The continuous random variable X has cdf given by xS-1 F (x) -) ar+a 2a x+a -1srs0 Osrs1 3a otherwise Determine the value of a; (i) the pdf of X. (b) In an examination, the marks obtained by students are normally distributed with mean u and standard deviation o. If 30% of the students have more than 70 marks and 12% of students have scored less than 55 marks, find the value u and o.
The continuous random variable X has cdf given by xS-1 F (x) -) ar+a 2a x+a -1srs0 Osrs1 3a otherwise Determine the value of a; (i) the pdf of X. (b) In an examination, the marks obtained by students are normally distributed with mean u and standard deviation o. If 30% of the students have more than 70 marks and 12% of students have scored less than 55 marks, find the value u and o.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![(a),
The continuous random variable X has cdf given by
xS-1
-1srs0
F (x) - ar+a
2a x+a
Osrs1
3a
otherwise
Determine
) the value of a;
(i) the pdf of X.
(b) In an examination, the marks obtained by students are normally
distributed with mean u and standard deviation o. If 30% of the
students have more than 70 marks and 12% of students have scored less
than 55 marks, find the value u and o.
(c)
A die is tossed 60 times and the following frequencies are observed.
|outcome
Observed frequency
12 3 4| 5| 6
4 7
16
8.
8 7
Using a x test, test at 5% level whether the die is fair.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F792113aa-8952-4be0-b0a2-7328b30572ad%2F2fb97290-543d-471c-8749-8743ac01e350%2F9fib8tv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a),
The continuous random variable X has cdf given by
xS-1
-1srs0
F (x) - ar+a
2a x+a
Osrs1
3a
otherwise
Determine
) the value of a;
(i) the pdf of X.
(b) In an examination, the marks obtained by students are normally
distributed with mean u and standard deviation o. If 30% of the
students have more than 70 marks and 12% of students have scored less
than 55 marks, find the value u and o.
(c)
A die is tossed 60 times and the following frequencies are observed.
|outcome
Observed frequency
12 3 4| 5| 6
4 7
16
8.
8 7
Using a x test, test at 5% level whether the die is fair.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman