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 Ō₂ = 12(n-1) n 52 where n is the sample size (a) Simulate 10.000 such samples from a Uniform (020) distribution For each sample
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 Ō₂ = 12(n-1) n 52 where n is the sample size (a) Simulate 10.000 such samples from a Uniform (020) distribution For each sample
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 53E
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Question
e
![(e) In fact, both the estimators of theta above are unsatisfactory. Why is that the case and
can you suggest a better estimator? (You do not need to justify your choice).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2e686e7-76ae-4321-b7a6-3ee040859ac1%2F00d1634a-8eb6-4496-aee6-b09cda84efda%2F7qahus6_processed.png&w=3840&q=75)
Transcribed Image Text:(e) In fact, both the estimators of theta above are unsatisfactory. Why is that the case and
can you suggest a better estimator? (You do not need to justify your choice).
![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%2F00d1634a-8eb6-4496-aee6-b09cda84efda%2F7lyyeik_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.
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