You are asked to advise a researcher the estimator they should use to find the value of 0 from a set of experimental results that they know come from a Uniform (0, 0) distribution. You decide to simulate a collection of independent and identically distributed random samples of size 10 from a Uniform (0, 0) distribution. There are two different estimators that you would like to consider. 2X and = 1 02 where n is the sample size (a) Simulate 10,000 such samples from a Uniform (0, 20) distribution. For each sample, calculate the value for each estimator of 0. Use the following code: set.seed (6) 12(n-1) 52 n =
You are asked to advise a researcher the estimator they should use to find the value of 0 from a set of experimental results that they know come from a Uniform (0, 0) distribution. You decide to simulate a collection of independent and identically distributed random samples of size 10 from a Uniform (0, 0) distribution. There are two different estimators that you would like to consider. 2X and = 1 02 where n is the sample size (a) Simulate 10,000 such samples from a Uniform (0, 20) distribution. For each sample, calculate the value for each estimator of 0. Use the following code: set.seed (6) 12(n-1) 52 n =
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
d
Transcribed Image Text:(d) Give an advantage of using theta.1 as an estimator and an advantage of using theta.2
as an estimator.
![You are asked to advise a researcher the estimator they should use to find the value of 0
from a set of experimental results that they know come from a Uniform (0, 0) distribution.
You decide to simulate a collection of independent and identically distributed random
samples of size 10 from a Uniform (0, 0) distribution. There are two different estimators
that you would like to consider.
Ô₁
2X and
-S² where n is the sample size
(a) Simulate 10,000 such samples from a Uniform (0, 20) distribution. For each sample,
calculate the value for each estimator of 0. Use the following code:
Ō₂
}
=
set.seed (6)
theta.1=rep(0,10000)
theta.2=rep(0,10000)
for (i in 1:10000) {
x=runif(10,0,20)
theta.1[i]=2*mean(x)
theta.2[i]=sqrt((12*9/10)*var(x))
12(n-1)
n
Obtain the five-number summary statistics for the samples of theta.1 and theta.2 and also
the mean and variance of the samples. (Five-number summaries are the maximum and
minimum values, the lower and upper quartiles, and the median). Give your answers to 2
decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2e686e7-76ae-4321-b7a6-3ee040859ac1%2F9e299538-a979-4b59-992d-b8437eb2d01e%2Fhfjs2qb_processed.png&w=3840&q=75)
Transcribed Image Text:You are asked to advise a researcher the estimator they should use to find the value of 0
from a set of experimental results that they know come from a Uniform (0, 0) distribution.
You decide to simulate a collection of independent and identically distributed random
samples of size 10 from a Uniform (0, 0) distribution. There are two different estimators
that you would like to consider.
Ô₁
2X and
-S² where n is the sample size
(a) Simulate 10,000 such samples from a Uniform (0, 20) distribution. For each sample,
calculate the value for each estimator of 0. Use the following code:
Ō₂
}
=
set.seed (6)
theta.1=rep(0,10000)
theta.2=rep(0,10000)
for (i in 1:10000) {
x=runif(10,0,20)
theta.1[i]=2*mean(x)
theta.2[i]=sqrt((12*9/10)*var(x))
12(n-1)
n
Obtain the five-number summary statistics for the samples of theta.1 and theta.2 and also
the mean and variance of the samples. (Five-number summaries are the maximum and
minimum values, the lower and upper quartiles, and the median). Give your answers to 2
decimal places.
Expert Solution
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 3 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON