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Introduction to Probability and Statistics 131B Lecture 3
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Title  Introduction to Probability and Statistics 131B Lecture 3 
Title of Series  Introduction to Probability and Statistics 131B 
Part Number  3 
Number of Parts  15 
Author 
Cranston, Michael C.

License 
CC Attribution  ShareAlike 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
DOI  10.5446/13603 
Publisher  University of California Irvine (UCI) 
Release Date  2013 
Language  English 
Content Metadata
Subject Area  Mathematics 
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Transcript
00:06
both what's he to but because have to teach quick or if if it does cause it a I saw at shoe the book now if With put forward but but but but core some particular reversible random sample the random rebels of are not independent because there are repetitive discovery be 0 7 grayer some wild dependence between them back for a 3rd
01:39
Earl on
01:45
Wikinews that but compared various 30 sample means where think we're my Obama Sekhet your review as a face West repeated who chief but if bad but what about the other 2 sepsis with the karaoke so sub was a somberly Colray sore all possible bias chased but at the back from but there's dressmaker see there's a difference between died and share the same bicycle Italia Pfizer from Ontario best solution but the sum often NJ the same analytical rates of excise excise variants and I would look at this terms by differ from J E a parent a bomb that 1st course also lawyer I figured I should put you're eye injury Eagle One by J. which I should because that's where we 1st child it was natural but was wrong right now as because in this Iowa we don't include by which has so you wanna Red Square here every town squares we have them gives and Sigma squared here every terrorist Midas a seamless squared overcapitalize minus 1 him there are bad times and miners spot quieter and times and my response terms or and squared minus and close the previous summer and squared terms and spread firms were suffered out of here that means that and where some must occur that yes it would be buying factor ROOM 1st as a plus factor will air base it was where such factor this out and this less and less ever 1 here and a little a less what or Kaplan West so that's the rates of parte a sample various set by Fraser sample grab sample Florida base of being held there at random samples at lesson plans for the book all the standard this be rewritten although both at by fighting Cowell abiding a cover about where we cap OS minus 1 Soria capelin 1 their divided by Kaplan writes 1 why combined Omri recapitalize 1 whether we are rare Kaplan minus 11 because there was attracting this so Aksu adding no 1 in the rhetoric and the recent have a capital and minus 1 the was canceled Capel by and this are under way OK so if we're
06:58
faced with a problem of our tribe measure that population near populated areas which struck or population aged ribeye fighter copper several some air war that sell what contain a dot population being where 5 probability of cliff but she but if he or she but
08:06
K I sewer ire my son's arrest for the population thought a scholar coffer several 5th with a group of the day plant as opposed to 208 . yes OK so the approach is to use a settlement she will but with with with but but we to each what if we were with the period writing was laid a day if the sap but anger stuff that was replaced by you . ID Southall but at every move would save us where we could but that if back yes sir but above all are by should n s for distribution of call for or but as a proxy with all if if but would 0 rest what guess 0 0 with replaced as a with about that that's circle was part of a variation but not at all so there's a right that out a solicitor that's a great question but some the important distinction here it's done with or without replacement and they they are independent that's simple red except for that son was a throwback and sample Prozac and try to get them back their decision will be same out every truck but if you keep 1 out there changes but the book talked about the composition of the population and disuse watching OK so yeah salsa new was out on but Segner squared is known for auto crash so how how or why did with so that are bad he could not go to war with we have this approximation This is a proxy normal and honorable means rates once those distribution function for a venerable is normal distribution function now last time I introduce this notation from a book ZEL floor 2 Maine the following here's a novel Bessie I with that 2 much this safe area which is L Florida zeal Florida was a number on the reallife so the theory under the graphic novel means progress when density of the right that point L 2 but now what is this part a says that absolute value think of this thing busy has a sensory this means that the rhinorrhea while has absolute value less than 0 or to set means trapped between 0 2 and open over to sort the lighter 0 2 is ER star I said 0 2 I off it over is ready rare wood frenzy of and my this is about 4 OK so worthy of the probability the random variable what they proxy all this between here and here but probably the Joanna rebels between these 2 points the above 1 minus Alpha because it's 1 might probably it's outside valuable what the province outside what probably right itself over to cover its laughter this is over to the public its outside Alpha problems insiders myself some OK so that means with the probability while myself but this rather rare what is between here at the plant soak back the loss of a drugs
