Question: . Let X1, , Xn be i.i.d. with exponential density function f(x|) = (1 /) (e ^(x/))for x > 0 and f(x|) = 0 otherwise,

. Let X1, , Xn be i.i.d. with exponential density function f(x|) = (1 /) (e ^(x/))for x > 0 and f(x|) = 0 otherwise, where the parameter is unknown

  • . Show that the maximum likelihood estimator (MLE) = X, the sample mean.
  • Define = 2 . What is the MLE of ?
  • By the delta-method, derive the central limit theorem of

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