14. Poisson Processes
|
|
- Randell Farmer
- 6 years ago
- Views:
Transcription
1 4. Posso Processes I Lecure 4 we roduced Posso arrvals as he lmg behavor of Bomal radom varables. Refer o Posso approxmao of Bomal radom varables. From he dscusso here see Lecure 4 " arrvals occur a P e erval of durao "! 0 4- where p µ T µ T 4- arrvals arrvals 0 T Fg T
2 I follows ha refer o Fg. 4. " arrvals occur a 0 P e erval of durao "! 4-3 sce ha case p µ T µ. 4-4 T From Posso arrvals over a erval form a Posso radom varable whose parameer depeds o he durao of ha erval. Moreover because of he Beroull aure of he uderlyg basc radom arrvals eves over ooverlappg ervals are depede. We shall use hese wo ey observaos o defe a Posso process formally. Refer o Example 9-5 Tex Defo: 0 represes a Posso process f he umber of arrvals a erval of legh s a Posso radom varable wh parameer. Thus
3 P{ } e 0 4-5! ad If he ervals ad 3 4 are ooverlappg he he radom varables ad 3 4 are depede. Sce 0 ~ P we have ad E[ E[ ] E[ 0 ] 4-6 ] E[ 0 ] To deerme he auocorrelao fuco R le > he from above 0 ad are depede Posso radom varables wh parameers ad respecvely. Thus E[ 0 ] E[ 0 ] E[ ]
4 4 Bu ad hece he lef sde f 4-8 ca be rewre as Usg ogeher wh 4-8 we oba Smlarly Thus 0 0 ]. [ }] { [ E R E 4-9. ] [ E R R < +. m R +
5 Posso arrvals From 4- oce ha he Posso process does o represe a wde sese saoary process. 0 Y Defe a bary level process Y + Fg ha represes a elegraph sgal Fg. 4.. Noce ha he raso sas { } are radom. see Example 9-6 Tex for he mea ad auocorrelao fuco of a elegraph sgal. Alhough does o represe a wde sese saoary process 5
6 s dervave does represe a wde sese saoary process. d d Fg. 4.3 Dervave as a LTI sysem To see hs we ca mae use of Fg. 4.7 ad From here dµ d µ d d a cosa 4-4 ad R R + > U ad R R +. δ 4-6 6
7 From 4-4 ad 4-6 follows ha s a wde sese saoary process. Thus osaoary pus o lear sysems ca lead o wde sese saoary oupus a eresg observao. Sum of Posso Processes: If ad represe wo depede Posso processes he her sum + s also a Posso process wh parameer Follows from 6-86 Tex ad he defo +. of he Posso process ad. Radom seleco of Posso Pos: Le represe radom arrval pos assocaed wh a Posso process wh parameer ad assocaed wh each arrval po defe a depede Beroull radom Fg. 4.4 varable N where P N p P N 0 q p
8 8 Defe he processes we clam ha boh Y ad Z are depede Posso processes wh parameers ad respecvely. Proof: Bu gve we have so ha ad Subsug o 4-9 we ge p q P Y P Y }. { } { 4-9 ; Y N Z N Y 4-8 ~ p B N Y { } 0 P Y p q 4-0 { }.! P e 4-
9 pe PY { } e pq! q!!!!! q e p p p e 0!! ~ P p. 4- More geerally e q P{ Y Z m} P{ Y Y m} PY { + m} PY { + mp } { + m} + m m m p p q q + pq e e e + m!! m! PY PZ m PY { } PZ { m} 4-3 9
10 whch complees he proof. Noce ha Y ad Z are geeraed as a resul of radom Beroull selecos from he orgal Posso process Fg. 4.5 where each arrval ges ossed over o eher Y wh probably p or o Z wh probably q. Each such sub-arrval sream s also p p p Y ~ P p p a Posso process. Thus ~ P radom seleco of Posso pos preserve he Posso aure of he resulg q q processes. However as we shall see deermsc seleco from a Posso Z ~ P process desroys he Posso Fg. 4.5 propery for he resulg processes. q 0
11 τ Ier-arrval Dsrbuo for Posso Processes Le deoe he me erval delay d o he frs arrval from ay fxed po I s arrval 0. To deerme he probably 0 τ dsrbuo of he radom varable τ we argue as follows: Observe ha Fg. 4.6 he eve " τ > " s he same as or he compleme eve " τ " s he same as he eve > 0. Hece he dsrbuo fuco of τ s gve by F P{ τ } P{ > 0} P{ + > 0} τ 0 0 P { + 0} e 0 0 h arrval 4-4 use 4-5 ad hece s dervave gves he probably desy fuco for τ o be dfτ fτ e d.e. τ s a expoeal radom varable wh parameer so ha E τ /.
