Let X1,…,Xn be i.i.d. uniform random variables in [0,θ], for some θ>0. Denote by Mn=maxi=1,…,nXi.
Let X1,…,Xn be i.i.d. uniform random variables in [0,θ], for some θ>0. Denote by Mn=maxi=1,…,nXi.
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
Let X1,…,Xn be i.i.d. uniform random variables in [0,θ], for some θ>0. Denote by
Mn=maxi=1,…,nXi.
|
Compute the cumulative distribution
Fn(t)=
Compute the following limit.
limn→∞Fn(t)=
Next, we will use the previous question to find an interval I of the form I=[Mn,Mn+c], that does not depend on θ and such that
P[I∋θ]→.95, as n→∞.
|
The strategy now is to use a plug-in estimator for θ to replace it in the expression for c. Parts (a) and (b) suggest that we use c of the form (tn)Mn, where t ought to equal a certain value in order for P[I∋θ]→.95. What is the appropriate numerical value of t?
t=
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 5 images
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.Similar questions
- Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman