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Unformatted text preview: A and B . 5. Let p k ( t, s ) = X tX s , where X t is a homoegenous Poisson counting process with rate λ . Show that the di²erential equation ∂ ∂t p k ( t, s ) = λ [ p k1 ( t, s )p k ( t, s )] is solved by p k ( t, s ) = eλ ( ts ) ( λ ( ts )) k k ! k = 0 , 1 , . . . , t > s ≥ . 1 6. Let p k ( t, s ) = X tX s , where X t is an inhomoegenous Poisson counting process with timevaryng rate λ t . Show that the diferential equation ∂ ∂t p k ( t, s ) = λ t [ p k1 ( t, s )p k ( t, s )] is solved by p k ( t, s ) = eλ R t s λ x dx ( R t s λ x dx ) k k ! k = 0 , 1 , . . . , t > s ≥ . 2...
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This note was uploaded on 03/01/2012 for the course ECE 6010 taught by Professor Stites,m during the Spring '08 term at Utah State University.
 Spring '08
 Stites,M

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