Unformatted text preview: θ . Show work. L( θ ) = ( ) ∏ =n i i x 1 & 1 & . ln L( θ ) = ( ) & = ⋅n i i x n 1 ln & 1 & ln . ( ) & == n i i d d x n 1 ln 1 & & & L ln = 0. & = + = n i i x n 1 ln 1 & ˆ . b) (5) Ω = { θ > 2 }. Find the method of moments estimator & ~ of θ . Show work. E(X) = ( ) ( ) 2 & 1 & 1 & 1 & X== ± ± ∞ ∞ ∞⋅ ⋅ dx x x dx x f x . 2 & 1 & 1 1= = & = ⋅ x x n n i i . 1 1 2 & ~= x x ....
View
Full Document
 Spring '08
 AlexeiStepanov
 Normal Distribution, Probability, Probability theory, probability density function, Estimation theory, Likelihood function, ln xi

Click to edit the document details