15:50
by probably why why I South 5 coup for the a mail the aura of I saw this inequality from you'll back if with cool who if at all or would or it was a sewer probably approximately 1 myself up newer lies between here and there so a in the case Sigma is Apple Computer X far from that samples find busy course myself from the table to park what so we'll keep your book and you'll have it always with you that Iraq could recover as a of a comet handing tho it apart we saw back and look it up online however watching her your books anyway so this is the from year to year scholar while times 1 myself opera set copper settle off for a meal or or problem newest be trimmer to end points here's 1 myself Price what it saw as little changed what is not over rude and cigarette overrode enters the various fans WIC by CIA governance but left from from a last year as reuse us where we use that were using for use of its was revised revived the settlement that you need IDE means fire fire so you out here ahead of it this reword this a little bit since the very next bars Sigma over Baron but we can rewrite the car presser all the old or that they Edison faced the same borrowed out here with various Parcells's Pierce is a case of sampling have lowered replaced by E. Martin Oh thank you and so I better put that here down here but so what and I'll see how but a different name days elects bar in this case of sampling without replacement here and was replaced with replacement terms on large Jack up because it's a signal rude here the following year there so it's that's very well what this would be when you're out independent rather also was doctors there so Razorbacks Boras that I want signal rude and ranks of ballots cast the case sat waiting at a cost but if we want but these are a simple random sample now or sap going with our replacement enter as is typical you'll end say was square around should we still y cover several from your house How do well the population is large clubs as they race but we dependence between excise next is very small populations large Member call rates of excise Austria's said where over capital unless 1 Capel misery Big Jack Evans is very small and their versions of the supplement store so subtle that there will stall Bright Malay as Irish old but the cap by is of much larger store a case of a big population anger Rice's actual sample size but not big enough to be close to tabloid vendors sold a friend of this and lack of others Lack of dependents Soto supplement their results said they there were still that is a bad expression be approximately normal and so we could go through all these steps finally arrival ever Steve
23:56
answerable where Razorbacks resists but there's a flaw in using that as a conference call that duo computer yet to able say or get Axel number I've left and right and point where the numbers are not but this and Ms. cover Sigma Sigma and we don't know Sigma so defined wait estimates of various effects are where to find a way to that that OK so boy with NAS shit they know everywhere was a sample
25:00
swear few was day data from a sample some Arthur S. Grant said that's part by unbiased as mayor of that means that whatever I use for the estimate some be some parts of data expected value of about should be the very part another words expected by West where should be covered from or where to go over some functionally excise there about Igel vacillate resurrects foreigners expected value should be the thing were every replace Razorbacks here that estimate so well but starter where is he fell say at but square people too 1 over Air some 5 equal 1 2 and minus sectors squared if this ZEO average squared deviations from the mean average square deviation from me is deviation from the mean square for the ice venerable when Adam 0 up these squared deviations and by having reads as the average square deviation from means will with with from the settlement of DEC's saw bob This is a fist City captors somehow but the various APEC parte best appear expected by
27:21
yes if she was
27:35
books from arm what we will do what he he where sigh with us too does this type thing several times varied and expand the square off about a valueadded off by persevere water revenue times a summer XI swear whoa you get when you had up boat was far let cool order as throughout 1st revealed that somebody XI squares minus 2 0 End act bar squares arrived from here because that's isolated sizes and types that are there's another far below you and terms here so fast X bar squares of abuse some of its I swear Meyer said NEC's from where for your 2 Oh OK Bravo exchange somber expected I hear area expected Iive XI square and we found this
30:11
competition already bomb what's
30:15
