Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below. f(x) = {0x³(1-x) <<1 (a) Graph the pdf. otherwise f(x) 4 3 2 1 f(x) 3 2 1 x 0.2 0.4 0.6 0.8 1.0 Obtain the cdf of X. x 0.2 0.4 0.6 0.8 1.0 0 x < 0 F(x) = 0 ≤ x ≤ 1 1 x > 1 Graph the cdf of X. F(X) 1.0 0.8 0.6 0.4 0.2 F(X) 1.0 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 f(x) 4 3 2 1 f(x) 3 2 1 F(X) ཀྲྀཎྜ ཨཱུ་ ུ་ཛྱཱ་ སྦེ 1.0 F(X) 1.0 0.8 0.6 0.4 0.2 WebAssign Plot x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 (b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.) 0.2 0.4 0.6 0.8 1.0 (c) Using the cdf from (a), what is P(0.25 < x < 0.65)? (Round your answer to four decimal places.) What is P(0.25 ≤ X ≤ 0.65)? (Round your answer to four decimal places.) (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) (e) Compute E(X) and x. (Round your answers to four decimal places.) E(X) = (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below. f(x) = {0x³(1-x) <<1 (a) Graph the pdf. otherwise f(x) 4 3 2 1 f(x) 3 2 1 x 0.2 0.4 0.6 0.8 1.0 Obtain the cdf of X. x 0.2 0.4 0.6 0.8 1.0 0 x < 0 F(x) = 0 ≤ x ≤ 1 1 x > 1 Graph the cdf of X. F(X) 1.0 0.8 0.6 0.4 0.2 F(X) 1.0 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 f(x) 4 3 2 1 f(x) 3 2 1 F(X) ཀྲྀཎྜ ཨཱུ་ ུ་ཛྱཱ་ སྦེ 1.0 F(X) 1.0 0.8 0.6 0.4 0.2 WebAssign Plot x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 (b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.) 0.2 0.4 0.6 0.8 1.0 (c) Using the cdf from (a), what is P(0.25 < x < 0.65)? (Round your answer to four decimal places.) What is P(0.25 ≤ X ≤ 0.65)? (Round your answer to four decimal places.) (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) (e) Compute E(X) and x. (Round your answers to four decimal places.) E(X) = (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.4: Logarithmic Functions
Problem 45E
Related questions
Question
![Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.
f(x) = {0x³(1-x) <<1
(a) Graph the pdf.
otherwise
f(x)
4
3
2
1
f(x)
3
2
1
x
0.2
0.4
0.6
0.8
1.0
Obtain the cdf of X.
x
0.2
0.4
0.6
0.8
1.0
0
x < 0
F(x) =
0 ≤ x ≤ 1
1
x > 1
Graph the cdf of X.
F(X)
1.0
0.8
0.6
0.4
0.2
F(X)
1.0
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
f(x)
4
3
2
1
f(x)
3
2
1
F(X)
ཀྲྀཎྜ ཨཱུ་ ུ་ཛྱཱ་ སྦེ
1.0
F(X)
1.0
0.8
0.6
0.4
0.2
WebAssign Plot
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
(b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)
0.2
0.4
0.6
0.8
1.0
(c) Using the cdf from (a), what is P(0.25 < x < 0.65)? (Round your answer to four decimal places.)
What is P(0.25 ≤ X ≤ 0.65)? (Round your answer to four decimal places.)
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
(e) Compute E(X) and x. (Round your answers to four decimal places.)
E(X) =
(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%2Fbedd5747-9476-45b7-ab2c-0211874b0421%2F2ae2c88f-ca01-401b-8ff8-dda3ddc9e15b%2Fzpmk4po_processed.png&w=3840&q=75)
Transcribed Image Text:Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.
f(x) = {0x³(1-x) <<1
(a) Graph the pdf.
otherwise
f(x)
4
3
2
1
f(x)
3
2
1
x
0.2
0.4
0.6
0.8
1.0
Obtain the cdf of X.
x
0.2
0.4
0.6
0.8
1.0
0
x < 0
F(x) =
0 ≤ x ≤ 1
1
x > 1
Graph the cdf of X.
F(X)
1.0
0.8
0.6
0.4
0.2
F(X)
1.0
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
f(x)
4
3
2
1
f(x)
3
2
1
F(X)
ཀྲྀཎྜ ཨཱུ་ ུ་ཛྱཱ་ སྦེ
1.0
F(X)
1.0
0.8
0.6
0.4
0.2
WebAssign Plot
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
(b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)
0.2
0.4
0.6
0.8
1.0
(c) Using the cdf from (a), what is P(0.25 < x < 0.65)? (Round your answer to four decimal places.)
What is P(0.25 ≤ X ≤ 0.65)? (Round your answer to four decimal places.)
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
(e) Compute E(X) and x. (Round your answers to four decimal places.)
E(X) =
(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 9 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning