Some Applications of the Poisson Process
|
|
|
- Iris Bates
- 6 years ago
- Views:
Transcription
1 Applid Maaics, 24, 5, 3-37 Publishd Oli Novbr 24 i SciRs. hp:// hp://dx.doi.org/.4236/a So Applicaios of Poisso Procss Kug-Ku s Dpar of Maaics, Ka Uivrsiy, Uio, USA Eail: s@a.du Rcivd 24 Augus 24; rvisd 2 Spbr 24; accpd 8 Ocobr 24 Copyrigh 24 by auor ad Sciific Rsarch Publishig Ic. his wor is licsd udr Craiv Coos Aribuio Iraioal Lics (CC BY. hp://craivcoos.org/licss/by/4./ Absrac h Poisso procss is a sochasic procss a odls ay ral-world phoa. W prs dfiiio of Poisso procss ad discuss so facs as wll as so rlad probabiliy disribuios. Fially, w giv so w applicaios of procss. Kywords Poisso Procsss, Gaa Disribuio, Ir-Arrival i, Mard Poisso Procsss. Iroducio Poisso procss is usd o odl occurrcs of vs ad i pois a which vs occur i a giv i irval, such as occurrc of aural disasrs ad arrival is of cusors a a srvic cr. I is ad afr Frch aaicia Siéo Poisso ( I is papr, w firs giv dfiiio of Poisso procss (Scio 2. h w sad so ros rlad o Poisso procss (Scio 3. Fially, w giv so xapls ad copu rlva quaiis associad wi procss (Scio Wha Is Poisso Procss? λ > is a faily of rado variabls { } A Poisso procss wi parar (ra N, saisfyig followig propris: N. 2 N N,,, N N 2 N N ar idpd rado variabls whr < < <. λ( s 3 P( N Ns ( λ ( s for > s.! N N, ca b ough of ubr of arrivals up o i or ubr of occurrcs up o i. ( ] How o ci is papr: s, K.-K. (24 So Applicaios of Poisso Procss. Applid Maaics, 5, hp://dx.doi.org/.4236/a
2 K.-K. s 3. So Facs abou Poisso Procss W giv so propris associad wi Poisso procss. h proofs ca b foud i [] or [2]. If w l, W b i of arrival ( W, ad w l X W W,, b irarrival i X W. h w hav followig ors: ( hor h arrival i has Γ -disribuio wi dsiy fucio fw ( x ( x ( λ λ! x >. hor 2 h irarrival is X, X2, ar idpdly xpoially disribud rado variabls wi parar λ. hor 3 Codiiod o N, rado variabls W, W2,, W hav oi dsiy probabiliy fucio! fw (,,, for., W N w w < w < < w hor 4 If Y is a rado variabl associad wi v i a Poisso procss wi parar λ. W assu a Y, Y 2, ar idpd, idpd of Poisso procss, ad shar coo disribuio fucio G( y PY ( y. h squc of pairs ( W, Y,( W2, Y2, is calld a ard Poisso procss. h ( W, Y,( W2, Y2, for a wo-disioal ohoogous Poisso poi procss i, y pla, whr a ubr of pois i a rgio A is giv by ( ( A g( ydy d. µ λ h ard Poisso procsss hav b applid i so goric probabiliy ara [3]. 4. Exapls of Poisso Procsss A Suppos ubr of calls o a pho ubr is a Poisso procss N, wi parar λ ad xp( µ is duraio of ach call. I is rasoabl o assu a is idpd of Poisso procss. Wha is probabiliy p a ( s call gs a busy sigal, i.. i cos wh usr is sill rspodig o call? For a fixd, ( ( ( λ λ x PW > W PW W < P X < λ dx ( ( ( λ µ ( λ µ λ ( µ d µ d µ p PW > W f d PW > W µ d λ µ 2 O avrag, how ay calls arriv wh usr is o pho? Suppos usr is alig o call, (, ] (, ] E N W W E N E N λ λ E N( W, W ] E[ λ ] λe[ ] µ 3 I a sigl srvr sys, cusors arriv i a ba accordig o a Poisso procss wi parar λ ad ach cusor spds xp( µ i wi o ad oly o ba llr. If llr is srvig a cusor, w cusors hav o wai i a quu ill llr fiishs srvig. How log o avrag dos llr srvs cusors up o i? (i.. How log is srvr uavailabl? N N λ E E N P( N E N ( λ! λ λ λ λ ( ( ( ( λ λ λ λ E λ λ λ! µ! µ! µ µ λx, for 32
3 K.-K. s 4 Suppos a A ad a B ar gagig i a spor copiio. h pois scord by a A follows a Poisso procss M wi parar λ ad pois scord by a B follows a Poisso procss N wi parar µ. Assu a M ad N ar idpd, wha is probabiliy a ga is? a A wis? a B wis? L b duraio of copiio. ( ga is ( (, P P M N P M N ( ( P M P N ( A wis ( > (, P P M N P M N ( ( P M P N ( B wis ( > (, P P N M P N M ( ( P N P M ( λ ( µ λ µ!! ( ( λ µ ( λ µ ( (!! µ λ ( µ λ!! 5 Giv a r ar pois scord i a ach (by bo a A ad a B, wha is probabiliy a a A scors pois, whr? ( (, (, ( λ ( µ! (! ( (! (! (, P( M N ( ( P M M N P M M N P M N P M P N P M N P M P N ( ( λ µ λµ λµ λ µ λ µ ( λ µ λµ 6 Wh dos a car accid happ? Suppos a sr is fro ws o as ad aor is fro sou o or, wo srs irsc a a poi O. Cars goig fro ws o as arrivs a O follows a Poisso procss W i wi parar λ ad cars goig fro sou o as arrivs a O follows a Poisso procss W wi parar µ. I is rasoabl o assu a s wo procsss ar idpd. If cars do slow dow ad sop a irscio O, collisio happs. h car goig fro sou o or his i car goig fro sou o as if ad oly if W i W Wi, whr is i i as for car's ail o rach O, has dsiy fucio f (. i ( ( ( ( λ x µ y x ( λ λ x µ µ y PWi W Wi dd yx x i!! ( car fro sou o or his i car fro ws o as PW ( i W Wi f ( d P i ( x ( i ( y ( λ x µ y x λ λ µ µ dd yx f( d x!! 33
4 K.-K. s P( car collisio P car fro sou o or his i car fro ws o as i, P i car fro ws o as his car fro sou o or i, i, x x i ( x ( i ( y ( λ x µ y λ λ µ µ!! ( y ( i ( x ( i dydx f ( d µ y λx y µ µ λ λ dd xy f( d y i,!! 7 Occurrcs of aural disasrs follow a Poisso procss wi parar λ. Suppos a i i as o rcovr ad rbuild afr disasr is Y, assu a Y, Y 2, ar idpd rado variabls havig coo disribuio fucios G( y PY ( y. hr ar N disasrs up o i, wha is probabiliy a vryig is bac o oral a i? his ca also b usd as a odl for isurac clais. W is i for isurac copay o rciv clai ad Y is i isurac copay as o sl i. Wha is probabiliy a isurac copay is o worig o ay clai a i? whr U,, U ( ax { } ax { } i N i N P( ax{ Wi Yi} < N ( ( P W Y < P W Y < N P N i i i i i ( λ (,, ( PU! Y<,, U Y < ( λ λ (,, ( λ λ! PW Y< W Y < N λ! PU Y< U Y < ar idpd ad uiforly disribud o (, ]. λ P( ax { Wi Yi} < PU ( Y < ( λ i N λ ( λ! PU Y < U u d u ( d λ P Y < uu u u ( λ ( d λ PY< u u ( λ λ G ( u du ( λ λ λ λ G ( z dz λ G z dz λ ( ( λ 8 Suppos a W is i a isurac copay rcivs clai ad Y is i copay as o sl clai. Wha is avrag i o sl all clais rcivd bfor i? h avrag i o sl all clais rcivd bfor is ( 34
5 K.-K. s Suppos, whr U,, U E ax { W Y}. N ( ( ( ax { } < ax { } < N N λ P( ax{ W Y} < N ( λ P W Y P W Y N P N! λ PW Y< W Y < N! (,, ( λ λ PU! Y <,, U Y <! ( ( λ ar idpd ad uiforly disribud o (, ]. λ P( ax { W Y} < PU ( Y < ( λ N ( N Clarly, { } PU Y< U u d u ( d λ P Y < uu u u ( λ λ PY ( u du ( λ < λ G( u du ( λ λ ( ( λ λ G( z dz ( λ P ax W Y < for <. λ λ λ G( z dz λ G z dz ( ( ax { } N E ax { W Y } P ax { W } d Y > N N P W Y > d λ d λ G( z dz 9 Cusors arriv a a shoppig all follows a Poisso procss wi parar λ. h i cusors spd i sor Y, Y 2, ar idpd rado variabls havig coo disribuio fucio G( y PY ( y. L M b ubr of cusors xis up o closig i. Wha is xpcd ubr of cusors i all a i? Codiio o N ad l W,, W b arrival i of cusors. h cusor xiss i all a i if ad oly if W Y. L rado variabl if W Y, if W Y <. { W Y } ( 35
6 K.-K. s h { } W Y if ad oly if whr U, U2,, U N P( M N P { W Y } N cusor xiss i all a i. hus { } { } P W Y N P U Y P U Y is ar idpd ad uiforly disribud o (, ]. { } bioial disribuio i which Hc, p PU ( Y PU ( Y U u d u PY ( d ( d uu u u PY u u G( u du G( z dz ( ( ( P M P M N P N ( ( λp ( p ( λ! (! ( λ! p ( p!!! λ λ p ( λp ( ( λp λ p λ!! ha is, ubr of cusors xisig a i has a Poisso disribuio wi a ( λp λ G y d. y h avrag ubr of cusors xis a all closig i is E[ M ]. λ G( y dy Cusors arrivig a a srvic cour follows a Poisso procss wi parar λ. L M b ubr of cusors srvd logr a up o i. Wha is disribuio of M? Codiio o N ad l W,, W b arrival i of cusors. L rado variabl if Y >, { Y > } if Y. h { Y > } if ad oly if λ cusor srvd logr a. hus N P( M N P { Y > } N P { Y > } N P { Y > }, 36