12 Smlarly le represe he h radom arrval po for a Posso process. The F P{ } P{ } ad hece P{ < } e! df x x x f x e + e dx!! x x x x e x 0! whch represes a gamma desy fuco..e. he wag me o he h Posso arrval sa has a gamma dsrbuo. Moreover τ
13 where τ s he radom er-arrval durao bewee he h ad h eves. Noce ha τ s are depede decally dsrbued radom varables. Hece usg her characersc fucos follows ha all er-arrval duraos of a Posso process are depede expoeal radom varables wh commo parameer..e. f e τ Aleravely from we have s a expoeal radom varable. By repeag ha argume afer shfg 0 o he ew po Fg. 4.6 we coclude ha τ s a expoeal radom varable. Thus he sequece τ are depede τ τ expoeal radom varables wh commo p.d.f as 4-5. τ Thus f we sysemacally ag every m h oucome of a Posso process wh parameer o geerae a ew process e he he er-arrval me bewee ay wo eves of e s a gamma radom varable. 3
14 Noce ha E[ e ] m / ad f mµ he E[ e ] / µ. The er-arrval me of e ha case represes a Erlag-m radom varable ad e a Erlag-m process see 0-90 Tex. I summary f Posso arrvals are radomly redreced o form ew queues he each such queue geeraes a ew Posso process Fg However f he arrvals are sysemacally redreced I s arrval o I s couer d arrval o d couer m h o m h m + s arrval o I s couer he he ew subqueues form Erlag-m processes. Ieresgly we ca also derve he ey Posso properes 4-5 ad 4-5 by sarg from a smple axomac approach as show below: 4
The Poisson Process Properties of the Poisson Process
Posso Processes Summary The Posso Process Properes of he Posso Process Ierarrval mes Memoryless propery ad he resdual lfeme paradox Superposo of Posso processes Radom seleco of Posso Pos Bulk Arrvals ad
More informationContinuous Time Markov Chains
Couous me Markov chas have seay sae probably soluos f a oly f hey are ergoc, us lke scree me Markov chas. Fg he seay sae probably vecor for a couous me Markov cha s o more ffcul ha s he scree me case,
More information8. Queueing systems lect08.ppt S Introduction to Teletraffic Theory - Fall
8. Queueg sysems lec8. S-38.45 - Iroduco o Teleraffc Theory - Fall 8. Queueg sysems Coes Refresher: Smle eleraffc model M/M/ server wag laces M/M/ servers wag laces 8. Queueg sysems Smle eleraffc model
More informationSolution. The straightforward approach is surprisingly difficult because one has to be careful about the limits.
ose ad Varably Homewor # (8), aswers Q: Power spera of some smple oses A Posso ose A Posso ose () s a sequee of dela-fuo pulses, eah ourrg depedely, a some rae r (More formally, s a sum of pulses of wdh
More information(1) Cov(, ) E[( E( ))( E( ))]
Impac of Auocorrelao o OLS Esmaes ECON 3033/Evas Cosder a smple bvarae me-seres model of he form: y 0 x The four key assumpos abou ε hs model are ) E(ε ) = E[ε x ]=0 ) Var(ε ) =Var(ε x ) = ) Cov(ε, ε )
More informationLeast Squares Fitting (LSQF) with a complicated function Theexampleswehavelookedatsofarhavebeenlinearintheparameters
Leas Squares Fg LSQF wh a complcaed fuco Theeampleswehavelookedasofarhavebeelearheparameers ha we have bee rg o deerme e.g. slope, ercep. For he case where he fuco s lear he parameers we ca fd a aalc soluo
More informationFault Tolerant Computing. Fault Tolerant Computing CS 530 Probabilistic methods: overview
Probably 1/19/ CS 53 Probablsc mehods: overvew Yashwa K. Malaya Colorado Sae Uversy 1 Probablsc Mehods: Overvew Cocree umbers presece of uceray Probably Dsjo eves Sascal depedece Radom varables ad dsrbuos
More informationAML710 CAD LECTURE 12 CUBIC SPLINE CURVES. Cubic Splines Matrix formulation Normalised cubic splines Alternate end conditions Parabolic blending
CUIC SLINE CURVES Cubc Sples Marx formulao Normalsed cubc sples Alerae ed codos arabolc bledg AML7 CAD LECTURE CUIC SLINE The ame sple comes from he physcal srume sple drafsme use o produce curves A geeral
More informationInternational Journal Of Engineering And Computer Science ISSN: Volume 5 Issue 12 Dec. 2016, Page No.
www.jecs. Ieraoal Joural Of Egeerg Ad Compuer Scece ISSN: 19-74 Volume 5 Issue 1 Dec. 16, Page No. 196-1974 Sofware Relably Model whe mulple errors occur a a me cludg a faul correco process K. Harshchadra
More informationReal-Time Systems. Example: scheduling using EDF. Feasibility analysis for EDF. Example: scheduling using EDF
EDA/DIT6 Real-Tme Sysems, Chalmers/GU, 0/0 ecure # Updaed February, 0 Real-Tme Sysems Specfcao Problem: Assume a sysem wh asks accordg o he fgure below The mg properes of he asks are gve he able Ivesgae
More informationFundamentals of Speech Recognition Suggested Project The Hidden Markov Model
. Projec Iroduco Fudameals of Speech Recogo Suggesed Projec The Hdde Markov Model For hs projec, s proposed ha you desg ad mpleme a hdde Markov model (HMM) ha opmally maches he behavor of a se of rag sequeces
More informationFALL HOMEWORK NO. 6 - SOLUTION Problem 1.: Use the Storage-Indication Method to route the Input hydrograph tabulated below.
