This is one question but I couldn't fit the whole question in one photo so I attached two photos, thank you :)
This is one question but I couldn't fit the whole question in one photo so I attached two photos, thank you :)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 11E: A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into...
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This is one question but I couldn't fit the whole question in one photo so I attached two photos, thank you :)
![Substitute a and b into the left side of the formula from the previous step and express the integral as a limit.
b
fro
- 7x dx = lim
7x dx
area =
7 e
7e
a
Next, determine F(x). First, find the antiderivative of f.
7x
dx =
Let C= 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [0,00) using the far right side of the formula for the area.
lim [O-0]
area =
As b approaches ∞, e
cb
approaches infinity where c is a constant. Use this fact to calculate the limits from the previous step.
area =
+1
Is Property 2 of the definition of a probability density function over the given interval now verified? Choose the correct answer below.
O A. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 1.
B. Property 2 of the definition of a probability density function over the given interval has not been verified because the expression in the previous step does not simplify to the expected area value.
OC. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 0.
O D. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to o.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee2e25dc-949a-49f9-893c-6a598612cdf0%2F4b298d96-0aea-4b97-b3da-d2ed5c1659a0%2Fg66xw5_processed.png&w=3840&q=75)
Transcribed Image Text:Substitute a and b into the left side of the formula from the previous step and express the integral as a limit.
b
fro
- 7x dx = lim
7x dx
area =
7 e
7e
a
Next, determine F(x). First, find the antiderivative of f.
7x
dx =
Let C= 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [0,00) using the far right side of the formula for the area.
lim [O-0]
area =
As b approaches ∞, e
cb
approaches infinity where c is a constant. Use this fact to calculate the limits from the previous step.
area =
+1
Is Property 2 of the definition of a probability density function over the given interval now verified? Choose the correct answer below.
O A. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 1.
B. Property 2 of the definition of a probability density function over the given interval has not been verified because the expression in the previous step does not simplify to the expected area value.
OC. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 0.
O D. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to o.
![Verify Property 2 of the definition of a probability density function over the given interval.
f(x) = 7 e -7x
[0,0)
What is Property 2 of the definition of a probability density function?
O A. The area under the graph of f over the interval [a,b] is a.
O B. The area under the graph of f over the interval [a,b] is 1.
OC. The area under the graph of f over the interval [a,b] is b.
Since the given interval, [0,0), has a right-endpoint of infinity, the area under the graph of f will be calculated using an improper integral. Choose the correct formula for an improper integral over the interval [a,co]
below.
O A. 00
b
f(x) dx = lim
f(x) dx = lim [F(x)] = lim (F(a)- F(b))
a
O A. 0
f(x) dx = lim [F(x)] = lim (F(a) - F(b))
b-00 a
f(x) dx = lim
a
О В.
b
00
f(x) dx = lim f(x) dx = lim [F(x)] = lim (F(b) -F(a))
%3D
b 0 a
b 00
a
O C. 0
f(x) dx = lim f(x) dx = lim [F(x)] = lim (F(b)- F(a))
b00 a
a
O D. 00
b.
S) ax = lim frox) dx= lim [F(x); = lim (F(a)- F(b)
f(x) dx = lim [F(×)] = lim (F(a)- F(b))
b 00 a
b00
a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee2e25dc-949a-49f9-893c-6a598612cdf0%2F4b298d96-0aea-4b97-b3da-d2ed5c1659a0%2Fa4cxb2_processed.png&w=3840&q=75)
Transcribed Image Text:Verify Property 2 of the definition of a probability density function over the given interval.
f(x) = 7 e -7x
[0,0)
What is Property 2 of the definition of a probability density function?
O A. The area under the graph of f over the interval [a,b] is a.
O B. The area under the graph of f over the interval [a,b] is 1.
OC. The area under the graph of f over the interval [a,b] is b.
Since the given interval, [0,0), has a right-endpoint of infinity, the area under the graph of f will be calculated using an improper integral. Choose the correct formula for an improper integral over the interval [a,co]
below.
O A. 00
b
f(x) dx = lim
f(x) dx = lim [F(x)] = lim (F(a)- F(b))
a
O A. 0
f(x) dx = lim [F(x)] = lim (F(a) - F(b))
b-00 a
f(x) dx = lim
a
О В.
b
00
f(x) dx = lim f(x) dx = lim [F(x)] = lim (F(b) -F(a))
%3D
b 0 a
b 00
a
O C. 0
f(x) dx = lim f(x) dx = lim [F(x)] = lim (F(b)- F(a))
b00 a
a
O D. 00
b.
S) ax = lim frox) dx= lim [F(x); = lim (F(a)- F(b)
f(x) dx = lim [F(×)] = lim (F(a)- F(b))
b 00 a
b00
a
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