Let X denote the amount of space occupied by an article placed in a 1-ft packing container. The pdf of X is below. S72x²(1 – x) f(x) = 0 < x < 1 otherwise (a) Graph the pdf. f(x) f(x) 4 4 3 3 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) 4 4 3 2 2 X 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 < 0 F(x) = OSX<1 x > 1
Let X denote the amount of space occupied by an article placed in a 1-ft packing container. The pdf of X is below. S72x²(1 – x) f(x) = 0 < x < 1 otherwise (a) Graph the pdf. f(x) f(x) 4 4 3 3 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) 4 4 3 2 2 X 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 < 0 F(x) = OSX<1 x > 1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
[72x7(1 – x)
0 < x < 1
f(x)
otherwise
(a) Graph the pdf.
f(x)
f(x)
4
4
3
3
2
2
1
X
X
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
1
1
X
X
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 < 0
F(X)
0 < x< 1
=
1
x > 1
![(b) What is P(X < 0.6) [i.e., F(0.6)]? (Round your answer to four decimal places.)
(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.)
What is P(0.25 < X < 0.6)? (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 o y. (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%2Ffea4cb18-f853-4dd5-87f1-44780e7d8dd9%2F1334e8bd-1b1c-4e17-9983-d5e537dfc68f%2Fi8rovdj_processed.png&w=3840&q=75)
Transcribed Image Text:(b) What is P(X < 0.6) [i.e., F(0.6)]? (Round your answer to four decimal places.)
(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.)
What is P(0.25 < X < 0.6)? (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 o y. (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.)
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