Jorge A. Ramírez HOMEWORK NO. 6 - SOLUTION Problem 1.: Use he Sorage-Idcao Mehod o roue he Ipu hydrograph abulaed below. Tme (h) Ipu Hydrograph (m 3 /s) Tme (h) Ipu Hydrograph (m 3 /s) 0 0 90 450 6 50
More informationQR factorization. Let P 1, P 2, P n-1, be matrices such that Pn 1Pn 2... PPA
QR facorzao Ay x real marx ca be wre as AQR, where Q s orhogoal ad R s upper ragular. To oba Q ad R, we use he Householder rasformao as follows: Le P, P, P -, be marces such ha P P... PPA ( R s upper ragular.
More informationCyclone. Anti-cyclone
Adveco Cycloe A-cycloe Lorez (963) Low dmesoal aracors. Uclear f hey are a good aalogy o he rue clmae sysem, bu hey have some appealg characerscs. Dscusso Is he al codo balaced? Is here a al adjusme
More information-distributed random variables consisting of n samples each. Determine the asymptotic confidence intervals for
Assgme Sepha Brumme Ocober 8h, 003 9 h semeser, 70544 PREFACE I 004, I ed o sped wo semesers o a sudy abroad as a posgraduae exchage sude a he Uversy of Techology Sydey, Ausrala. Each opporuy o ehace my
More informationFORCED VIBRATION of MDOF SYSTEMS
FORCED VIBRAION of DOF SSES he respose of a N DOF sysem s govered by he marx equao of moo: ] u C] u K] u 1 h al codos u u0 ad u u 0. hs marx equao of moo represes a sysem of N smulaeous equaos u ad s me
More informationDensity estimation. Density estimations. CS 2750 Machine Learning. Lecture 5. Milos Hauskrecht 5329 Sennott Square
Lecure 5 esy esmao Mlos Hauskrec mlos@cs..edu 539 Seo Square esy esmaos ocs: esy esmao: Mamum lkelood ML Bayesa arameer esmaes M Beroull dsrbuo. Bomal dsrbuo Mulomal dsrbuo Normal dsrbuo Eoeal famly Noaramerc
More informationMoments of Order Statistics from Nonidentically Distributed Three Parameters Beta typei and Erlang Truncated Exponential Variables
Joural of Mahemacs ad Sascs 6 (4): 442-448, 200 SSN 549-3644 200 Scece Publcaos Momes of Order Sascs from Nodecally Dsrbued Three Parameers Bea ype ad Erlag Trucaed Expoeal Varables A.A. Jamoom ad Z.A.
More informationOutline. Queuing Theory Framework. Delay Models. Fundamentals of Computer Networking: Introduction to Queuing Theory. Delay Models.
Oule Fudaeals of Couer Neworg: Iroduco o ueug Theory eadg: Texboo chaer 3. Guevara Noubr CSG5, lecure 3 Delay Models Lle s Theore The M/M/ queug syse The M/G/ queug syse F3, CSG5 Fudaeals of Couer Neworg
More informationOutline. Computer Networks: Theory, Modeling, and Analysis. Delay Models. Queuing Theory Framework. Delay Models. Little s Theorem
Oule Couer Newors: Theory, Modelg, ad Aalyss Guevara Noubr COM35, lecure 3 Delay Models Lle s Theore The M/M/ queug syse The M/G/ queug syse F, COM35 Couer Newors Lecure 3, F, COM35 Couer Newors Lecure
More information4. THE DENSITY MATRIX
4. THE DENSTY MATRX The desy marx or desy operaor s a alerae represeao of he sae of a quaum sysem for whch we have prevously used he wavefuco. Alhough descrbg a quaum sysem wh he desy marx s equvale o
More informationJORIND 9(2) December, ISSN
JORIND 9() December, 011. ISSN 1596 8308. www.rascampus.org., www.ajol.o/jourals/jord THE EXONENTIAL DISTRIBUTION AND THE ALICATION TO MARKOV MODELS Usma Yusu Abubakar Deparme o Mahemacs/Sascs Federal
More informationDensity estimation III.
Lecure 4 esy esmao III. Mlos Hauskrec mlos@cs..edu 539 Seo Square Oule Oule: esy esmao: Mamum lkelood ML Bayesa arameer esmaes MP Beroull dsrbuo. Bomal dsrbuo Mulomal dsrbuo Normal dsrbuo Eoeal famly Eoeal
More informationQuantum Mechanics II Lecture 11 Time-dependent perturbation theory. Time-dependent perturbation theory (degenerate or non-degenerate starting state)
Pro. O. B. Wrgh, Auum Quaum Mechacs II Lecure Tme-depede perurbao heory Tme-depede perurbao heory (degeerae or o-degeerae sarg sae) Cosder a sgle parcle whch, s uperurbed codo wh Hamloa H, ca exs a superposo
More informationAvailable online Journal of Scientific and Engineering Research, 2014, 1(1): Research Article
Avalable ole wwwjsaercom Joural o Scec ad Egeerg Research, 0, ():0-9 Research Arcle ISSN: 39-630 CODEN(USA): JSERBR NEW INFORMATION INEUALITIES ON DIFFERENCE OF GENERALIZED DIVERGENCES AND ITS APPLICATION
More informationMoment 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
More informationFor the plane motion of a rigid body, an additional equation is needed to specify the state of rotation of the body.