7 K.-K. s which is bioial disribuio wi p PY ( G( >. Hc, ( ( ( P M P M N P N ( ( λp ( p ( λ! (! ( λ! p ( p!!! λ λ p ( λp ( ( λp λ p λ!! ha is, ubr of cusors srvd logr a has a Poisso disribuio wi a 5. Coclusio ( ( λp λ G. Poisso procss is o of os ipora ools o odl aural phoo. So ipora disribuios aris fro Poisso procss: Poisso disribuio, xpoial disribuio ad Gaa disribuio. I is also usd o build or sophisicad rado procss. Rfrcs [] aylor, H.M. ad Karli, S. (998 A Iroducio o Sochasic Modlig. Acadic Prss, Wala. [2] Ross, S.M. (993 Iroducio o Probabiliy Modls. 5 Ediio, Acadic Prss, Wala. [3] Pros, M.D. (2 Cral Lii hors for -Nars Nighbor Disacs. Sochasic Procsss ad ir Applicaios, 85, hp://dx.doi.org/.6/s34-449(998- λ 37
8
1973 AP Calculus BC: Section I
97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f
Poisson Arrival Process
1 Poisso Arrival Procss Arrivals occur i) i a mmorylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = 1 λδ + ( Δ ) P o P j arrivals durig Δ = o Δ for j = 2,3, ( ) o Δ whr lim =
Poisson Arrival Process
Poisso Arrival Procss Arrivals occur i) i a mmylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = λδ + ( Δ ) P o P j arrivals durig Δ = o Δ f j = 2,3, o Δ whr lim =. Δ Δ C C 2 C
What Is the Difference between Gamma and Gaussian Distributions?
Applid Mahmaics,,, 85-89 hp://ddoiorg/6/am Publishd Oli Fbruary (hp://wwwscirporg/joural/am) Wha Is h Diffrc bw Gamma ad Gaussia Disribuios? iao-li Hu chool of Elcrical Egirig ad Compur cic, Uivrsiy of
Mixing time with Coupling
Mixig im wih Couplig Jihui Li Mig Zhg Saisics Dparm May 7 Goal Iroducio o boudig h mixig im for MCMC wih couplig ad pah couplig Prsig a simpl xampl o illusra h basic ida Noaio M is a Markov chai o fii
) and furthermore all X. The definition of the term stationary requires that the distribution fulfills the condition:
Assigm Thomas Aam, Spha Brumm, Haik Lor May 6 h, 3 8 h smsr, 357, 7544, 757 oblm For R b X a raom variabl havig ormal isribuio wih ma µ a variac σ (his is wri as ~ (,) X. by: R a. Is X ) a urhrmor all
Chapter 2 The Poisson Process
Chapr 2 Th oisso rocss 2. Expoial ad oisso disribuios 2... Th Birh Modl I scods, a oal of popl ar bor. Sarig a ay poi i im, wha is h waiig im for h firs birh? I milliscods, a oal of lpho calls arriv a
Modeling of the CML FD noise-to-jitter conversion as an LPTV process
Modlig of h CML FD ois-o-ir covrsio as a LPV procss Marko Alksic. Rvisio hisory Vrsio Da Comms. //4 Firs vrsio mrgd wo docums. Cyclosaioary Nois ad Applicaio o CML Frqucy Dividr Jir/Phas Nois Aalysis fil
( A) ( B) ( C) ( D) ( E)
d Smsr Fial Exam Worksh x 5x.( NC)If f ( ) d + 7, h 4 f ( ) d is 9x + x 5 6 ( B) ( C) 0 7 ( E) divrg +. (NC) Th ifii sris ak has h parial sum S ( ) for. k Wha is h sum of h sris a? ( B) 0 ( C) ( E) divrgs
Response of LTI Systems to Complex Exponentials
3 Fourir sris coiuous-im Rspos of LI Sysms o Complx Expoials Ouli Cosidr a LI sysm wih h ui impuls rspos Suppos h ipu sigal is a complx xpoial s x s is a complx umbr, xz zis a complx umbr h or h h w will
Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions
IOSR Joural of Applid Chmisr IOSR-JAC -ISSN: 78-576.Volum 9 Issu 8 Vr. I Aug. 6 PP 4-8 www.iosrjourals.org Numrical Simulaio for h - Ha Equaio wih rivaiv Boudar Codiios Ima. I. Gorial parm of Mahmaics
THE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE 1
TH ROAL TATITICAL OCIT 6 AINATION OLTION GRADAT DILOA ODL T oci i providig olio o ai cadida prparig or aiaio i 7. T olio ar idd a larig aid ad old o b a "odl awr". r o olio old alwa b awar a i a ca r ar
8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system
8. Quug sysms Cos 8. Quug sysms Rfrshr: Sml lraffc modl Quug dscl M/M/ srvr wag lacs Alcao o ack lvl modllg of daa raffc M/M/ srvrs wag lacs lc8. S-38.45 Iroduco o Tlraffc Thory Srg 5 8. Quug sysms 8.
