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Unformatted text preview: 2 2 / (Hints: read pages 69-70 of the Keener book; available at bspace) 4.4. Let 1 Z and 2 Z be independent standard normal random variables. Find 1 2 | / | E Z Z . (Hints: again use the materials on the pages 69-70 of the Keener book) 4.5. Regularity Conditions are Needed for the information inequality . Let (0, ) X U be the uniform distribution on (0, ) . Note that log ( , ) p x is differentiable for all x > , that is, with probability 1 for each , and we can thus define moments of / log ( , ) T p X = . Show that, however, a) 1 log ( , ) E p X = - . b) log ( , ) Var p X = and 2 2 ( ) 1/ I ET = = . c) 2 X is unbiased for and has variance 2 2 (1/ 3) (1/ ( )) I < = ....
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This note was uploaded on 10/17/2009 for the course STAT 210a taught by Professor Staff during the Fall '08 term at University of California, Berkeley.
- Fall '08