I need help for number 6 please!! thanks!! 4. Suppose we have a sample of three

Question

I need help for number 6 please!! thanks!! 4. Suppose we have a sample of three numbers from a continuous uniform (0,1) distribution, but we don't know what the mean of that distribution is, so we estimate it. One possible estimator is the sample mean, whose properties we already know. Another estimator might be the average of the minimum and maximum element of the sample What is the expected value of this estimator? 5. Reminding ourselves now what the true mean of the uniform is, what property does the new estimator in 4) have that is good and that is common with the sample mean? 6. Determine which of the two estimators, the sample mean or the one introduced in 4), is more efficient. Don't try to do this analytically do it using an Excel simulation instead. The problem with trying to do it analytically is that the min and max are correlated, so the variance of the new estimator is not trivial to derive. It is within your mathematical grasp, but probably too much work for a homework assignment. Instead, generate 10,000 triplets of independent uniform (0,1) random variables in Excel, and for each triplet, compute the sample mean, the minimum, the maximum, and the new estimator. Aslk Excel for the sample variances of the sample mean and the new estimator, and compare the results

Explanation / Answer

To generate 10,000 uniform random variables use RAND function in Excel which will give 10,000 values. Do it in three columns of Excel - A, B and C. Then find the mean, min, max, and average of min and max of these three values 10,000 times. Then find the variances of the sample mean and new estimator which is average of min and max. If the new estimator has the less variance then it is better estimator than the estimator found by the means of the triplets which is sample mean. The values in Excel will differ because of randomization.

My Variance values are

Sample mean variance = 0.027589

New Estimator variance = 0.024766

Hence, new estimator is the better one.

It is not possible to show or paste 10,000 values from Excel here.

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