Fourier Series: main points
BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca
Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
Continous system: differential equations
/6/008 Coious sysm: diffrial quaios Drmiisic modls drivaivs isad of (+)-( r( compar ( + ) R( + r ( (0) ( R ( 0 ) ( Dcid wha hav a ffc o h sysm Drmi whhr h paramrs ar posiiv or gaiv, i.. giv growh or rducio
Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Par B: rasform Mhods Profssor E. Ambikairaah UNSW, Ausralia Chapr : Fourir Rprsaio of Sigal. Fourir Sris. Fourir rasform.3 Ivrs Fourir rasform.4 Propris.4. Frqucy Shif.4. im Shif.4.3 Scalig.4.4 Diffriaio
Chapter 3 Linear Equations of Higher Order (Page # 144)
Ma Modr Dirial Equaios Lcur wk 4 Jul 4-8 Dr Firozzama Darm o Mahmaics ad Saisics Arizoa Sa Uivrsi This wk s lcur will covr har ad har 4 Scios 4 har Liar Equaios o Highr Ordr Pag # 44 Scio Iroducio: Scod
(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is
[STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
Software Development Cost Model based on NHPP Gompertz Distribution
Idia Joural of Scic ad Tchology, Vol 8(12), DOI: 10.17485/ijs/2015/v8i12/68332, Ju 2015 ISSN (Pri) : 0974-6846 ISSN (Oli) : 0974-5645 Sofwar Dvlopm Cos Modl basd o NHPP Gomprz Disribuio H-Chul Kim 1* ad
x, x, e are not periodic. Properties of periodic function: 1. For any integer n,
Chpr Fourir Sri, Igrl, d Tror. Fourir Sri A uio i lld priodi i hr i o poiiv ur p uh h p, p i lld priod o R i,, r priodi uio.,, r o priodi. Propri o priodi uio:. For y igr, p. I d g hv priod p, h h g lo
Probability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
ELECTROMAGNETIC COMPATIBILITY HANDBOOK 1. Chapter 12: Spectra of Periodic and Aperiodic Signals
ELECTOMAGNETIC COMPATIBILITY HANDBOOK Chapr : Spcra of Priodic ad Apriodic Sigals. Drmi whhr ach of h followig fucios ar priodic. If hy ar priodic, provid hir fudamal frqucy ad priod. a) x 4cos( 5 ) si(
2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function
Chapr VII Spcial Fucios Ocobr 7, 7 479 CHAPTER VII SPECIAL FUNCTIONS Cos: Havisid sp fucio, filr fucio Dirac dla fucio, modlig of impuls procsss 3 Si igral fucio 4 Error fucio 5 Gamma fucio E Epoial igral
EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D. S. Palimkar
Ieraioal Joural of Scieific ad Research Publicaios, Volue 2, Issue 7, July 22 ISSN 225-353 EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D S Palikar Depare of Maheaics, Vasarao Naik College, Naded
Nuclear Chemistry -- ANSWERS
Hoor Chstry Mr. Motro 5-6 Probl St Nuclar Chstry -- ANSWERS Clarly wrt aswrs o sparat shts. Show all work ad uts.. Wrt all th uclar quatos or th radoactv dcay srs o Urau-38 all th way to Lad-6. Th dcay
EE Control Systems LECTURE 11
Up: Moy, Ocor 5, 7 EE 434 - Corol Sy LECTUE Copyrigh FL Lwi 999 All righ rrv POLE PLACEMET A STEA-STATE EO Uig fc, o c ov h clo-loop pol o h h y prforc iprov O c lo lc uil copor o oi goo y- rcig y uyig
DETERMINATION OF THERMAL STRESSES OF A THREE DIMENSIONAL TRANSIENT THERMOELASTIC PROBLEM OF A SQUARE PLATE
DRMINAION OF HRMAL SRSSS OF A HR DIMNSIONAL RANSIN HRMOLASIC PROBLM OF A SQUAR PLA Wrs K. D Dpr o Mics Sr Sivji Co Rjr Mrsr Idi *Aor or Corrspodc ABSRAC prs ppr ds wi driio o prr disribio ow prr poi o
OPTIMUM ORDER QUANTITY FOR DETERIORATING ITEMS IN LARGEST LIFETIME WITH PERMISSIBLE DELAY PERIOD S. C. SHARMA & VIVEK VIJAY
Iraioal Joural of Mahaics a opur Applicaios Rsarch (IJMAR) ISSN(P): 9-6955; ISSN(E): 9-86 Vol. 6, Issu, Aug 6, - @JPR Pv. L. OPIMUM ORDER QUANIY FOR DEERIORAING IEMS IN LARGES LIFEIME WIH PERMISSIBLE DELAY
ON H-TRICHOTOMY IN BANACH SPACES
CODRUTA STOICA IHAIL EGA O H-TRICHOTOY I BAACH SPACES Absrac: I his papr w mphasiz h oio of skw-oluio smiflows cosidrd a gralizaio of smigroups oluio opraors ad skw-produc smiflows which aris i h sabiliy
Motivation. We talk today for a more flexible approach for modeling the conditional probabilities.
