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(X1 – X)²: n-1 1) Assume that X is equal to the average of the first 5 numbers in your dataset, and s²

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Chapter1: Combinatorial Analysis
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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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Question 2
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-1(X{ – X)²:
1) Assume that X is equal to the average of the first 5 numbers in your dataset, and S?
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
o? = s² calculated in the first part. You have to show how you derive MOM estimator.
%3D
Transcribed Image Text:Question 2 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-1(X{ – X)²: 1) Assume that X is equal to the average of the first 5 numbers in your dataset, and S? 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 o? = s² calculated in the first part. You have to show how you derive MOM estimator. %3D
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