STAT 333 Lecture 33: STAT 333 Lecture 33 Spring 2016

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29 Jul 2016
Department
Course
Professor
Lecture 33
Last lecture :
What can we do from R= ?
(1) II to &Esty obtain It
(2) B- can be used to recover IHI by
zctkexp HE )=¥otf¥ .
(3) Li ~
exp (-tii )&Eij =.tt#jfi
.
Birth -Death process :{XHI , £30 ]
Conditions
Birth
(i)If XH )=i , the process can only jump to {it
t death
12 )When XCE )=i ,
-7 Birthrate
LBI = waiting time for abirth ~exp Hi )
;
=
-
. -. - -death ~exp 1M¥ Death rate
Remark
(i)condition Itells us
Only Eiiti &Ei , it can be positive
Ei ,j=0 if lj -it 32
(2) condition 2 tells us
li = min (LBI ,;)~exp (Dit M;) -rii =Jitµi
~ex§lai )2exp( ni )
vii =-Glitmij
Exit =p (Li =↳i )=p Gump =birth )
=p (LBI amin (↳i ,lpi ))=di/witµt )
Ein 't = pllia ;)=p (jump -death )
=p (Lai =mih(↳i ,LDID =Nikita .i )
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