Baysia Ntworks Motivatio Th coditioal idpdc assuptio ad by aïv Bays classifirs ay s too rigid spcially for classificatio probls i which th attributs ar sowhat corrlatd. W talk today for a or flibl approach
(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
On The Eneström-Kakeya Theorem
Applied Mahemaics,, 3, 555-56 doi:436/am673 Published Olie December (hp://wwwscirporg/oural/am) O The Eesröm-Kakeya Theorem Absrac Gulsha Sigh, Wali Mohammad Shah Bharahiar Uiversiy, Coimbaore, Idia Deparme
UNIT III STANDARD DISTRIBUTIONS
UNIT III STANDARD DISTRIBUTIONS Biomial, Poisso, Normal, Gomric, Uiform, Eoial, Gamma disribuios ad hir roris. Prard by Dr. V. Valliammal Ngaiv biomial disribuios Prard by Dr.A.R.VIJAYALAKSHMI Sadard Disribuios
EXERCISE - 01 CHECK YOUR GRASP
DEFNTE NTEGRATON EXERCSE - CHECK YOUR GRASP. ( ) d [ ] d [ ] d d ƒ( ) ƒ '( ) [ ] [ ] 8 5. ( cos )( c)d 8 ( cos )( c)d + 8 ( cos )( c) d 8 ( cos )( c) d sic + cos 8 is lwys posiiv f() d ( > ) ms f() is
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
The Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations,
Shiraz Uivrsiy of Tchology From h SlcdWorks of Habibolla Laifizadh Th Dvlopm of Suiabl ad Wll-foudd Numrical Mhods o Solv Sysms of Igro- Diffrial Equaios, Habibolla Laifizadh, Shiraz Uivrsiy of Tchology
Exercise 3 Stochastic Models of Manufacturing Systems 4T400, 6 May
Exercise 3 Sochasic Models of Maufacurig Sysems 4T4, 6 May. Each week a very popular loery i Adorra pris 4 ickes. Each ickes has wo 4-digi umbers o i, oe visible ad he oher covered. The umbers are radomly
An Asymptotic Expansion for the Non-Central Chi-square Distribution. By Jinan Hamzah Farhood Department of Mathematics College of Education
A Asypoic Expasio fo h o-cal Chi-squa Disibuio By Jia Hazah ahood Dpa of Mahaics Collg of Educaio 6 Absac W div a asypoic xpasio fo h o-cal chi-squa disibuio as wh X i is h o-cal chi-squa vaiabl wih dg
The Exile Began. Family Journal Page. God Called Jeremiah Jeremiah 1. Preschool. below. Tell. them too. Kids. Ke Passage: Ezekiel 37:27
Faily Jo Pag Th Exil Bg io hy u c prof b jo ou Shar ab ou job ab ar h o ay u Yo ra u ar u r a i A h ) ar par ( grp hav h y y b jo i crib blo Tll ri ir r a r gro up Allo big u r a i Rvi h b of ha u ha a
APPENDIX: STATISTICAL TOOLS
I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.
From Fourier Series towards Fourier Transform
From Fourir Sris owards Fourir rasform D D d D, d wh lim Dparm of Elcrical ad Compur Eiri D, d wh lim L s Cosidr a fucio G d W ca xprss D i rms of Gw D G Dparm of Elcrical ad Compur Eiri D G G 3 Dparm
1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
Institute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
Actuarial Society of India
Acuarial Sociey of Idia EXAMINAIONS Jue 5 C4 (3) Models oal Marks - 5 Idicaive Soluio Q. (i) a) Le U deoe he process described by 3 ad V deoe he process described by 4. he 5 e 5 PU [ ] PV [ ] ( e ).538!
