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Let X be a random variable with mean µ and with variance o². You have a sample of size n with sample mean X and sample variance S² =E,(X; – X)²: n-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

Let X be a random variable with mean µ and with variance o². You have a sample of size n with sample mean X and sample variance S² =E,(X; – X)²: n-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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 51E
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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.
Transcribed Image 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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Transcribed Image Text:[65747668 4 2676234674 664 664 85 6 4 6]
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