expected viaduct side heartsease knew what the various of XI beards said was where competition authority for simple random sample and be variants of God but so what's the various it's 3 seconds bias the 1st moment squared it's kind of been 2nd moment by 1st moments squared words this 2nd moment acts I expected IXI squared it is the variance plus 1st moments where the 1st moment of Newark so every that 1st some things were lost Paris where that is a 2nd MoMA memorandum woes various caused me for us way of saying that variances 2nd or less 1st so every term here is Sigma squared plus square and then there's 0 yeah we out entire saw the expected died over that ran rural squared Serbia its variants plus its mean squared with the drinks of are well all right this way and what Cimmino X bar its cost of case so now we add this up that May 8 times that rear end times this but would divide by so the 1st song after what is whether 1 or and becomes as no emulsifier water and times this we get minus the Razorbacks car bus news where knowing vexed Barrios buenos there in terms of great the Meuse courts cancel they must use this expression here show what is it was shut up that ahead a house pour off but how How OK see square wars minus up where my little lowend over lowend types capital and wife where can simplify bite finding common about where so the column about later this at add up here there's no way out of that sort saying it a writer without little at times cover bias once bias capital and minus 0 what should be a little at a time out however minus Cabello because here we're minor slow and here we plus gluons the canceled a fight . the capital will and Myers 1 scab Solomon aware we will bias want struggle receiver I saw trail what say this is what you get if El Al is good but he is but why a combined haste to target their I really want this way the comedy on that practice numerator from that 1 of the Lewis canceled that so this is the expected value of sigma hats August remind ourselves Ozark old aren't we want to find unbiased estimator of the Razorbacks bar that is we wanna find some expressions who is expected value is this or this I guess we found somebody was expected by that has a Sigma squared in there we just multiply hat swear by something that pans and and the proper thing for right about estimator so want defined a number see depending on air so that expected value of and they have squared it is equal to the very but far stigma square Over and capital and minus little or Chapel minus 1 they were somewhat quiet cigarettes were by something so it would get back 0 0 with such sets number see of K soyabean don't plant expected value over a tub cigarettes square is going to be a must where Milan minus 1 at and form the ladder capital at minus 1 I would want this to be able to but us thank short K story what does the Razorbacks bar uh grew I've got Bicester later that arrived by Cecil where arranged the story will see something like that where will be gone by says yeah but but with but we ought the rest of ex by Cecil
38:03
air means that they are source as late as a success virus equal delaying its posters OK so it is that the proceeding With Carey based go but 1st I guess wake and capsule Hussein was caught some both sides we cancel little on both sides waiting gets a little capital and minus 1 on both sides parent where does the star I virus number air crew that for who OK so here's our hats weirdo spot piracy whose water we get I had for X Y Y Smith back 0 4 with now but With with each with a quote if if with with before his trip with God with food for sure that Byron rearranging things and thought to theirs 5 foot BEN minus 1 from being missing the slaughter Iran's comes out here and then the rest of city goes over here I have accounted for a and reason to do this is the same parenthesisfree already that's our friend s where which only in the case was the unbiased estimator for the various overland Times as saying I guess I could rewrite that is 1 minus the letter Kaplan says this thing is far less squared with fight so are unbiased estimator resists some rights but they were put back with but but but but but but but but but but but but but but how how old is she or old older it is a low a colleague Zabel Reyes a socalled the sample areas and they a better KaiserTech a solid effort population down Bicester assembled a sovereign states but there's this population correction factor in a case of like OK so Indiana Maryland well what is our staff reasonable road bike so we replace selects bar by the unbiased estimator for and thus kill both big givers named S X square is defined commuters 3 lines means that the fight to be that's the definition back to 4 4 with a 4 4 0 0 but for the . like a bird SX bar areas but hazardous for Dole but but he over with a the day so everything in here can be computed from needed data the sample for the table for a normal the station CXR bar and yes back spa are computable from the sample so you could actually area near his South up there you could do it because it had various that bar which was the city squares you don't know what your vote but some replaced by something we get from the data past 3 estimated rates bus sparked by a select spots where would place respect our bites on unbiased at and Nairobi Conference what today so it's either break of the see I it back be adjusted to what problems are due on Monday we haven't gotten were covered all material salt or reduce the problems of the OK let's thus . joined fire this us path to lure were very dichotomy is faced crew they
45:42
