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 1 = 12(n-1) 52 n where n is the sample size (a) Simulate 10,000 such samples from a Uniform (0, 20) 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 1 = 12(n-1) 52 n where n is the sample size (a) Simulate 10,000 such samples from a Uniform (0, 20) distribution. For each sample,
A First Course in Probability (10th Edition)
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![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%2Fac5e7a8e-a3dd-4100-b001-89b4ddaf0411%2Ff4kdevi_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.
Transcribed Image Text:(c) Use R to estimate the bias and mean squared error (MSE) of each estimator. (Perform
your calculations to 1 decimal place).
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