e and f
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 52E
Related questions
Question
e and f
![Obtain the cdf of X.
x< 0
F(x) = {x° (10 – 9x)
OSxs1
x> 1
Graph the cdf of X.
F(x)
F(X)
1.0f
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
F(x)
F(x)
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
(b) What is P(X s 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)
0.0860
(c) Using the cdf from (a), what is P(0.3 < X s 0.65)? (Round your answer to four decimal places.)
0.0858
What is P(0.3 s Xs 0.65)? (Round your answer to four decimal places.)
0.0858
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
0.9036
(e) Compute E(X) and oy. (Round your answers to four decimal places.)
E(X) =0.7500
(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c6a01b0-4ae0-4ca1-ad67-33bc0447d8ff%2F27ed6222-b658-460d-9b4a-f919cb5c03f7%2Fa85rsp_processed.png&w=3840&q=75)
Transcribed Image Text:Obtain the cdf of X.
x< 0
F(x) = {x° (10 – 9x)
OSxs1
x> 1
Graph the cdf of X.
F(x)
F(X)
1.0f
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
F(x)
F(x)
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
(b) What is P(X s 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)
0.0860
(c) Using the cdf from (a), what is P(0.3 < X s 0.65)? (Round your answer to four decimal places.)
0.0858
What is P(0.3 s Xs 0.65)? (Round your answer to four decimal places.)
0.0858
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
0.9036
(e) Compute E(X) and oy. (Round your answers to four decimal places.)
E(X) =0.7500
(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
Transcribed Image Text:Let X denote the amount of space occupied by an article placed in a 1-ft packing container. The pdf of X is below.
Fs) = {90
90x (1 - x)
0 <x<1
otherwise
(a) Graph the pdf.
f(x)
f(x)
4|
4
3-
3-
2
2
1
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
f(x)
f(x)
4|
4|
3
3
2
2
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
Obtain the cdf of X.
x° (10 – 9x)
F(x) =
Osxs1
x> 1
Graph the cdf of X.
F(X)
F(X)
1.0|
1.0}
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
1,
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