hw2_1 - Homework 2(due Feb 1 1 Which of the following...

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Homework 2 (due Feb. 1) 1. Which of the following statistics are unbiased estimators for the pop- ulation mean μ ? For those which are not unbiased, find the bias. a) X 1 + X 3 2 b) X 1 + X 3 + X n 3 c) X 1 + X 3 +3 X 2 - X 4 5 d) 3 X 1 - 2 X 3 e) X 1 - X 2 + X n/ 2 - X n - 1 + X n 2. For the estimators in problem 1, find their mean square error. Which appears to be the most efficient one (with the smallest MSE) if the standard deviation of the population is equal to its mean (
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Unformatted text preview: σ = μ )? 3. Consider the Poisson distribution f ( x ) = e-λ λ x x ! , x = 0 , 1 , 2 ,... Find the maximum likelihood estimator or λ , based on a random sample of size n . 4. Suppose the size n sample comes from a distribution uniform on the interval [ a,b ] with both a and b unknown parameters. Find the MLE for a and b . 1...
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  • Spring '08
  • Perevalov
  • Normal Distribution, maximum likelihood estimator, mean square error, Bias of an estimator, unbiased estimators

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