also all 4 days then said a mule user notation gay hat for x bar at Yaddo as is lesser later bye says therefore virtual population portion for what which at sir but with well the 4 or the that's cap but there what would guess Square D in this case but but that but so are examples of this you do I know what course of operations 1st a chocolate I standard the Mandela said sorry to Newt individual gets a wonderfully light chocolate rather than allies fame is 0 forget that I know better than you sample people nestled you like soccer better than our basic topic want that person here once they said LU 0 so severe people that talk to open up their more Porter examples but when new people respond to our medications or are you might assign a 1 person recovers from analysts ethereal and a medication and 0 they don't stop yet would force the population of your sample that up recovered when given a certain medication other exempt might we public opinion polling more serious than wealth said what could be more serious ice and preferences presidentelect OK so I would ask where In this case which with but offered with with with With so old or toxic yes or no With yet 1 I will With With so this still that didn't on economists were not at if it were Birnell bug what's Piatt its water or enzymes Osama so some must be at times say during the summers and dance br piano already times Asansol but us I was 0 accessories I told yet no answer that's important point but site near Athens years
49:41
excise Wernecke scientists and ITI skip step excise tax experts and why what were 0 1 nite square 0 1 with 0 1 sources say whether Cyrus I scored
49:58
assault OK they so I know what I said Brad 1st was by said this is this this is the same as that but it's like not that's true whether excise orders from but I thought it was set up at population or not this is true therefrom by economists faster because when you square 0
50:28
user of winners where 1 you want sex XI car thank God so the 1st becomes an ex parte he got worse when its earlier minus F P have squared here and so it becomes about Over and Midas what she had times online skier but what so thank
51:02
and so are what would are as mayor being fought by Carla West still what a
51:12
still BS Reyes a gap fish with with 4 4 4 4 4 4 0 0 4 4 4 or 4 or how drop results in that where lawyer mayor award abiding by the land here so they can solve so you're Piatt 1 act over and my 1 and then the structural factors for fired population 4 4 she saga struck think what will be open when led L with Scarborough said what's and bad harness case I the pass Over get but X Florida's Key at 4 but 2 or or but all or but but but at and abuse square root out I but what also it was also but but but over but but over all but but or but but but the but but but the search but also for all but 4 of 4 or or or was but but but but but
53:36
that's a CIA so there's a better example on the box example off see Gates true 13 ship their both but good
54:12
Apple says that fears is fast bebop or some hospitals that fewer than 1 thousand discharges that it turns out by 4 for all of the but will also is a world where all yes who will also is yet or not if he or if old where I was and I think we got that matters but there was on what banking 68 I'm sought yeah that's the true value of 3 pretend you're not right until you a sample of 50 was 2nd with 4 or 4 I think that could turn it yes but with now end 26 fewer than 1 thousand discharges for that type or or or or so essayist Whoa yes yes B 1 already time some of its eyes that size or wonder 0 1 there are fewer than thousand charges 0 otherwise so we won 50 times 26 . 6 over 50 which is quite 5 2 for a start I think cricketer such what's Eli S. associate with 4 4 4 4 4 4 4 4 but why are we ever so I was they are Bicester where a well How is right that in their 1st Piatt what West yes batch was or yes . 5 to 1 Meyers would be . 4 8 the sample size with 50 so visibly 49 while minus 50 over a thousand train and what is a
58:10
sequel to the ore . 0 0 4 5 great you do that you hundreds of laughter I have been playing a a was zeros 0 0 4 5 object which ship or OK so let's find
58:50
or date for 90 per cent CI for cake for war based on a state that the total yes thousands
59:09
of regrets but don't answer noted no idea I took a wrong number here I what work was a thriller 92 retrieved the 393 war Mr. a sad book redirect to but 393 thank you serve but this number was still right and thus best Piatt was says in their wares would only . 0 assists takes about this case us find a 90 percent CI for 4 days so always organ the numbers here not so 90 is Versailles guess you expressed 90
1:00:10
years 100 times 1 myself a walk or so means authors said up quite where where 1 leg Elfers . 1 L floor is . 0 5 How are you 0 for 2 that means that there is a will switch notation from here to tables novels that table took over the or as a sector any good victors lovers Aesop PA it is the use of clean it is a number so that very under the normal Betsy total laughter his EPA sup is With 4 With so woes what was sealed off there was a number so the area of the rights of zeal Alpha was Elf so hurry relate Z E sub p from the table and most of zeal of Elf yes drink From the table lookup c sub 1 minus Elfa fewer of pressure we wanna know CEO voice Elf over to me on my niece of 1 or 2 words we want to carry out here to be off over to a some user orders to be 1 myself over in that table they have this picture so that means if we want
