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
icon
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.
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
steps

Step by step

Solved in 2 steps with 5 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
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.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman