Let F be a continuous distribution function . If U is uniformly distributed on ( 0 , 1 ) , find the distribution function of Y = F − 1 ( U ) , where F − 1 is the inverse function of F. (That is, y = F − 1 ( x ) if F ( y ) = x )
Let F be a continuous distribution function . If U is uniformly distributed on ( 0 , 1 ) , find the distribution function of Y = F − 1 ( U ) , where F − 1 is the inverse function of F. (That is, y = F − 1 ( x ) if F ( y ) = x )
Let F be a continuous distribution function. If U is uniformly distributed on
(
0
,
1
)
, find the distribution function of
Y
=
F
−
1
(
U
)
, where
F
−
1
is the inverse function of F. (That is,
y
=
F
−
1
(
x
)
if
F
(
y
)
=
x
)
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Answer questions 8.3.3 and 8.3.4 respectively
8.3.4 .WP An article in Medicine and Science in Sports and
Exercise [“Electrostimulation Training Effects on the Physical Performance of Ice Hockey Players” (2005, Vol. 37, pp.
455–460)] considered the use of electromyostimulation (EMS) as
a method to train healthy skeletal muscle. EMS sessions consisted of 30 contractions (4-second duration, 85 Hz) and were carried
out three times per week for 3 weeks on 17 ice hockey players.
The 10-meter skating performance test showed a standard deviation of 0.09 seconds. Construct a 95% confidence interval of the
standard deviation of the skating performance test.
8.6.7 Consider the tire-testing data in Exercise 8.2.3. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss the difference in interpretation of these two intervals.
8.6.2 Consider the natural frequency of beams described in
Exercise 8.2.8. Compute a 90% prediction interval on the
diameter of the natural frequency of the next beam of this type
that will be tested. Compare the length of the prediction interval
with the length of the 90% CI on the population mean.
8.6.3 Consider the television tube brightness test described in
Exercise 8.2.7. Compute a 99% prediction interval on the brightness of the next tube tested. Compare the length of the prediction
interval with the length of the 99% CI on the population mean.
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
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