Question 2 Let X be a random variable with mean u and with variance o?. You have a sample of size n with sample mean X and sample variance S2 E,(X¡ – X)²: п-1 1) Assume that X is equal to the average...


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Question 2<br>Let X be a random variable with mean u and with variance o?. You have a sample of size n with<br>sample mean X and sample variance S2<br>E,(X¡ – X)²:<br>п-1<br>1) Assume that X is equal to the average of the first 5 numbers in your dataset, and S2<br>is equal to the sum of the first 5 numbers in your dataset. Further suppose that n is equal to<br>the sum of the last five numbers in your dataset. Write down the asymptotic distribution of X<br>and construct an approximate 95% confidence interval for the µ;<br>2) Suppose that S2 and n has the same value as in the previous part. Write down the distribution<br>of S? and construct 98% confidence interval for o?. Hint: Remember the example we solved<br>in asymptotics lecture.<br>3) What is the mean square error of Method of Moments estimator of the mean, µ, assuming<br>o2 = S2 calculated in the first part. You have to show how you derive MOM estimator.<br>

Extracted text: Question 2 Let X be a random variable with mean u and with variance o?. You have a sample of size n with sample mean X and sample variance S2 E,(X¡ – X)²: п-1 1) Assume that X is equal to the average of the first 5 numbers in your dataset, and S2 is equal to the sum of the first 5 numbers in your dataset. Further suppose that n is equal to the sum of the last five numbers in your dataset. Write down the asymptotic distribution of X and construct an approximate 95% confidence interval for the µ; 2) Suppose that S2 and n has the same value as in the previous part. Write down the distribution of S? and construct 98% confidence interval for o?. Hint: Remember the example we solved in asymptotics lecture. 3) What is the mean square error of Method of Moments estimator of the mean, µ, assuming o2 = S2 calculated in the first part. You have to show how you derive MOM estimator.
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Extracted text: [65747668 4 2676234674 664 664 85 6 4 6]

Jun 01, 2022
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