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Suppose X_1, X_2, … X_n is a random sample from a population with density f(x) =...

Suppose X_1, X_2, … X_n is a random sample from a population with density f(x) = (2/theta)*x*e^(-x^2/theta) for x greater or equal to zero.

  1. Determine if Theta-Hat_1 (MLE) is a minimum variance unbiased estimator for thet
  2. Determine if Theta-Hat_2 (MOM) is a minimum variance unbiased estimator for theta.
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Answer #1

a) MLE :

b) Method of Moment:

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