6 Consider a renewal process (TV( ), t 0) having a gamma ( , A) inter arrival distribution That is, the interarrivai density is (a) Show that (b) Show that ) (r i) ' x 0 (0 i r e x kty i where r is the largest integer less than or equal to i r Hint Use the relationship between the gamma (r, A) dis...

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6. Consider a renewal process (TV(/), t > 0) having a gamma (/, A) inter arrival distribution....

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*6. Consider a renewal process (TV(/), t > 0) having a gamma (/*, A)

inter arrival distribution. That is, the interarrivai density is

(a) Show that

(b) Show that

Ë ÷ ) = (r-i)! ' x >0

ÑßÌÏ ^ /é} = Ó

^(0 = Ó [i/r]e-x\kty/i\

where [//r] is the largest integer less than or equal to i/r.

Hint: Use the relationship between the gamma (r, A) distribution and the sum of r independent exponentials with rate A, to define TV(/) in terms of a Poisson process with rate A.

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Introduction To Probability Models

ISBN: 9780125984553

5th Edition

Authors: Sheldon M. Ross

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Question Posted: Aug 31, 2024 12:00 PM

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*6. Consider a renewal process (TV(/), t > 0) having a gamma (/*, A) inter arrival distribution....

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Introduction To Probability Models

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6. Consider a renewal process (TV(/), t > 0) having a gamma (/, A) inter arrival distribution....