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Unformatted text preview: STAT 409 Examples for 09/02/2009 Fall 2009 1. If the random variable Y denotes an individuals income, Paretos law claims that P ( Y y ) = y k , where k is the entire populations minimum income. It follows that f Y ( y ) = 1 1 + y k , y k ; 1. Assume k is known. a) Recall that the method of moments estimator ~ of , is k- = Y Y ~ . Show that ~ is a consistent estimator of . ( 29 1 1 Y E 1 - = = = - + k dy y k dy y k y k k . By WLLN, ( 29 1 Y E Y- = k P . a P n X , g is continuous at a ( 29 ( 29 X a g g P n Consider g ( x ) = k x x- . Then g ( x ) is continuous at 1 - = k a . ( 29 ~ Y Y Y = =- k g ( 29 1 1 = =--- k k k a g ....
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- Spring '11