Show that if X has density function f. then E [ g ( X ) ] = ∫ − ∞ ∞ g ( x ) f ( x ) d x Hint: Using Theoretical Exercise 5.2, start with E [ g ( X ) ] = ∫ 0 ∞ P { g ( x ) > y } d y − ∫ 0 ∞ P { g ( x ) < − y } d y and then proceed as in the proof given in the text when g ( x ) > 0 .
Show that if X has density function f. then E [ g ( X ) ] = ∫ − ∞ ∞ g ( x ) f ( x ) d x Hint: Using Theoretical Exercise 5.2, start with E [ g ( X ) ] = ∫ 0 ∞ P { g ( x ) > y } d y − ∫ 0 ∞ P { g ( x ) < − y } d y and then proceed as in the proof given in the text when g ( x ) > 0 .
Solution Summary: The author explains that E[g(X)] can be written as follows.
Show that if X has density function f. then
E
[
g
(
X
)
]
=
∫
−
∞
∞
g
(
x
)
f
(
x
)
d
x
Hint: Using Theoretical Exercise 5.2, start with
E
[
g
(
X
)
]
=
∫
0
∞
P
{
g
(
x
)
>
y
}
d
y
−
∫
0
∞
P
{
g
(
x
)
<
−
y
}
d
y
and then proceed as in the proof given in the text when
g
(
x
)
>
0
.
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.
3. A different 7-Eleven has a bank of slurpee fountain heads. Their available flavors are as follows: Mountain
Dew, Mountain Dew Code Red, Grape, Pepsi and Mountain Dew Livewire. You fill five different cups full
with each type of flavor. How many different ways can you arrange the cups in a line if exactly two Mountain
Dew flavors are next to each other?
3.2.1
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.
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY