(See Solution) (2 marks) Assume X is a Uniform random variable on the interval (-  , ), where  > 0 and is unknown. A random sample of size n of X , denoted


Question: (2 marks)

Assume X is a Uniform random variable on the interval (- , ), where > 0 and is unknown.

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

  1. Obtain E( X ) and E( X 2 ) and then use one of these to define a method of moments estimator of .
  2. Obtain E( X 4 ) and then use this to define a different method of moments estimator of .

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