hw3 - AMS 553: Homework 3 1. (L&K 8.7) For a < b,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
AMS 553: Homework 3 a < b , the right-triangular distribution has density function f R ( x ) = ( 2( x - a ) ( b - a ) 2 if a x b 0 otherwise. (1) and the left-triangular distribution has density function f L ( x ) = ( 2( b - x ) ( b - a ) 2 if a x b 0 otherwise. (2) These distributions are denoted by RT ( a,b ) and LT ( a,b ), respectively. (a) Show that if X RT (0 , 1), then X 0 = a + ( b - a ) X RT ( a,b ); verify the same relation between LT (0 , 1) and LT ( a,b ). Thus it is sufficient to generate from RT (0 , 1) and LT (0 , 1). (b) Show that if X RT (0 , 1), then 1 - X LT (0 , 1). Thus it is enough to restrict our attention further to generating from RT (0 , 1). (c) Derive the inverse-transform algorithm for generating from RT (0 , 1). Despite the result in ( b ), also derive the inverse-transform algorithm for generating directly from LT (0 , 1). (d) As an alternative to the inverse-transform method, show that if
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online