The kecs of rgd bodes reas he relaoshps bewee he exeral forces acg o a body ad he correspodg raslaoal ad roaoal moos of he body. he kecs of he parcle, we foud ha wo force equaos of moo were requred o defe
More informationChapter 8. Simple Linear Regression
Chaper 8. Smple Lear Regresso Regresso aalyss: regresso aalyss s a sascal mehodology o esmae he relaoshp of a respose varable o a se of predcor varable. whe here s jus oe predcor varable, we wll use smple
More informationLeast squares and motion. Nuno Vasconcelos ECE Department, UCSD
Leas squares ad moo uo Vascocelos ECE Deparme UCSD Pla for oda oda we wll dscuss moo esmao hs s eresg wo was moo s ver useful as a cue for recogo segmeao compresso ec. s a grea eample of leas squares problem
More informationThe Signal, Variable System, and Transformation: A Personal Perspective
The Sgal Varable Syem ad Traformao: A Peroal Perpecve Sherv Erfa 35 Eex Hall Faculy of Egeerg Oule Of he Talk Iroduco Mahemacal Repreeao of yem Operaor Calculu Traformao Obervao O Laplace Traform SSB A
More informationKey words: Fractional difference equation, oscillatory solutions,
OSCILLATION PROPERTIES OF SOLUTIONS OF FRACTIONAL DIFFERENCE EQUATIONS Musafa BAYRAM * ad Ayd SECER * Deparme of Compuer Egeerg, Isabul Gelsm Uversy Deparme of Mahemacal Egeerg, Yldz Techcal Uversy * Correspodg
More informationSome Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
Joural of Sceces Islamc epublc of Ira 6(: 63-67 (005 Uvers of ehra ISSN 06-04 hp://scecesuacr Some Probabl Iequales for Quadrac Forms of Negavel Depede Subgaussa adom Varables M Am A ozorga ad H Zare 3
More informationMidterm Exam. Tuesday, September hour, 15 minutes
Ecoomcs of Growh, ECON560 Sa Fracsco Sae Uvers Mchael Bar Fall 203 Mderm Exam Tuesda, Sepember 24 hour, 5 mues Name: Isrucos. Ths s closed boo, closed oes exam. 2. No calculaors of a d are allowed. 3.
More informationThe Mean Residual Lifetime of (n k + 1)-out-of-n Systems in Discrete Setting
Appled Mahemacs 4 5 466-477 Publshed Ole February 4 (hp//wwwscrporg/oural/am hp//dxdoorg/436/am45346 The Mea Resdual Lfeme of ( + -ou-of- Sysems Dscree Seg Maryam Torab Sahboom Deparme of Sascs Scece ad
More informationThe Linear Regression Of Weighted Segments
The Lear Regresso Of Weghed Segmes George Dael Maeescu Absrac. We proposed a regresso model where he depede varable s made o up of pos bu segmes. Ths suao correspods o he markes hroughou he da are observed
More informationLecture 3 Topic 2: Distributions, hypothesis testing, and sample size determination
Lecure 3 Topc : Drbuo, hypohe eg, ad ample ze deermao The Sude - drbuo Coder a repeaed drawg of ample of ze from a ormal drbuo of mea. For each ample, compue,,, ad aoher ac,, where: The ac he devao of
More informationProbability Bracket Notation and Probability Modeling. Xing M. Wang Sherman Visual Lab, Sunnyvale, CA 94087, USA. Abstract
Probably Bracke Noao ad Probably Modelg Xg M. Wag Sherma Vsual Lab, Suyvale, CA 94087, USA Absrac Ispred by he Drac oao, a ew se of symbols, he Probably Bracke Noao (PBN) s proposed for probably modelg.
