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 < 1f(x)otherwise(a) Graph the pdf.f(x)f(x)4433221XX0.20.40.60.81.00.20.40.60.81.0f(x)f(x)44|332211XX0.20.40.60.81.00.20.40.60.81.0Obtain the cdf of X.X < 0F(X)0 < x< 1=1x > 1 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 oy. (Round your answers to four decimal places.)E(X) =0x =(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)

Answered: (72x²(1 – x) 0 < x < 1 f(x) = otherwise…

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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Related questions

Question

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

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 oy. (Round your answers to four decimal places.)
E(X) =
0x =
(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

Step 1

The CDF of the distribution can be mathematically written as:

$\begin{array}{rcl} F (x) & = & \int_{0}^{x} f (t) d t \\ = & \int_{0}^{x} 72 t^{7} (1 - t) d t \\ = & 72 \int_{0}^{x} t^{7} (1 - t) d t \\ = & 72 \times \int_{0}^{x} (t^{7} - t^{8}) d t \\ = & 72 \times ({[\frac{t^{8}}{8}]}_{0}^{x} - {[\frac{t^{9}}{9}]}_{0}^{x}) \\ = & 72 ((\frac{x^{8}}{8}) - (\frac{x^{9}}{9})) \end{array}$