7.1.1 Verify the following equivalences for the age and the excess life in a renewal process N(t): (Assume t> x.) Pr{8x, y} = Pr{N(t-x) = N(t+y)} = Pr{Wkt+y} k=0 = [1 - F(t+y)] t-x ΣΤ +Σ [1 − F(t+y−z)]dFk(z). k=10 Carry out the evaluation when the interoccurrence times are exponentially dis- tributed with parameter λ, so that dFk is the gamma density xkzk-1 e dFk (z) = -zdz for z> 0. (k-1)!
7.1.1 Verify the following equivalences for the age and the excess life in a renewal process N(t): (Assume t> x.) Pr{8x, y} = Pr{N(t-x) = N(t+y)} = Pr{Wkt+y} k=0 = [1 - F(t+y)] t-x ΣΤ +Σ [1 − F(t+y−z)]dFk(z). k=10 Carry out the evaluation when the interoccurrence times are exponentially dis- tributed with parameter λ, so that dFk is the gamma density xkzk-1 e dFk (z) = -zdz for z> 0. (k-1)!
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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