, R we have. x x. ) 1 x. R and is a positive bounded. det. International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:06 11
raioal Joral of asic & ppli Scics JS-JENS Vol: No:6 So Dirichl ors a Pso Diffrial Opraors wih Coiioall Epoial Cov cio aa. M. Kail Dpar of Mahaics; acl of Scic; Ki laziz Uivrsi Jah Sai raia Eail: fkail@ka..sa
ECE594I Notes set 6: Thermal Noise
C594I ots, M. odwll, copyrightd C594I Nots st 6: Thrmal Nois Mark odwll Uivrsity of Califoria, ata Barbara rodwll@c.ucsb.du 805-893-344, 805-893-36 fax frcs ad Citatios: C594I ots, M. odwll, copyrightd
Note 6 Frequency Response
No 6 Frqucy Rpo Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada. alyical Exprio
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics
![F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics](/thumbs/89/97771684.jpg "F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics")
F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mahemaics Prelim Quesio Paper Soluio Q. Aemp ay FIVE of he followig : [0] Q.(a) Defie Eve ad odd fucios. [] As.: A fucio f() is said o be eve fucio if
Microscopic Flow Characteristics Time Headway - Distribution
CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,
MA6451-PROBABILITY AND RANDOM PROCESSES
MA645-PROBABILITY AND RANDOM PROCESSES UNIT I RANDOM VARIABLES Dr. V. Valliammal Darm of Alid Mahmaics Sri Vkaswara Collg of Egirig Radom variabl Radom Variabls A ral variabl whos valu is drmid by h oucom
Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
Mathematical Preliminaries for Transforms, Subbands, and Wavelets
Mahmaical Prlimiaris for rasforms, Subbads, ad Wavls C.M. Liu Prcpual Sigal Procssig Lab Collg of Compur Scic Naioal Chiao-ug Uivrsiy hp://www.csi.cu.du.w/~cmliu/courss/comprssio/ Offic: EC538 (03)5731877
Series of New Information Divergences, Properties and Corresponding Series of Metric Spaces
Srs of Nw Iforao Dvrgcs, Proprs ad Corrspodg Srs of Mrc Spacs K.C.Ja, Praphull Chhabra Profssor, Dpar of Mahacs, Malavya Naoal Isu of Tchology, Japur (Rajasha), Ida Ph.d Scholar, Dpar of Mahacs, Malavya
Ring of Large Number Mutually Coupled Oscillators Periodic Solutions
Iraioal Joural of horical ad Mahmaical Physics 4, 4(6: 5-9 DOI: 59/jijmp446 Rig of arg Numbr Muually Coupld Oscillaors Priodic Soluios Vasil G Aglov,*, Dafika z Aglova Dparm Nam of Mahmaics, Uivrsiy of
PURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b
![4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b](/thumbs/71/65779443.jpg "4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b")
4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs
Laguerre wavelet and its programming
Iraioal Joural o Mahaics rds ad chology (IJM) Volu 49 Nubr Spbr 7 agurr l ad is prograig B Sayaaraya Y Pragahi Kuar Asa Abdullah 3 3 Dpar o Mahaics Acharya Nagarjua Uivrsiy Adhra pradsh Idia Dpar o Mahaics
LINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS
Diol Bgyoko (0) I.INTRODUCTION LINEAR d ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS I. Dfiiio All suh diffril quios s i h sdrd or oil form: y + y + y Q( x) dy d y wih y d y d dx dx whr,, d
A Simple Representation of the Weighted Non-Central Chi-Square Distribution
SSN: 9-875 raoa Joura o ovav Rarch Scc grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr A S Rrao o h Wgh No-Cra Ch-Squar Drbuo Dr ay A hry Dr Sahar A brah Dr Ya Y Aba Proor D o Mahaca Sac u o Saca Su a Rarch
Web-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite
Wb-basd Supplmary Marials for Sampl siz cosidraios for GEE aalyss of hr-lvl clusr radomizd rials by Sv Trsra, Big Lu, oh S. Prissr, Tho va Achrbrg, ad Gorg F. Borm Wb-appdix : macro o calcula h rag of
Lecture 15 First Properties of the Brownian Motion
Lecure 15: Firs Properies 1 of 8 Course: Theory of Probabiliy II Term: Sprig 2015 Isrucor: Gorda Zikovic Lecure 15 Firs Properies of he Browia Moio This lecure deals wih some of he more immediae properies
Poisson process Markov process
E2200 Quuing hory and lraffic 2nd lcur oion proc Markov proc Vikoria Fodor KTH Laboraory for Communicaion nwork, School of Elcrical Enginring 1 Cour oulin Sochaic proc bhind quuing hory L2-L3 oion proc
Infinite Continued Fraction (CF) representations. of the exponential integral function, Bessel functions and Lommel polynomials
Ifii Coiu Fraio CF rraio of h oial igral fuio l fuio a Lol olyoial Coiu Fraio CF rraio a orhogoal olyoial I hi io w rall h rlaio bw ifi rurry rlaio of olyoial orroig orhogoaliy a aroria ifii oiu fraio
