10
Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number of claims on a workers' compensation insurance 3. The total revenue of cable TV company Homework: Kao, E. (1997): Ch. 2, Sec. 5 Problems: 2 # 9, 25, 27, 29

1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

  • Upload
    others

  • View
    1

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

Filtered Poisson Process

1. The number of criminals incarcerated at time t

2. The number of claims on a workers' compensation insurance

3. The total revenue of cable TV company

Homework: Kao, E. (1997): Ch. 2, Sec. 5

Problems: 2 # 9, 25, 27, 29

Page 2: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

________ S __T---.,•......--A.J :l9J_\-\ -t-A.------- LI_O _

-------, ----------------------1- £~e-te,-eoJ Pcu is s ~h Pno cg41= --- ---

-A- s-/-v J{<»,-b-c- e"", C!Uv\ 0L+~{-?~

J'S c ~ ~ ~-=fe(';lj;i(4 ~ l's~-';;;-7 I ~ CVV1

.t f Nff-)

_________x c+) ~? .~.>- s~J:J----------------L :::-1

s; _ Qle- ~ Qrrtv~f5:--~ c..----------r~ _. .__..__.. . _

---1t----==- ~ -;- Lt. £. CO ~ fe' nUJ) Ct::S__ r:..-_L/,_, _' __ > __ ,_.__

----J~-Lu=nJ=- -----.------..-----.------~~.~~~--.---L+u~~., g i~-~~¥:PI~e--~=

--_._-------_._._-----~-_ ...__ .----G;c~f&_:1)-7:f W (-t-{ /(' 1 ~ ) :=. .I+~_i }-.-----

._-._--------_.- ..

L )(Ct) = l'=." C<....- frn-s=" f IS c.e-¥.' .__

!!!'(f . d~--------- ...--.---. . 1& (.iTTti)-=---~·e-.-{..f=~-~7\----·-·-·-.-...--...----.-- ....

Page 3: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

xct) .::::c' '.> <:L co ~/20 C(nc/A/f+-) I

X (?-) -=- 2. ~,<

_____ .2~..~_t2~-X.;l~~ 2. s:~1__ H__I-Ci!~~ eu~_~

'( - (~Il-~ )(

- \ I ----.'G 5", 1:-

t

{{~ ~

/ ,--f{,... fot1..Ctl l Vl'7f d-~ J- (

f\

A')~:::. -c---- - • .

~2. \

J-..:-.~(

, ~\• !1..-<-

\'.:1

(

r ""'"(,~---.- hi' - ~--y\ ..:: -- (

\. ~ -. I . -I'"

0 5( ~--_. + ~SJ-.:3 1 -~-

f'J.{f-) _------ __- 1Ut2::? - tJ -t--:--S-<l --<-~-·_---7--~1_.~(+) = Z

L::-I t f-\Ai lUL w c;' C'L, ~) ':= 1 ;> C+ 10 <. ~ <.. ~

Page 4: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

____ If- we- ekh'~ ~ X (+) ~ ~

a J7'ZD unA:- &f r-e-mad u ftcJ Xd: 1/ " c..e...... ?-r htfL----

_____ ~-=-& C&4b~ wkQ are-_' __ -fL~~ d filM.€- 7::,

tt-e",

----~.J- CJ~9 E4 0<s<.)'3

(Jo_1SJ-) ::::--S rj OL. s <-,YJ-----------~ALi:/::)'------------------

X (f) = ~ WQ (t- ::;"'7;)_______ . "1-1--- _

_ . - ~) (.l ~S~) -i t 0~1-S, L ILiJ--'1-1

.£ ~&..- 2' S-"' 2-. ~ Jt4M-~ d----C.L l·)'YU~#.a__=_=_,t';---<:> _

________________ Tn daAce-rcvfe/ d '6'qte -6-,-____ S'_~·----&~_a -I- wlud crirrl-t'~ aL-e.. ~·nc.a/'CLra-&t-----Y: ----&--& 11~~_..s:.e--h t~ ee...-

L f ~-7U]-;----Y~i0 <: :> c: :I] / w~ oS;;: 7~sr-~ --IX-~/+---+-)----------- _

______ X_(~~ij.=o?~' 00 {~ •• > z:)--------7..=-/

-_._----------_.-----~--~, -_._-----_._------_._-----t'> 10- nu~ .d.. e-ri"rrt-lnaLs ittceu-cru-a/ecI d ~~f:

Page 5: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

tkid

~. -/s i:L {..,-~~ L,V,~~ ['4 aCc-<:'dt? ,L

t2 ce...u.-r$' a;/--- W()rc .

