Unformatted text preview: n be a random sample of size n from a distribution having pdf f ( x ; θ ) = 2 x θ 2 I (0 ,θ ] ( x ) . Find the MLE for the median of the distribution. (The median for X is the value ξ such that P ( X ≤ ξ ) = 1 / 2.) 5. Let X 1 , X 2 , . . . , X n be a random sample from the Γ( α, β ) distribution (as iven y the table handed out in class. Suppose that α is ±xed and known. (a) Find the MME of β . (b) Find the MLE of β . (c) Which estimator (MME or MLE) has smaller variance. (d) [Required for 5520 only] Show that your MLE is a consistent estimator of β . 6. [Required for 5520 only] Suppose that ˆ θ is the MLE for a parameter θ . Let τ ( θ ) be an invertible function of θ . Show that τ ( ˆ θ ) is the MLE of τ ( θ ). ie: Show that ˆ τ ( θ ) = τ ( ˆ θ )....
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This note was uploaded on 02/07/2012 for the course APPM 4520 taught by Professor Manuel during the Fall '11 term at University of Colorado Denver.
- Fall '11