Continuous probability distributions
Continuous probability distributions Many continuous probability distributions, including: Uniform Normal Gamma Eponntial Chi-Squard Lognormal Wibull EGR 5 Ch. 6 Uniform distribution Simplst charactrizd
ENGG 1203 Tutorial. Difference Equations. Find the Pole(s) Finding Equations and Poles
ENGG 03 Tutoial Systms ad Cotol 9 Apil Laig Obctivs Z tasfom Complx pols Fdbac cotol systms Ac: MIT OCW 60, 6003 Diffc Equatios Cosid th systm pstd by th followig diffc quatio y[ ] x[ ] (5y[ ] 3y[ ]) wh
Time : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
Practice papers A and B, produced by Edexcel in 2009, with mark schemes. Practice Paper A. 5 cosh x 2 sinh x = 11,
Prai paprs A ad B, produd by Edl i 9, wih mark shms Prai Papr A. Fid h valus of for whih 5 osh sih =, givig your aswrs as aural logarihms. (Toal 6 marks) k. A = k, whr k is a ral osa. 9 (a) Fid valus of
Moment Generating Function
1 Mome Geeraig Fucio m h mome m m m E[ ] x f ( x) dx m h ceral mome m m m E[( ) ] ( ) ( x ) f ( x) dx Mome Geeraig Fucio For a real, M () E[ e ] e k x k e p ( x ) discree x k e f ( x) dx coiuous Example
CSE 202: Design and Analysis of Algorithms Lecture 16
CSE 202: Desig ad Aalysis of Algorihms Lecure 16 Isrucor: Kamalia Chaudhuri Iequaliy 1: Marov s Iequaliy Pr(X=x) Pr(X >= a) 0 x a If X is a radom variable which aes o-egaive values, ad a > 0, he Pr[X a]
Further Results on Pair Sum Graphs
Applid Mathmatis, 0,, 67-75 http://dx.doi.org/0.46/am.0.04 Publishd Oli Marh 0 (http://www.sirp.org/joural/am) Furthr Rsults o Pair Sum Graphs Raja Poraj, Jyaraj Vijaya Xavir Parthipa, Rukhmoi Kala Dpartmt
OTHER TPOICS OF INTEREST (Convection BC, Axisymmetric problems, 3D FEM)
OTHER TPOICS OF INTEREST (Convction BC, Axisymmtric problms, 3D FEM) CONTENTS 2-D Problms with convction BC Typs of Axisymmtric Problms Axisymmtric Problms (2-D) 3-D Hat Transfr 3-D Elasticity Typical
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.265/15.070J Fall 2013 Lecture 4 9/16/2013. Applications of the large deviation technique
MASSACHUSETTS ISTITUTE OF TECHOLOGY 6.265/5.070J Fall 203 Lecure 4 9/6/203 Applicaios of he large deviaio echique Coe.. Isurace problem 2. Queueig problem 3. Buffer overflow probabiliy Safey capial for
Chap 2: Reliability and Availability Models
Chap : lably ad valably Modls lably = prob{s s fully fucog [,]} Suppos from [,] m prod, w masur ou of N compos, of whch N : # of compos oprag corrcly a m N f : # of compos whch hav fald a m rlably of h
EE415/515 Fundamentals of Semiconductor Devices Fall 2012
3 EE4555 Fudmls of Smicoducor vics Fll cur 8: PN ucio iod hr 8 Forwrd & rvrs bis Moriy crrir diffusio Brrir lowrd blcd by iffusio rducd iffusio icrsd mioriy crrir drif rif hcd 3 EE 4555. E. Morris 3 3
Paper Introduction. ~ Modelling the Uncertainty in Recovering Articulation from Acoustics ~ Korin Richmond, Simon King, and Paul Taylor.
Paper Iroducio ~ Modellig he Uceraiy i Recoverig Ariculaio fro Acousics ~ Kori Richod, Sio Kig, ad Paul Taylor Tooi Toda Noveber 6, 2003 Proble Addressed i This Paper Modellig he acousic-o-ariculaory appig
Strictly as per the compliance and regulations of :
Global Joural of Scic Froir Rsarch Mahaics & Dcisio Scics Volu Issu Vrsio. Typ : Doubl lid Pr Rviwd Iraioal Rsarch Joural Publishr: Global Jourals Ic. US Oli ISSN: 9-66 & i ISSN: 975-5896 Oscillaory Fr
DISTRIBUTION OF DIFFERENCE BETWEEN INVERSES OF CONSECUTIVE INTEGERS MODULO P
DISTRIBUTION OF DIFFERENCE BETWEEN INVERSES OF CONSECUTIVE INTEGERS MODULO P Tsz Ho Chan Dartmnt of Mathmatics, Cas Wstrn Rsrv Univrsity, Clvland, OH 4406, USA txc50@cwru.du Rcivd: /9/03, Rvisd: /9/04,
NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES
Digst Joural of Naomatrials ad Biostructurs Vol 4, No, March 009, p 67-76 NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES A IRANMANESH a*, O KHORMALI b, I NAJAFI KHALILSARAEE c, B SOLEIMANI
ECEN620: Network Theory Broadband Circuit Design Fall 2014
ECE60: work Thory Broadbad Circui Dig Fall 04 Lcur 6: PLL Trai Bhavior Sam Palrmo Aalog & Mixd-Sigal Cr Txa A&M Uivriy Aoucm, Agda, & Rfrc HW i du oday by 5PM PLL Trackig Rpo Pha Dcor Modl PLL Hold Rag
5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t
AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =
On a problem of J. de Graaf connected with algebras of unbounded operators de Bruijn, N.G.