£Ka-r g, S-:,q lj X(.,t:) ~ "l.. t ·~Ce.v'LJ'U<g rLC&1.'~ 2-It-L~ tJ-~-~-,~--T- v Cd? ~~~_? ~-r-E£~..LXJ- _70 I£'f ~~,_,

tJ-oJs.-J}-) =- .s .-L/-s~oJ----~ .-#{+}--::

XCi:;) - T (+-~.j /'-t =-1

~ S~~.~_:£i~_& CLrr/v'd<' 6'-~ ~£ -i-fh ~~~ .. _.

Page 6: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

-.....-•....~1~:.•.•.•.••·X-Z±)~~-.;z-(:)~:•.0i~~-s:~~Y:~:...=7-1=~~••·--_-:.•...•..

. ' _.._.J ':::.J._._ _ _ __ .

...__.._.....-p-._..._-...._.....__.._._.....-_..__....-...-.....__....._.._..__..------....._-------...--._._.-._.._....__...._.-_._..._...-..._._.._..-'-_.---~.-...._.._....._.._.__..--S8~<;l~'>1"'" ;s.(" ... _'tk_~~ -~~~a ..-:j-l.<J'J;o"

--_ _._- . .---. -_ .. _-_ _---_. - '- ---- _. -- - --_.- ------ ..-- .....•... __ ._---- .__ ._.- - -- - _.-----.-. --_. ---_._- ----- ---- -- -_. __ .. ._-_ .. --_._-_ ' ---_ .•._-_ ..•._-_ .._.'_._--_ _---- .- _-_.

== .:•. -~ .•.._e~~l~):.=:;~E:-..C?_:(~~-~)~~:~.-.-_--- :_==_= ..-:::-__ ._.. _ .• ,_ .• •• " .'_ .._, •.. ~ ." ._, ..•... __• __ ._. __ • . H. ,_.__ •.••.• _ .••• ._ •..__ ._ .•.•_. _._ •.• • .". .0. '._. ._._ •. •..• _."."" __ •• _.••••• _... _••• _.__••_.•• " . __ •. _ . _.____ ... _•• _. _•••..• __ ", • ..• _

--.----..---..-....--..--.---.....------...[- -,.:t:lW{ b-~ '(-~-~----7r------ --

=._.::~~:::~~e.....-~-•._~.~••=~~-.--_'--'-_-~.~~.~=~Y__~~_•..~_._~~_~(l~=- _ •• _ ••••• --_. __ .•• - ~-- '.--- ••• - ••• __ • __ .~--_.-.~ - ••• __ ._-_ •.••••• _._--_.- •• - • - '.----."---- --~-_ •• _.-- _.,. -.---- -- •• _-, ••• -< .•••• _-- • - _ •• _ •• , -- - ••• _- - - ••• ' - •••. -,-. • •• _--- •• --_. -_ •• -, ••• _-_. -_._ ••••• -." -_._ •• -_.-t- .__ '. •• _ ••..• __ ._ •• _. - • - .• • •• __ •• - •• - • • __ ••• __ • • ••• _._ • __ ••• __ .• • __ 0 • _._ ~ • __ ••.••• _. __ • __ •••••• • __ ._. •• • __ • ." " • • __ ._ •• 0_' __ . ._+. _

=- ·•••·•..·---·.-:~--l5<T~~5')-~I~=:~n(z:;l-l)i:X'J)·· ..·..·l-i-=..==:=--=-=--.- .---..- ..-.--- - .-'.-.--'-' --.- --.--.-- -- ----.-.--9.--- --.-----.--- .. --.-..--. _ - -.--. -'" --..- .. ---- .--.. - ..- - --. -.._-

-_.._--- .. _ .._ _ __ .. - _.- ..•.•..... - __ ._ •..... -._-_ - .- -_ ..•... _ ..- ~ ._ __ .__ ._-_ .._--_._._ .._-..__ ._..__ .- -._ .•.._ ..__ ._._ __ _._-_._._ _.._.._--