More informationAsymptotic Behavior of Solutions of Nonlinear Delay Differential Equations With Impulse
P a g e Vol Issue7Ver,oveber Global Joural of Scece Froer Research Asypoc Behavor of Soluos of olear Delay Dffereal Equaos Wh Ipulse Zhag xog GJSFR Classfcao - F FOR 3 Absrac Ths paper sudes he asypoc
More informationGeneral Complex Fuzzy Transformation Semigroups in Automata
Joural of Advaces Compuer Research Quarerly pissn: 345-606x eissn: 345-6078 Sar Brach Islamc Azad Uversy Sar IRIra Vol 7 No May 06 Pages: 7-37 wwwacrausaracr Geeral Complex uzzy Trasformao Semgroups Auomaa
More informationBianchi Type II Stiff Fluid Tilted Cosmological Model in General Relativity
Ieraoal Joural of Mahemacs esearch. IN 0976-50 Volume 6, Number (0), pp. 6-7 Ieraoal esearch Publcao House hp://www.rphouse.com Bach ype II ff Flud led Cosmologcal Model Geeral elay B. L. Meea Deparme
More informationth m m m m central moment : E[( X X) ] ( X X) ( x X) f ( x)
1 Trasform Techiques h m m m m mome : E[ ] x f ( x) dx h m m m m ceral mome : E[( ) ] ( ) ( x) f ( x) dx A coveie wa of fidig he momes of a radom variable is he mome geeraig fucio (MGF). Oher rasform echiques
More informationPartial Molar Properties of solutions
Paral Molar Properes of soluos A soluo s a homogeeous mxure; ha s, a soluo s a oephase sysem wh more ha oe compoe. A homogeeous mxures of wo or more compoes he gas, lqud or sold phase The properes of a
More informationModeling of the linear time-variant channel. Sven-Gustav Häggman
Moelg of he lear me-vara chael Sve-Gusav Häggma 2 1. Characerzao of he lear me-vara chael 3 The rasmsso chael (rao pah) of a rao commucao sysem s mos cases a mulpah chael. Whe chages ae place he propagao
More informationExercise 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
More informationSolution set Stat 471/Spring 06. Homework 2
oluo se a 47/prg 06 Homework a Whe he upper ragular elemes are suppressed due o smmer b Le Y Y Y Y A weep o he frs colum o oba: A ˆ b chagg he oao eg ad ec YY weep o he secod colum o oba: Aˆ YY weep o
More informationChapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
More informationθ = θ Π Π Parametric counting process models θ θ θ Log-likelihood: Consider counting processes: Score functions:
Paramerc coug process models Cosder coug processes: N,,..., ha cou he occurreces of a eve of eres for dvduals Iesy processes: Lelhood λ ( ;,,..., N { } λ < Log-lelhood: l( log L( Score fucos: U ( l( log
More informationAs evident from the full-sample-model, we continue to assume that individual errors are identically and
Maxmum Lkelhood smao Greee Ch.4; App. R scrp modsa, modsb If we feel safe makg assumpos o he sascal dsrbuo of he error erm, Maxmum Lkelhood smao (ML) s a aracve alerave o Leas Squares for lear regresso
More informationSolving fuzzy linear programming problems with piecewise linear membership functions by the determination of a crisp maximizing decision
Frs Jo Cogress o Fuzzy ad Iellge Sysems Ferdows Uversy of Mashhad Ira 9-3 Aug 7 Iellge Sysems Scefc Socey of Ira Solvg fuzzy lear programmg problems wh pecewse lear membershp fucos by he deermao of a crsp
More informationRATIO ESTIMATORS USING CHARACTERISTICS OF POISSON DISTRIBUTION WITH APPLICATION TO EARTHQUAKE DATA
The 7 h Ieraoal as of Sascs ad Ecoomcs Prague Sepember 9-0 Absrac RATIO ESTIMATORS USING HARATERISTIS OF POISSON ISTRIBUTION WITH APPLIATION TO EARTHQUAKE ATA Gamze Özel Naural pulaos bolog geecs educao
More informationCyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles
Ope Joural of Dsree Mahemas 2017 7 200-217 hp://wwwsrporg/joural/ojdm ISSN Ole: 2161-7643 ISSN Pr: 2161-7635 Cylally Ierval Toal Colorgs of Cyles Mddle Graphs of Cyles Yogqag Zhao 1 Shju Su 2 1 Shool of
More informationPricing Asian Options with Fourier Convolution
Prcg Asa Opos wh Fourer Covoluo Cheg-Hsug Shu Deparme of Compuer Scece ad Iformao Egeerg Naoal Tawa Uversy Coes. Iroduco. Backgroud 3. The Fourer Covoluo Mehod 3. Seward ad Hodges facorzao 3. Re-ceerg
More informationASYMPTOTIC EQUIVALENCE OF NONPARAMETRIC REGRESSION AND WHITE NOISE. BY LAWRENCE D. BROWN 1 AND MARK G. LOW 2 University of Pennsylvania
The Aals of Sascs 996, Vol., No. 6, 38398 ASYMPTOTIC EQUIVALENCE OF NONPARAMETRIC REGRESSION AND WITE NOISE BY LAWRENCE D. BROWN AND MARK G. LOW Uversy of Pesylvaa The prcpal resul s ha, uder codos, o
More informationDetermination of Antoine Equation Parameters. December 4, 2012 PreFEED Corporation Yoshio Kumagae. Introduction
refeed Soluos for R&D o Desg Deermao of oe Equao arameers Soluos for R&D o Desg December 4, 0 refeed orporao Yosho Kumagae refeed Iroduco hyscal propery daa s exremely mpora for performg process desg ad
