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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 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
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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(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).
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.
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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