### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Week 8 Notes - Probability Theory and Statistics 3341

UTD

GPA 3.3

### View Full Document

## About this Document

## 13

## 0

## Popular in Probability Theory and Statistics

## Popular in General Engineering

This 5 page Class Notes was uploaded by Michelle Schmutz on Saturday April 2, 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 13 views. For similar materials see Probability Theory and Statistics in General Engineering at University of Texas at Dallas.

## Similar to 3341 at UTD

## Reviews for Week 8 Notes - Probability Theory and Statistics

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 04/02/16

Weekly ¥8 Notes Mondayarc21,2016 JoiPMF Marginal range JointMF Giv:n SkyofX&Y E@# )={0,014,014,1B circ,its onlyvalioutcomes Outcomarindependent 11£ , jointF ×=#aoa,tP(N=otlstrajeotiRnR -0.01- " Pxtx,y)=PK=X,y=y) ,=co .mil/RA.s8jEY*pE#T*stTAtRd-on ={ m:} 'D Y=ex)T estn=2 ojm.io?sYbKl0zkY RA=o9 ¥Fdm ' AAȾq¥⾨ .io?h*o sincyourconcentratingirtwote,ywillnever bemorethemz MarginalMF ' edpxxd 21=1 0.090.09 0 -2 21=2KI0; 081 oy;oej2 Bytx ,y)y=o yit y k¥ 0 =§p×,y#y, ×=0 0.01 0 0 0.18 0.090.09 0 .GivenfdoiY snEo 010.110.0910-8110.811=0 O 0.81 0.81 px.ycx.gl ) P4#={oiliYE;y=z pyly Fin: 1¥ o ;ow. ,EHtEtp =§P#Ky) marginal P PMF qkntpylgh Ryt,y)y=yity-2 k¥ EKH 0*0.014*0.181.2*0.×=o 01 the insidofthmdvix can'beassemblejustnowing =L, EET :(110.0.810.81 Pxlxbmdpyly,especiallyincee PMF's are Pylgl 1- independent Ely= -2Px# 0*0.1+1*0-12*0.PX=0)y=oyity o± x; 0.1/0.0910-81 JointPME carrytherelationshiptween xdyso =1.71=0.09+1.62 081,01 itsmoreinformathanMarginalME'S Pg)/ U.S ABH ElgkD=§gaDPk=X) Pxytxy ) EEGK ,yB=£5g(x,y)P(×=x,y=y) " X&Yam2" signals gk ,y)=maxGY}=W than covered gk ,y)=m;n{qy}=w .TK#earsoneisweekesthantheothenhesit : ex Find Elw,whereW=×y %={ 0,44} ECWKEGY ) Byk,y)y=㱺y=z =o*#I*ooa+*o$ ¥÷*#*xteww±EFkYY±{8!¥hE¥ 0 &W. w=X+ay ; 0.09+3.24=3.33 fnwayIn} Covariance -it's wayzMmwȼwetln 'technique less work ) evaluatehefunctiofereverypossikkxoy ,make E{9(×,y)}=§§g(x,y)p(×=x,y=y matr,tpoihtwiseultiplication 't x 0 I I 2 00 0 I 0 I 2 * 010.090.090=>(1*0.09)+(4*0.81) - EK 001040 4 40 081 3.33 - EG ,yj 2 0 jointMF ED Given Pxycx ,y)=P(x=X,Y=y) youngexpectations ) 4 , gash gkiytgknptgzknptgnkiysinghwayMf23Eg.(x.y)2st...tEEGnK,p §, a . .to#yBPK=kY=y) . §, , y)=ElW) . ) .tgn(x,y)P(*x,y=y Ea j=fq{g±(x,=F§{9±C*LH y)P(×,'FyH Y=yH =fEy{g±Cx, } ybreakdownSum § Know how muchexperimentsviate Varcx)=E{C×#xD2} =E{ G- EKDK .EKD } U.S soitits>° > www.anasalwaysa# ,it's , F {G- EKDGHIYD Covk ,y positive ⾨ inttyxraryiyinaposilinefuncticn Learne: sideinfotellsyouxK) ,thereforeyouexpeoty>ElD . t.fi/ouKnowone,youcanexpecttheelationshipthlheothes Wednesday , March 23,2016 - Rytx,y)y=o yit y-2 P×# veullsolvingforthis thigivesmore ×=0 0.01 O 0 # Pw(w)=P(W=w) (sideinfohan X=' 00.1/0.09/0.81# ,s°Ⱦ x=z o o =p(w㱺 , P4#=µibt0.81;y=2 This isbetter /.810.81 T =P(×y=O) o ;ow. pyl) ELYHH =EP×y(x,y) thisisall know c:xy㱺 Suppose you recaECW)=333.EC/y=t8,Ely)=tH coulgo eitheway ,fw-on average Cork ,y)=E{4- EKDCYEKD } ZO 㾎 itsgreater < l't > if × > EK) c- sidinfo texpeo) y >Fty) knowingEtptwvk ,y improveyourestimates mathematical expectations sung expectations qaswm tghkpr EEGK ,y)}=E{kµ -×Xy -MD } dq.mx/uyt#=yEksCovk.-)=EElx-ELxD(y-Ely)B=O constants Know : EEXY xµȾ-yµ±tµ×µ¥ =EE×y} .EE#B-EEyit3tEEkB E{ax}=aE{×} )=Eky7µ xµ y =E{xy}-µyE{×}-µ×E{y}tµxµy =EExy}-µyµx-µxTµtµXµY - version calculations corky simplified for 㾎 -33-18*1.71pbetween RV 's Gv(xy)=3= 3.33-3.08 positivmovinggethernhesamedirection = 0.25>0 Ⱦ negativemovinin directions opposite 0€ cork ,y)=E{k- EKDCYEKDBEO • y*¥÷g max max aj" lower upper as• bound bound e×) Given: hkxtay Pxxlx ,y) Ftwtttxtay ) Find : =ECDtECay ) ) ECWHECDTAECD VWCWHJWZ >0 Know : µw=µxtaµG ookstaut AtB2=A2+B2t2AB where µ w=xtaty w=ECw VarH=Jw2=E{(w -w)2 examinefor =E{ ktay - µraµy7} ⾨¥+y,a±dg÷,a=td§ w =E{[C*µ×)+a(y-µyD2} =E{⾨D2ta4y-µy)2t2ak-µx)(y-µy) } =E{(x-µ×)}ta2EE( x.tn/)23t2aEE(x-uxXytuyB=2x2+a2d2yt2aavCx.y) >0 oh Ⱦw=㱺 - µw=µ×tµy Jw2aJx2tdy2tZcovk@0highervarianekriminabtCrimiraldconstant.com beanythinf] a= - Jw2=2x2 .tt/y2g2fEcovk,y) >0 -dxdyoeaovcxiykdxdy Ty -025¥ + 㱺 2×2+2×2 cork -2¥ ;p>oȾ2Pw +1<-6%5×34+1 ) ^ covariancermalized 㱺2Hx2>&2#covk,y byslandarddeviation 㱺J× > cork ) 's, ,y tfpxyea Laurelton 㱺wv(×,y)EJxJ£ utpmdog coefficient GVCX,y Px ,a@u px=l=ȾY=axtb,yHO a@ .y px uncorrelainndated Weather today correlates tomorro's. However ,Texas weather is independent of tothatof daily less correlated thanasizona 's pt correlation ) >O EQY EGPEO X >0 orthogonal a o

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.