More informationρ < 1 be five real numbers. The
Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace
More informationSTOCHASTIC CALCULUS I STOCHASTIC DIFFERENTIAL EQUATION
The Bk of Thld Fcl Isuos Polcy Group Que Models & Fcl Egeerg Tem Fcl Mhemcs Foudo Noe 8 STOCHASTIC CALCULUS I STOCHASTIC DIFFERENTIAL EQUATION. ก Through he use of ordry d/or prl deres, ODE/PDE c rele
More information1 Introduction and main results
The Spacgs of Record Values Tefeg Jag ad Dag L 2 Ocober 0, 2006 Absrac. Le {R ; } be he sequece of record values geeraed from a sequece of..d. couous radom varables, wh dsrbuo from he expoeal famly. I
More informationINTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY
[Mjuh, : Jury, 0] ISSN: -96 Scefc Jourl Impc Fcr: 9 ISRA, Impc Fcr: IJESRT INTERNATIONAL JOURNAL OF ENINEERIN SCIENCES & RESEARCH TECHNOLOY HAMILTONIAN LACEABILITY IN MIDDLE RAPHS Mjuh*, MurlR, B Shmukh
More informationReal-time Classification of Large Data Sets using Binary Knapsack
Real-me Classfcao of Large Daa Ses usg Bary Kapsack Reao Bru bru@ds.uroma. Uversy of Roma La Sapeza AIRO 004-35h ANNUAL CONFERENCE OF THE ITALIAN OPERATIONS RESEARCH Sepember 7-0, 004, Lecce, Ialy Oule
More informationTHE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA
THE ROYAL STATISTICAL SOCIETY 3 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA PAPER I STATISTICAL THEORY & METHODS The Socety provdes these solutos to assst caddates preparg for the examatos future years ad
More informationParameter, Statistic and Random Samples
Parameter, Statstc ad Radom Samples A parameter s a umber that descrbes the populato. It s a fxed umber, but practce we do ot kow ts value. A statstc s a fucto of the sample data,.e., t s a quatty whose
More informationComplementary Tree Paired Domination in Graphs
IOSR Joural of Mahemacs (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X Volume 2, Issue 6 Ver II (Nov - Dec206), PP 26-3 wwwosrjouralsorg Complemeary Tree Pared Domao Graphs A Meeaksh, J Baskar Babujee 2
More informationProbability Bracket Notation, Probability Vectors, Markov Chains and Stochastic Processes. Xing M. Wang Sherman Visual Lab, Sunnyvale, CA, USA
Probably Bracke Noao, Probably Vecors, Markov Chas ad Sochasc Processes Xg M. Wag Sherma Vsual Lab, Suyvale, CA, USA Table of Coes Absrac page1 1. Iroduco page. PBN ad Tme-depede Dscree Radom Varable.1.
More informationD KL (P Q) := p i ln p i q i
Cheroff-Bouds 1 The Geeral Boud Let P 1,, m ) ad Q q 1,, q m ) be two dstrbutos o m elemets, e,, q 0, for 1,, m, ad m 1 m 1 q 1 The Kullback-Lebler dvergece or relatve etroy of P ad Q s defed as m D KL
More informationDensity estimation III.
Lecure 6 esy esmao III. Mlos Hausrec mlos@cs..eu 539 Seo Square Oule Oule: esy esmao: Bomal srbuo Mulomal srbuo ormal srbuo Eoeal famly aa: esy esmao {.. } a vecor of arbue values Objecve: ry o esmae e
More informationMixed Integral Equation of Contact Problem in Position and Time
Ieraoal Joural of Basc & Appled Sceces IJBAS-IJENS Vol: No: 3 ed Iegral Equao of Coac Problem Poso ad me. A. Abdou S. J. oaquel Deparme of ahemacs Faculy of Educao Aleadra Uversy Egyp Deparme of ahemacs
More informationThe algebraic immunity of a class of correlation immune H Boolean functions
Ieraoal Coferece o Advaced Elecroc Scece ad Techology (AEST 06) The algebrac mmuy of a class of correlao mmue H Boolea fucos a Jgla Huag ad Zhuo Wag School of Elecrcal Egeerg Norhwes Uversy for Naoales
More informationSquare law expression is non linear between I D and V GS. Need to operate in appropriate region for linear behaviour. W L
MOS Feld-Effec Trassrs (MOSFETs ecure # 4 MOSFET as a Amplfer k ( S Square law express s lear bewee ad. Need perae apprprae reg fr lear behaur. Cpyrgh 004 by Oxfrd Uersy Press, c. MOSFET as a Amplfer S
More informationCommon MidPoint (CMP) Records and Stacking
Evromeal ad Explorao Geophyscs II Commo MdPo (CMP) Records ad Sackg om.h.wlso om.wlso@mal.wvu.edu Deparme of Geology ad Geography Wes rga Uversy Morgaow, W Commo Mdpo (CMP) gaher, also ofe referred o as
More informationQueuing Theory: Memory Buffer Limits on Superscalar Processing
Cle/ Model of I/O Queug Theory: Memory Buffer Lms o Superscalar Processg Cle reques respose Devce Fas CPU s cle for slower I/O servces Buffer sores cle requess ad s a slower server respose rae Laecy Tme
More information1 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
More informationSolution of Impulsive Differential Equations with Boundary Conditions in Terms of Integral Equations
