≥ 0
0
, otherwise
The parameter ?=1, the population mean and standard deviations
are equal to 1/?. A sample size of n = 32 was generated from the
above population distribution for k = 10,000 times. One of these
samples is presented in the table below.
2.5689
0.7311
1.6212
0.0021
1.3902
0.0057...
The time that takes to complete a certain type of construction
projects has a mean of 35.5 months and a standard deviation of 1.5
months.
a. According to the Tchebysheff’s theorem, at least what
percentage of these projects must have taken between 26.5 months
and 44.5 months to complete?
b. If in addition we are told that the relative frequency curve
for the completion times is a bell-shaped curve, then approximately
what percentage of these projects would take more than...