1:02:46
find where the area to the right of appointive . 0 5 Emmys find be place were leftovers . 9 5 starts to look over the table quite and cover so you brothers by now 1 part I told you saw Europe 0 4 9 6 hours there was slower right Royce Our Brewer so we lawyer . 9 vibrate you . 9 7 5 1 . 9 6 years earlier this year by is 1 . 6 5 1 . 6 5 Zeddie survive Z E sub . 0 5 is approximately 1 . 6 5 baby is 1 . 6 4 that's a lot of it or or not OK so just like me your
1:04:03
Brazil that uh at that With 4 0 0 but the but for say for a SEK app we that was . 5 to to minus 1 . 6 5 so but we took the square this very point but possessed you have . 0 6 7 and then . 5 2 plus a number 4 no widened raising are covers a doctor but it but I would like to know what does it back contain the real deal so I never thought In a computer sovereignty chief Al tree bully Wang the pair Quayle borrowed ideas that will back for a long list of woes that seems a bit much this is less than 1 the miss vessel or . 6 address and the true value West Point 6
1:06:05
5 4 didn't missed it at all says well back at 1 time and so it can show up you are right that should governors incumbent also had head and bigger sample me was quite waste from Tremaine or what there were from radio sample sizes pretty small compared to population size of slow lap let's move but thrower ratios less rating ratios
1:07:13
plant by recession some . for the who will wear tho but that you that was small that and or well may maybe where has already resigned last was down 50 over 3 I reacted don't seem all that small 393 affairs better do bad luck by year 9 taxes or attend the wedding venue Lewis you could say about have a sunny happen 1 time intended does happen by accident something happened but probably 1 Moon 10 million that does happen somebody was a lottery OK so so aware 1 population in this chapter or lock us icecap however and 2 measurements are taking on individual square box this publisher if fee so at for plant what a face OOX while is no during summer quite a sojourn a visual 1 MY 1 is measuring some other quantities such individual 1 so this might be something like a of whole lot individual lives and how much popular visual drinks might be some are problem normally cigarettes that individuals spot or hot tall individual is bent but size for added 0 comedy cars and above number acres a farmer has come later received plants the 3rd quarter all kinds of things like this but I think some other lawyers are on Romania come over family dog SAT score of struck things like that so are but the study 0 Lazare's are related to each other so it is with to With boat dock try wiped out my by 1 overcapitalize doesn't change this ratio so I could really expresses says the true means further why mistrust divided by the trimming for early Texas roads and address in estimating far by taking us several for sir but yes I test of how how how well 18 yes population Comair as it could we or but or or crew who wore white absorber fish for war but for whom he or or or or which is so old 0 0 0 0 4 0 how they saw it a sleazy F. sample a uh we sample little and individuals and we take their XMY reference competition like the ones we did was burgers they would do that the core a sofa X bar physicists will do
1:13:54
this but why where Luria XI Street we did cope we deliveries of ex parte foreign leaders through the same computations worry place while reacts as buyers wires and carry who also are estimator are based on a sample will be Capitola With but all but 4 or or poor old old for old or or how which oddly also Reuters ex parte over Over but why bar I got part White Owl Cabrera confused this some pressure we were not yet begs for a August how where he but it for for how or so we estimated various of off I think so but but duo off top U.S. Malta of carcass job take through the year DTX ever see 3 I worried gathers of news of Iraq Aziz was passed off OK so out of this I teachers Hill and the head so here we have a function of was where a function to move there will federal Thaksin wine we want to know or approximated variants of that also was to Oh God is very also false Omar for court for how to say well or or 4 4 4 0 4 4 4 4 0 0 4 I was sure cool where a squat world Troy express listen terms it is now a E ahead of but there for urinary he's 1 Oberle case for war or or 0 0 0 0 0 4 0 4 0 now the perimeter wonder OK so where some functional or random variable follows where what parts various see him we know things about acts like me and that reds Oh you right June little axis equal to Geo news of capital X plus Alexis minus Newsom cap Alexis times you Prime of new of capital X plus onehalf X minus the use of capital X squared GE double prime of news of capital axis and this is approximately equal for blacks not far from the use of capital misses a city secondorder Taylor expensive Fergie if by acts as a pretty high probability of being meaning father and this is a good approximation for Teal cap Alexi closing at half or or or if at all but how with off OK look OK so what can we say that about the expected Uzi rock what but I expected by right hand side
1:20:25
