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Unformatted text preview: A and B . 5. Let p k ( t, s ) = X t-X 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 k-1 ( t, s )-p k ( t, s )] is solved by p k ( t, s ) = e-λ ( t-s ) ( λ ( t-s )) k k ! k = 0 , 1 , . . . , t > s ≥ . 1 6. Let p k ( t, s ) = X t-X s , where X t is an inhomoegenous Poisson counting process with time-varyng rate λ t . Show that the diferential equation ∂ ∂t p k ( t, s ) = λ t [ p k-1 ( t, s )-p k ( t, s )] is solved by p k ( t, s ) = e-λ 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