(1) Verify that the probability (p(t)=P(N(t)) is odd) satisfies [p(t)=F(t)-int_{0}^{t} p(t-x) f(x) d x, quad f(x)=F^{prime}(x)] (2)...
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(1) Verify that the probability \(p(t)=P(N(t)\) is odd) satisfies
\[p(t)=F(t)-\int_{0}^{t} p(t-x) f(x) d x, \quad f(x)=F^{\prime}(x)\]
(2) Determine this probability if the cycle lengths are exponential with parameter \(\lambda\).
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Related Book For 
Applied Probability And Stochastic Processes
ISBN: 9780367658496
2nd Edition
Authors: Frank Beichelt
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