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Week 4 - Probability Theory and Statistics

by: Michelle Schmutz

Week 4 - Probability Theory and Statistics 3341

Marketplace > University of Texas at Dallas > General Engineering > 3341 > Week 4 Probability Theory and Statistics
Michelle Schmutz
GPA 3.3

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About this Document

These are notes from Monday, February 8 and Wednesday, February 10. It's technically the 5th week of the class, but since last week, we had our first exam and just reviewed that Monday and took the...
Probability Theory and Statistics
Dr. Mohammed Saquib
Class Notes
Probability, probability theory, probability theory and statistics, Math, Statistics, saquib
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This 6 page Class Notes was uploaded by Michelle Schmutz on Saturday February 13, 2016. The Class Notes belongs to 3341 at University of Texas at Dallas taught by Dr. Mohammed Saquib in Winter 2016. Since its upload, it has received 26 views. For similar materials see Probability Theory and Statistics in General Engineering at University of Texas at Dallas.


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Date Created: 02/13/16
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Given : p=¥ Uzlo ) =p u=N$u=H$u=r$ ) ( ... =P (4=10 )+P(U=1DtP(U=Ht ...becausthey'rmutually exclusive factortry =(-p9Pt(1- )Pt .. pjnpt(tp tumblr.TL?QEnteghf=f.p)9EPtHoPHhP5Pt..j 㱺{P(u=Dtp(u㱺)tP(u=3)t . 㱺{P+CtD ¥1 'tKPTPT ...L} =p Pfa Dow # C) Ifthe tracker updates 100 what isthe PMF Y, the number incorrectupdated ? - packages , of of packages Pylyhptky ) ( ( ; a = . n { O on ; d) Ifthe more state. the -art truckers and the chances error reduce down to 0.01 post office got of of , what isthe probability 4=3 errors - ) = of Py (g) Ptky ( log)P4hp)9s What is the ' probability of Yes errors PC KD =P ('to $Y=1 UUU't 2*4=3 ) 9 ' ' remember =P ( to )tp(Y=1)+P( HHPN =3) its = " I PH-D 's He)* mutually (1000)p°(Huot ( 10)0 pytpj + ( :o) +¢o)P3( exclusive e) H the until the 's 3 What isthe the rank tracker Keeps updating post offices computes receives errors, PMFQZ , number packages updated ? of Given - # of trialsto 3 errors get '' 3 ' Pzfz (Q ) PYHD ; 2=3,4 ,,... p z= 2)=O )=PCz=zD={ 0 ; Ow - ( f) If p -0.25 , what isthe probability E- R packages updated until the computer of receives 3 eras ? P( -p) 9 = ' z=W=¢)p3a fly3(tPy㱺 A rangya sample space has all of the possible kountablxphysial outcomes range Cumulativdistribuproperty Poisson Px ,1,2 :a > 'Nt{o ;X=o ,range 0 TI ;ow . ex) Given : .pe#I=EoejgagF.ix=Q1.z Rat isproportionalo T㱺Xt=# constant XFX ED Some birds are sitting on a telephone wire . so can be on the wire at a time it starts Only many before getting cramped . If two more birds arrive what is the probabilityhat 5 will leave? , P(Bz=s ) The the 10- Poisson ED number of updated packages processed by postoffices computer in any Second intervalis a random Variable S ,L , with a- updates What isthe that there be in 10-second interval? $ probability will no updates processed a Given : Find : ¥10 sec P (no updates in EIO seconds =P (× s ,x=5 ,o=o)=et*€#[ e- X ,o=X10=>52 oj x=÷÷ What isthe probabilitythat attest two updates willbe processed in a second interval * PC 2 updates in F- 2 sec TPKZZZ ) = 1- PCKEO ) .PK#1)=teaokI . eȾk÷ ! =te¥ -@ For a discrete random variableX with PMFPXKD and Sx : range a) For x any , P×k)z0 b) Exesxpxiy 't c)For event BE Sx the that X in the set B is PCB ) any , probability is £ȾPx(x)=£㱺PCX=D Given : Find : Pxlxtpkx ) - Plotpxa } } } ; * * ={?§gxEe b) P(x€ -0.00004=0 ###¥n#I = * . :O£ £ 0. w . C) PCXEO ) 314 added theproperty d) P ( XE Of9991=3/4 CumulativeistributivectiKDF ) anxetto = e) P(x{ /) = f) p( X 1100 ) 1/4+3/4=14=2 . g) PCXEO Property Mass Function 㱺 Cumulative Distributiveunction D Fxfx ) - Pke -5=0 2) Fx too )=P(×< too) =L DX >¥' ' (XDZFXK ) Only when increasingrremainingonstan(non decreasingfunctio)CCDA 4) Xie Sx Jump occurs when there's a value inside the qx range Fx (X Fx ( - E) = - E a ;) X ; PXCXDTPG XD , where an arbitrary very small positiveNumber €0 5) that area remains flat Xicxlxi it FxW=F×Cx ;)


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