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(Solution Library) (2 marks) Suppose that the random variable, X , has density function f(x)=(1)/(varphi)e^-x/\varphi , x > 0, \varphi > 0. A random sample

Question: (2 marks)

Suppose that the random variable, X , has density function

\[f(x)=\frac{1}{\varphi }{{e}^{-x/\varphi }}\] , x > 0, \[\varphi \] > 0.

A random sample of size n of X , denoted by X 1 , X 2 , …, X n , is obtained.

  1. Derive the maximum-likelihood (ML) estimator for \[\varphi \] .
  2. Obtain E( X ) and Var ( X ).
  3. Use the results above to show that the ML estimator is asymptotically efficient.

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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