O a problm of J. d Graaf coctd with algbras of uboudd oprators d Bruij, N.G. Publishd: 01/01/1984 Documt Vrsio Publishr s PDF, also kow as Vrsio of Rcord (icluds fial pag, issu ad volum umbrs) Plas chck
Big O Notation for Time Complexity of Algorithms
BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time
Advanced Queueing Theory. M/G/1 Queueing Systems
Advand Quung Thory Ths slds ar rad by Dr. Yh Huang of Gorg Mason Unvrsy. Sudns rgsrd n Dr. Huang's ourss a GMU an ma a sngl mahn-radabl opy and prn a sngl opy of ah sld for hr own rfrn, so long as ah sld
Derangements and Applications
2 3 47 6 23 Journal of Intgr Squncs, Vol. 6 (2003), Articl 03..2 Drangmnts and Applications Mhdi Hassani Dpartmnt of Mathmatics Institut for Advancd Studis in Basic Scincs Zanjan, Iran mhassani@iasbs.ac.ir
BE.430 Tutorial: Linear Operator Theory and Eigenfunction Expansion
BE.43 Tuorial: Liear Operaor Theory ad Eigefucio Expasio (adaped fro Douglas Lauffeburger) 9//4 Moivaig proble I class, we ecouered parial differeial equaios describig rasie syses wih cheical diffusio.
Lectures 9 IIR Systems: First Order System
EE3054 Sigals ad Systms Lcturs 9 IIR Systms: First Ordr Systm Yao Wag Polytchic Uivrsity Som slids icludd ar xtractd from lctur prstatios prpard by McCllla ad Schafr Lics Ifo for SPFirst Slids This work
u 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
8(4 m0) ( θ ) ( ) Solutions for HW 8. Chapter 25. Conceptual Questions
Solutios for HW 8 Captr 5 Cocptual Qustios 5.. θ dcrass. As t crystal is coprssd, t spacig d btw t plas of atos dcrass. For t first ordr diffractio =. T Bragg coditio is = d so as d dcrass, ust icras for
Mathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem
Mahmacal ascs 8 Chapr VIII amplg Dsrbos ad h Cral Lm Thorm Fcos of radom arabls ar sall of rs sascal applcao Cosdr a s of obsrabl radom arabls L For ampl sppos h arabls ar a radom sampl of s from a poplao
S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]
![S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]](/thumbs/92/108666103.jpg "S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]")
S.Y. B.Sc. (IT) : Sm. III Applid Mahmaics Tim : ½ Hrs.] Prlim Qusion Papr Soluion [Marks : 75 Q. Amp h following (an THREE) 3 6 Q.(a) Rduc h mari o normal form and find is rank whr A 3 3 5 3 3 3 6 Ans.:
Fractal diffusion retrospective problems
Iraoa ora o App Mahac croc a Copr Avac Tchoo a Scc ISSN: 47-8847-6799 wwwaccor/iamc Ora Rarch Papr Fraca o rropcv prob O Yaro Rcv 6 h Ocobr 3 Accp 4 h aar 4 Abrac: I h arc w h rropcv vr prob Th rropcv
Types Ideals on IS-Algebras
Ieraioal Joural of Maheaical Aalyi Vol. 07 o. 3 635-646 IARI Ld www.-hikari.co hp://doi.org/0.988/ija.07.7466 Type Ideal o IS-Algebra Sudu Najah Jabir Faculy of Educaio ufa Uiveriy Iraq Copyrigh 07 Sudu
Midterm Examination (100 pts)
Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion
SAN JOSE CITY COLLEGE PHYSICAL EDUCATION BUILDING AND RENOVATED LAB BUILDING SYMBOL LIST & GENERAL NOTES - MECHANICAL
S SRUUR OR OORO SU sketch SYO SRPO OO OU O SUPPOR YP SUPPOR O UR SOS OVR SOS (xwx) X W (S) RR RWS U- R R OR ROO OR P S SPR SO S OS OW "Wx00"x0" 000.0, 8/7.0 Z U- R R UPPR ROO S S S SPR SO S OS OW 0"Wx0"x90"
Weights Interpreting W and lnw What is β? Some Endnotes = n!ω if we neglect the zero point energy then ( )
Sprg Ch 35: Statstcal chacs ad Chcal Ktcs Wghts... 9 Itrprtg W ad lw... 3 What s?... 33 Lt s loo at... 34 So Edots... 35 Chaptr 3: Fudatal Prcpls of Stat ch fro a spl odl (drvato of oltza dstrbuto, also
General Notes About 2007 AP Physics Scoring Guidelines
AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation