The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution. Mathematically, Xn X₂ →º N (µ‚, 2/² ). D n where →D means 'converges in distribution'; it's implied here that this convergence takes place as n, or the number of underlying random variables, grows. This is an extremely powerful result, because it holds no matter what the distribution of the underlying random variables is. Task Using software R, demonstrate that CLT holds on the example of the Exponential Distribution. Use λ = 5 for de-ix ,x ≥ 0.
The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution. Mathematically, Xn X₂ →º N (µ‚, 2/² ). D n where →D means 'converges in distribution'; it's implied here that this convergence takes place as n, or the number of underlying random variables, grows. This is an extremely powerful result, because it holds no matter what the distribution of the underlying random variables is. Task Using software R, demonstrate that CLT holds on the example of the Exponential Distribution. Use λ = 5 for de-ix ,x ≥ 0.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
could you produce 3 histogram ggplots for this question, similar to the ones i uploaded using R
- Plot the Histogram for the Exponential distribution
- Plot the Histogram for the Normal distribution
- plot for comparison between exponential and normal,
with a key and also could you outline the graphs with a normal curve and provide an explanation for th eobservations and what the graph tells us .
![04
I
Demonstrating Central Limit Theorem
1.
Value
The Distribution of Sample Means and the Uniform Distribution
04
Distribution of Means
Uno Distribution
00
ampla ass trearotidal variazas 14 0.001611049547
[1] "The hmber of similations in 2008
# [1] "The difference between sample and theoretical means is 0.00151247649783848"
# [1] "The difference between sample and theoretical variances is 0.0012342020050992"
Demonstrating Central Limit Theorem
Uniform Distribution
1500-
Value
Value
Type
Hulh
Normal Dibution
The Distribution of Sample Means and the Uniform Distribution
Value
Type
[1] "The Number of simulations is 10000"
[1] "the difference between sample and theoretical means is 0.000366877283006026"
# [1] "The difference between sample and theoretical variances is 0.008186210166330476
Demonstrating Central Limit Theorem
of Sample Man
bution of Sample Man
Nouton
Value
The Distribution of Sample Means and the Uniform Distribution
Distribution of Means
Uniform Distribution
Otribution of Sample Mean
Normal Dibution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2F919b6102-7a8d-4013-9751-62f8c2aafdef%2Fgt3hd0n_processed.png&w=3840&q=75)
Transcribed Image Text:04
I
Demonstrating Central Limit Theorem
1.
Value
The Distribution of Sample Means and the Uniform Distribution
04
Distribution of Means
Uno Distribution
00
ampla ass trearotidal variazas 14 0.001611049547
[1] "The hmber of similations in 2008
# [1] "The difference between sample and theoretical means is 0.00151247649783848"
# [1] "The difference between sample and theoretical variances is 0.0012342020050992"
Demonstrating Central Limit Theorem
Uniform Distribution
1500-
Value
Value
Type
Hulh
Normal Dibution
The Distribution of Sample Means and the Uniform Distribution
Value
Type
[1] "The Number of simulations is 10000"
[1] "the difference between sample and theoretical means is 0.000366877283006026"
# [1] "The difference between sample and theoretical variances is 0.008186210166330476
Demonstrating Central Limit Theorem
of Sample Man
bution of Sample Man
Nouton
Value
The Distribution of Sample Means and the Uniform Distribution
Distribution of Means
Uniform Distribution
Otribution of Sample Mean
Normal Dibution
Transcribed Image Text:The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution.
Mathematically,
X₁ +" N (1, 0-²)
9
n
Xn
where →
→D means 'converges in distribution'; it's implied here that this convergence takes place as ʼn, or the
number of underlying random variables, grows.
This is an extremely powerful result, because it holds no matter what the distribution of the underlying random
variables is.
Task Using software R, demonstrate that CLT holds on the example the Exponential Distribution. Use λ = 5 for
de-2x, x ≥ 0.
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 4 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education