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Unformatted text preview: ) = P ( Q n i =1 X i y ) = P ( n i =1-log X i -log y ). Now,-log X i exponential(1) = gamma(1 , 1). By Example 4.6.8, n i =1-log X i gamma( n, 1). Therefore, P ( Y y ) = Z -log y 1 ( n ) z n-1 e-z dz, and f Y ( y ) = d dy Z -log y 1 ( n ) z n-1 e-z dz =-1 ( n ) (-log y ) n-1 e-(-log y ) d dy (-log y ) = 1 ( n ) (-log y ) n-1 , < y < 1 ....
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This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.
- Spring '12