A machine works for an exponentially distributed time with rate μ and then fails
37.      A machine works for an exponentially distributed time with rate μ and then fails. A repair crew checks the machine at times distributed according to a Poisson process with rate λ; if the machine is found to have failed then it is immediately replaced. Find the expected time between replacements of machines.
38.      Let {Mi(t), t � 0}, i = 1, 2, 3 be independent Poisson processes with respective rates
λi , i = 1, 2, and set
N1(t) = M1(t) + M2(t),       N2(t) = M2(t) + M3(t)
The stochastic process {(N1(t), N2(t)), t � 0} is called a bivariate Poisson process.
(a)     Find P{N1(t) = n, N2(t) = m}.
(b)     Find CovtN1(t), N2(t)).
Answers
Status NEW
Posted 31 May 2017 08:05 AM
My Price 5.00
-----------
Attachments
1496220566-1488494_2_636317315916923093_media-d8a-d8ab2ce0-6cae-424e-8d10-1bdb822d683b-phpkcuCwG.png
1496220568-1488494_3_636317315916923093_media-92c-92c6c04a-e601-4af0-80c5-72203968302a-phpa8SwUi.png
file 1496220615-Answer.docx preview (53 words )
3-----------7, -----------The----------- ti-----------me -----------T b-----------etw-----------een----------- tw-----------o s-----------ucc-----------ess-----------ive----------- re-----------pla-----------cem-----------ent-----------s i-----------s t-----------he -----------sum----------- of----------- th-----------e l-----------ife-----------tim-----------e D----------- of----------- th-----------e m-----------ach-----------ine----------- an-----------d t-----------he -----------ela-----------pse-----------d t-----------ime----------- R -----------bet-----------wee-----------n t-----------he -----------mom-----------ent----------- wh-----------en -----------it -----------fai-----------ls -----------and----------- th-----------e m-----------ome-----------nt -----------whe-----------n i-----------t i-----------s r-----------epl-----------ace-----------d. -----------By -----------hyp-----------oth-----------esi-----------s D----------- is----------- ex-----------pon-----------ent-----------ial----------- wi-----------th -----------par-----------ame-----------ter----------- µ----------- an-----------d R----------- is----------- ex-----------pon-----------ent-----------ial----------- wi-----------th -----------par-----------ame-----------ter----------- ?
-----------
He-----------nce----------- E(-----------T)=-----------E(D-----------)+E-----------(R)-----------=1/-----------µ+-----------1/?-----------
-----------
Not Rated(0)