Joural of aheacs ad copuer Scece (4 39-38 Soluo of Ipulsve Dffereal Equaos wh Boudary Codos Ters of Iegral Equaos Arcle hsory: Receved Ocober 3 Acceped February 4 Avalable ole July 4 ohse Rabba Depare
More informationChapter 1 - Free Vibration of Multi-Degree-of-Freedom Systems - I
CEE49b Chaper - Free Vbrao of M-Degree-of-Freedo Syses - I Free Udaped Vbrao The basc ype of respose of -degree-of-freedo syses s free daped vbrao Aaogos o sge degree of freedo syses he aayss of free vbrao
More informationLinear Regression Linear Regression with Shrinkage
Lear Regresso Lear Regresso h Shrkage Iroduco Regresso meas predcg a couous (usuall scalar oupu from a vecor of couous pus (feaures x. Example: Predcg vehcle fuel effcec (mpg from 8 arbues: Lear Regresso
More informationRegression Approach to Parameter Estimation of an Exponential Software Reliability Model
Amerca Joural of Theorecal ad Appled Sascs 06; 5(3): 80-86 hp://www.scecepublshggroup.com/j/ajas do: 0.648/j.ajas.060503. ISSN: 36-8999 (Pr); ISSN: 36-9006 (Ole) Regresso Approach o Parameer Esmao of a
More informationMATH 507a ASSIGNMENT 4 SOLUTIONS FALL 2018 Prof. Alexander. g (x) dx = g(b) g(0) = g(b),
MATH 57a ASSIGNMENT 4 SOLUTIONS FALL 28 Prof. Alexader (2.3.8)(a) Le g(x) = x/( + x) for x. The g (x) = /( + x) 2 is decreasig, so for a, b, g(a + b) g(a) = a+b a g (x) dx b so g(a + b) g(a) + g(b). Sice
More informationVARIATIONAL ITERATION METHOD FOR DELAY DIFFERENTIAL-ALGEBRAIC EQUATIONS. Hunan , China,
Mahemacal ad Compuaoal Applcaos Vol. 5 No. 5 pp. 834-839. Assocao for Scefc Research VARIATIONAL ITERATION METHOD FOR DELAY DIFFERENTIAL-ALGEBRAIC EQUATIONS Hoglag Lu Aguo Xao Yogxag Zhao School of Mahemacs
More informationChapter 3: Maximum-Likelihood & Bayesian Parameter Estimation (part 1)
Aoucemes Reags o E-reserves Proec roosal ue oay Parameer Esmao Bomercs CSE 9-a Lecure 6 CSE9a Fall 6 CSE9a Fall 6 Paer Classfcao Chaer 3: Mamum-Lelhoo & Bayesa Parameer Esmao ar All maerals hese sles were
More informationOptimal Eye Movement Strategies in Visual Search (Supplement)
Opmal Eye Moveme Sraeges Vsual Search (Suppleme) Jr Naemk ad Wlso S. Gesler Ceer for Percepual Sysems ad Deparme of Psychology, Uversy of exas a Aus, Aus X 787 Here we derve he deal searcher for he case
More informationStochastic Petri Nets with Low Variation Matrix Exponentially Distributed Firing Time
Ieraoal Joural of Performably Egeerg Vol.7 No. 5 Sepember pp. 44-454. RAS Cosulas Pred Ida Sochasc Per Nes wh Low Varao arx Expoeally Dsrbued Frg Tme P. BUCHHOLZ A. HORVÁTH* ad. TELE 3 Iformak IV TU DormudD-44
More informationEE 6885 Statistical Pattern Recognition
EE 6885 Sascal Paer Recogo Fall 005 Prof. Shh-Fu Chag hp://www.ee.columba.edu/~sfchag Lecure 5 (9//05 4- Readg Model Parameer Esmao ML Esmao, Chap. 3. Mure of Gaussa ad EM Referece Boo, HTF Chap. 8.5 Teboo,
More informationEE 6885 Statistical Pattern Recognition
EE 6885 Sascal Paer Recogo Fall 005 Prof. Shh-Fu Chag hp://.ee.columba.edu/~sfchag Lecure 8 (/8/05 8- Readg Feaure Dmeso Reduco PCA, ICA, LDA, Chaper 3.8, 0.3 ICA Tuoral: Fal Exam Aapo Hyväre ad Erkk Oja,
More informationDensity estimation III. Linear regression.
Lecure 6 Mlos Hauskrec mlos@cs.p.eu 539 Seo Square Des esmao III. Lear regresso. Daa: Des esmao D { D D.. D} D a vecor of arbue values Obecve: r o esmae e uerlg rue probabl srbuo over varables X px usg
More informationON TESTING EXPONENTIALITY AGAINST NBARFR LIFE DISTRIBUTIONS
STATISTICA, ao LII,. 4, ON TESTING EPONENTIALITY AGAINST NBARR LIE DISTRIBUTIONS M. A. W. Mahmoud, N. A. Abdul Alm. INTRODUCTION AND DEINITIONS Tesg expoealy agas varous classes of lfe dsrbuos has go a
More informationMarch 14, Title: Change of Measures for Frequency and Severity. Farrokh Guiahi, Ph.D., FCAS, ASA
March 4, 009 Tle: Chage of Measures for Frequecy ad Severy Farroh Guah, Ph.D., FCAS, ASA Assocae Professor Deare of IT/QM Zarb School of Busess Hofsra Uversy Hesead, Y 549 Eal: Farroh.Guah@hofsra.edu Phoe:
More informationRedundancy System Fault Sampling Under Imperfect Maintenance
A publcao of CHEMICAL EGIEERIG TRASACTIOS VOL. 33, 03 Gues Edors: Erco Zo, Pero Barald Copyrgh 03, AIDIC Servz S.r.l., ISB 978-88-95608-4-; ISS 974-979 The Iala Assocao of Chemcal Egeerg Ole a: www.adc./ce
More informationAsymptotic Regional Boundary Observer in Distributed Parameter Systems via Sensors Structures
Sesors,, 37-5 sesors ISSN 44-8 by MDPI hp://www.mdp.e/sesors Asympoc Regoal Boudary Observer Dsrbued Parameer Sysems va Sesors Srucures Raheam Al-Saphory Sysems Theory Laboraory, Uversy of Perpga, 5, aveue
More informationMATH 247/Winter Notes on the adjoint and on normal operators.
