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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. 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)
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...
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(d) Give an advantage of using theta.1 as an estimator and an advantage of using theta.2 as an estimator.
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.
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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