Verify Property 2 of the definition of a probability density function over the given interval. f(x) = x*, [-3,3] %3D

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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Verify Property 2 of the definition of a probability density function over the given interval.
f(x) =
[-3,3]
486
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 1.
O B. The area under the graph of f over the interval [a,b] is a.
O C. The area under the graph of f over the interval [a,b] is b.
Identify the formula for calculating the area under the graph of the function y = f(x) over the interval [a,b]. Choose the correct answer below.
O A. b
O B. a
[rox) dx = [F(x); = F(b)-F(a)
F(x) dx = [F(x)1; = F(a) – F(b)
%3D
a
ОС. а
O D. b
f(x) dx = [F(x)], = F(b) – F(a)
f(x) dx = [F(x)l% = F(a) - F(b)
b
a
Substitute a, b, and f(x) into the left side of the formula from the previous step.
5
x* dx
486
area =
Transcribed Image Text:Verify Property 2 of the definition of a probability density function over the given interval. f(x) = [-3,3] 486 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 1. O B. The area under the graph of f over the interval [a,b] is a. O C. The area under the graph of f over the interval [a,b] is b. Identify the formula for calculating the area under the graph of the function y = f(x) over the interval [a,b]. Choose the correct answer below. O A. b O B. a [rox) dx = [F(x); = F(b)-F(a) F(x) dx = [F(x)1; = F(a) – F(b) %3D a ОС. а O D. b f(x) dx = [F(x)], = F(b) – F(a) f(x) dx = [F(x)l% = F(a) - F(b) b a Substitute a, b, and f(x) into the left side of the formula from the previous step. 5 x* dx 486 area =
Next, determine F(x). First, find the antiderivative of f.
.4
X dx =
486
Let C= 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [-3,3] using the far right side of the formula for the area.
O-D
area =
Simplify
%3D
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 equals 1.
O B. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step equals b.
O C. 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 equal the expected area valu
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 equals a.
Transcribed Image Text:Next, determine F(x). First, find the antiderivative of f. .4 X dx = 486 Let C= 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [-3,3] using the far right side of the formula for the area. O-D area = Simplify %3D 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 equals 1. O B. Property 2 of the definition of a probability density function over the given interval has been verified since the expression in the previous step equals b. O C. 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 equal the expected area valu 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 equals a.
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