MATH 47/Wter 00 Notes o the adjot ad o ormal operators I these otes, V s a fte dmesoal er product space over, wth gve er * product uv, T, S, T, are lear operators o V U, W are subspaces of V Whe we say
More information1.2 The Mean, Variance, and Standard Deviation. x x. standard deviation: σ = σ ; geometric series is. 1 x. 1 n xi. n n n
. The Mea, Varace, ad Sadard Devao mea: µ f ( u f ( u +... + ukf ( uk S k k varace: ( f ( ( u f ( u +... + ( u f ( u f ( S sadard devao: geomerc seres s [emrcal dsrbuo s] samle mea: [emrcal dsrbuo s] varace:
More informationLaw of Large Numbers
Toss a co tmes. Law of Large Numbers Suppose 0 f f th th toss came up H toss came up T s are Beroull radom varables wth p ½ ad E( ) ½. The proporto of heads s. Itutvely approaches ½ as. week 2 Markov s
More information[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5
TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres
More informationLecture 2 M/G/1 queues. M/G/1-queue
Lecure M/G/ queues M/G/-queue Posson arrval process Arbrary servce me dsrbuon Sngle server To deermne he sae of he sysem a me, we mus now The number of cusomers n he sysems N() Tme ha he cusomer currenly
More informationEfficient Estimators for Population Variance using Auxiliary Information
Global Joural of Mahemacal cece: Theor ad Praccal. IN 97-3 Volume 3, Number (), pp. 39-37 Ieraoal Reearch Publcao Houe hp://www.rphoue.com Effce Emaor for Populao Varace ug Aular Iformao ubhah Kumar Yadav
More information1 Solution to Problem 6.40
1 Soluto to Problem 6.40 (a We wll wrte T τ (X 1,...,X where the X s are..d. wth PDF f(x µ, σ 1 ( x µ σ g, σ where the locato parameter µ s ay real umber ad the scale parameter σ s > 0. Lettg Z X µ σ we
More informationSolving Non-Linear Rational Expectations Models: Approximations based on Taylor Expansions
Work progress Solvg No-Lear Raoal Expecaos Models: Approxmaos based o Taylor Expasos Rober Kollma (*) Deparme of Ecoomcs, Uversy of Pars XII 6, Av. du Gééral de Gaulle; F-94 Créel Cedex; Frace rober_kollma@yahoo.com;
More informationInterval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X
ECON 37: Ecoomercs Hypohess Tesg Iervl Esmo Wh we hve doe so fr s o udersd how we c ob esmors of ecoomcs reloshp we wsh o sudy. The queso s how comforble re we wh our esmors? We frs exme how o produce
More informationRandom Variables. ECE 313 Probability with Engineering Applications Lecture 8 Professor Ravi K. Iyer University of Illinois
Radom Varables ECE 313 Probablty wth Egeerg Alcatos Lecture 8 Professor Rav K. Iyer Uversty of Illos Iyer - Lecture 8 ECE 313 Fall 013 Today s Tocs Revew o Radom Varables Cumulatve Dstrbuto Fucto (CDF
More informationDelay-Dependent Robust Asymptotically Stable for Linear Time Variant Systems
Delay-Depede Robus Asypocally Sable for Lear e Vara Syses D. Behard, Y. Ordoha, S. Sedagha ABSRAC I hs paper, he proble of delay depede robus asypocally sable for ucera lear e-vara syse wh ulple delays
More informationBrownian Motion and Stochastic Calculus. Brownian Motion and Stochastic Calculus
Browa Moo Sochasc Calculus Xogzh Che Uversy of Hawa a Maoa earme of Mahemacs Seember, 8 Absrac Ths oe s abou oob decomoso he bascs of Suare egrable margales Coes oob-meyer ecomoso Suare Iegrable Margales
More informationCompetitive Facility Location Problem with Demands Depending on the Facilities
Aa Pacc Maageme Revew 4) 009) 5-5 Compeve Facl Locao Problem wh Demad Depedg o he Facle Shogo Shode a* Kuag-Yh Yeh b Hao-Chg Ha c a Facul of Bue Admrao Kobe Gau Uver Japa bc Urba Plag Deparme Naoal Cheg
More information