=.---.•·.•~-~.Y.ii-CX\tD-···::~·:~\=-~t~{i.~T~I~=ti=--.--."=-~._ _--< ---- --..---.-.------------ ---.--- -- ..--·-'---'--0---'--·'· - -------------- .- - - ----.-..-. ..-.. -.- ------ ..-..- -._-

Page 7: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

--6-

~-=-==~~-4kl-,=-~~--tS':I-=-ii1~J~Jt--~ .[fE7-) >,. \ -------------------

---------------------.-- ---vl:.---------------------------------------------

_ r::: '--::7 - _ ____________ ~ __C: k- -------- _

--------------------------------------------~---------------._-------------- ----------~~~~===__=~~~--tv{ II (J~ __-- __________--Btr --r--\--=-==~=-===- =----=-=_-. -.------

------ -----_._------------------------------_.------ ----- ""~-----(j wt-t)1t~y;)\-----' ---------=~~.~~-~-~-]j--=:~--------~~~~------------------_._--.•.

--------------\--4----

\A _------------- 'v-e:::::---

-----------------..~ ::_-.~-z= 0J L~~ )-----------_-------------

Page 8: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

-

~~_---=--_--_--_--=±--__-_~_---_- _----~-~1-__-=--_-- __-_------------V\..-----------~

t-~ ~ 1..0(1; l: "" ' --------.---------------------::::-----------~- I -'3__ l -----1--+--------------------------- '________________-,___ - __~ . ~_ckL _ _

_____________ . ._..D. ----------- ------_. .. . . _

---~----~~JL_-~f\.(.O~.ilit-().~-- .....?~~~-

~~~_---_=-~~~i~~I--2:E~~~~ilii)Jror~=~-=-------------------~ 0-- --------- -----------

--------.--~---~-p±-=tfi- . ~ C{ <: Y~-5-- -h.---f);(JI,--~-.---------.-------------=2:--- ---t-·--- ---~ __~-------l ..!'. . Y ,_.~-e..~+--_______ '"t.

___________________h.~ 0___ 0 , . . _..---------------------------------------- -------._----_._---

~=___===_= __~=±~=T~.-1; ~~~Lt-~Oq=~+--- ~ -) - ~ ------~'t;--

-----------=--~. -----Q- -L-. -- ---- e ----=:--.--------------·---------------·---------1-rl----------

'v\:::. 0 V\---------------------------- -~---------------

----_._----_ .._------------_._----~----

----------- ---tt~Gtt;I--Y,)-- -----_._----) *__________~~- ._~ =x.- -:: -------- -L -- _ -- ---

----------------------- \)

~-~--~~-~-w:~--- D~---------- ~.- ) ~

. ~Tt)

Page 9: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

----- ..-------.----.--"----- -- ..----- ----.--=-r----- ----.---- ...-------------.----.--.-------.- .------.11

m ~"

~CfL, C'{.... 1":- eo-B ~ ~/+£J-I •

I

.£X{f1=~ ( '-.b. w( f '(' Y \ ).T/ " ./

0

~ =&i!J< Xl+) ~;:tf ~ 2- ¥ L/~,1

W (Il:> t; j' c:- .0

-

~0VfS~& ~m~~~

'1-: f( ~a~ £. [:f. tk ,-.f1t 11LQ (00 r- tA..e.. uJL

r f~t~? ( g) . \

(;.)(t/L)Y):::- - Wo tl'-T) Y)-

Page 10: 1. The number of criminals incarcerated at time t 2. The ...rmnatsak/Note10_763spr09.pdf · Filtered Poisson Process 1. The number of criminals incarcerated at time t 2. The number

-----------_._---------------- .._-_.__ ....._ ..------ .__ .._;;::...~-_._._-----_.._ ..._._-------_._--------------------~ '-

Y#~>.q'~-Eh ~~.~.

. - +- -..--.-.-----, ~. r ~._($--'--V_~_.-S_.·_. _.,_ ..~ ..-----t--.z::~. _c'_~_ 8xcl-~ 2. 2. J-J-o

-;:pr--7 l''::' , :, .

....• •... ..•.---~--·-·--~-r ..-.:·-,--,- .....-------,--::...----;......,..r---,--_ .---.- '--:~~-~---\'" '.'( .