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A device has the failure rate function:
r(t) = { 1 + 9(1 − t), 0 ≤ t < 1
1, 1 ≤ t < 10
1 + 10(t − 10), t ≥ 10
}
Find the reliability function and the pdf of the lifetime of device
The lifetime T of a device is a Rayleigh random variable. (a) Find the reliability of the device. (b) Find the failure rate function. Does r(t) increase with time? (c) Find the reliability of two devices that are in series. (d) Find the reliability of two devices that are in parallel.
A component has a Weibull failure time distribution with parameters α = 0.25 and β = 3.0 (a) Find the probability that the component is still operating at time 5. (b) Find the probability that the component fails before time 3. (c) find the failure rate function. (d) How much more likely to suddenly fail is a component operating at time 5 compared with a component operating at time 3?
A component has an exponential failure time distribution with a mean time to failure of 35 days. (a) Find the probability that the component is still operating after 35 days. (b) Find the probability that the component fails within 40 days. (c) If six of these components are placed in series, find the probability that the system is still operating after 5 days?
Use the following information to calculate the standard deviation of Macadam Corp.'s returns.
StateProbability
Return
Boom20%
40%
Normal60%
15%
Recession20%
(20%)
a.
19.8%
b.
19.2%
c.
8.6%
d.
11.4%
One of the steps in finding probability is to determine the possible outcomes for a given event. The set of all possible outcomes is called the sample space. Take a look at this example:
Ten friends meet after school each Wednesday: Albert, Betty, Carlo, Dean, Elizabeth, Frank, Gina, Holly, Inez, and Julie. Each week, one person is chosen at random to bring food. What are all of the possible outcomes for the person who is bringing food this Wednesday?
In this case, the sample space is the set of all of the members of the group. It is written as:
S = {Albert, Betty, Carlo, Dean, Elizabeth, Frank, Gina, Holly, Inez, Julie}.
In 20 words or fewer, identify another way this sample space could be written so that it doesn’t take up so much room.
- A Box contains 3 blue balls and 5 yellow balls. A sample of 3 balls is selected from the Box without replacement. Let M be the number of blue balls contained in the sample, then find the probability distribution for M.
Two random samples are drawn from normal population are given below
Can we conclude that the two samples are drawn from the same
population? Test at 5% level of significance.
Sample I 17 27 18 25 27 29 13 17
Sample II 16 16 20 27 26 25 21
The following table gives the yields on 15 sample plots under three
varieties of seed:
A 20 21 23 16 20
B 18 20 17 15 25
C 25 28 22 18 32
Find out whether the average yield of land under different varieties of
seed show significant differences.
Shown here are four frequency distributions. Each is incorrectly constructed. State the
reason why.
#333702 on Dec 2022