that we are know what the right hand side Dougherty expected value swell a 1st term as a process is yet we such as is number of Jedi of Newark New selects what about the 2nd 1 figure expected by the 2nd thing here this
1:20:59
is his the number factor that out what's expected by acts biases means 0 virus from a 0 what's expected value of this term over onehalf and the dual by Casas would follow us with dated started directs might mean squared with that that's a very SOX they expect right from Rio half Juno I was saying my excellent squared off for or but threat Of course now s Votaw tour also it for or or or whether it it was or with or with a yes or old it will be over old as all of us or but was 0 4 0 0 ever echoing Colver saw person glossary very Corliss the vector the source for me us tour air back sorry that flight but we will go but old fish HC or call for 4 or could for will or with we say for a be a I did a French aid due respect extern and diarrhea God Bob byebye to remove due respect wide evaluated New and I get a 2nd order terms of but see old or or or with what we hope but for all but but with old old or or with now up with with yet we or will call for a quarter or will enter says a Fox sequel was such an order Taylor expansion for of 2 variables may ran out of steam there without OK so I'll for we get back to plant for 0 say audio the function of Struthers at 4 4 4 4 4 4 4 4 0 is savings with this virus cap but cap wireless data expected area get June 30 after me them yeah I put a cap lacks a data expected Irish Catholics places we find answers for that we will have be that can be 0 by capitalist lies near Luxor 0 but by Kabbah why most why would be 0 so that they expect viruses from Spanish expected tablets West New gray areas the variants of acts cited these site where are sick was setbacks square over 2 times a 2nd blueribbon acts at likewise Daggett 2nd it I'd it's the why scientists 2nd DAY and then plus what's at last summer vesicle Reyes Alexa wife us so they will find Cimex sector of the O. G. L. right so I would give you the expected value by in ornamental case look like that and 2 rebels look like this where what the various but say but see we the variants of approximation from while Russell case but yes or 4 4 4 4 4 0 or or old she old or older we will work with her but aware what would ZUO would work whether Fox labor spies that's a Fox by GEO of abusive X Meyer say whether X where overt Gedo Priolo new selects or scrap show Court how full of I should 1st uh Todd jolly variants competition backstop because 0 I did feel I wanted it be gone applied us about this or the survivor time today that while hourly skipper yet expected value as for the ratio
1:28:52
sort introduced by thing since I have 6 minutes left lawyer Richard Hill is 1 thing that that would be a continued to be continued Oh yes a cup with but but over but sees as a function go to burgle Saleh ratios what also apply I love this formula to functions what Geo exwife you go wire or X so what do we need a bar GDP where indeed Of these EDX GUY seconder secularism wire and being mixed Craigslist computer goes for different a like that's weird wires y over X where just saying a 2nd time with DEC's remote a sign so it to wire rescue if we different take a suspect a why for all or old boy get minus 1 over X for a 1st day DGY a but it is sworn or acts and D squared G T Y squared as their own orca E E so using this formula here DEC's bar why are we get the prospective buyers ratio cap OR is approximately equal to um we XRY are everywhere sewage this rate being Hewitt's city borrower renewal X buyer plus stigma squared eggs bar or truly said lurid acts it is to wired bar over exit Q. plus say Well why bar squared over show and then the 2nd rural idea 0 farcical areas of acts bar y bar I a mixture of which was minus works but as diarrhea the use of X as you select bars so on exit outside side that mule so that saw new survive are orders for Laura Musa vexed by and this is the city's valuator at Musa it is tough about said so is cigarette spots where so outlawed by of twice the use of wife are divided by use of ex parte you get 2 times a 2nd rebel or the 1st what said rebels Y box 1st proposed it would be so expected IOR replace series by what is revealed new borrower be new while X bars new acts for appeared to his castle the various elects bar they were replaced by city Wexford squared earlier news while over new wise use of X Q we're here with wouldn't say where exwife what over use that squared we divide followed by with factor use of acts uh new challenge calm but sir Our paradise formalist may be that we should keep this from and this is survived Fox where short that was writers formal but but the but what if so expected ratios approximately equal to the ratio of expected die use pass this pervasive trend by you would expect this to be Colorado which big new X over new wife some correction affirmed if secretary you ought to broad I should do Y or acts against a this would be that things would be OK but there's a Soros Crutzen away from that of bite so I think there's some
1:36:50
exercises with various Barnett site and Andrew Carpenter will brief rows of
1:37:05
dead stores value could see what concept is to within our rights both modified
00:00
Lecture/Conference
Mathematics
Sampling (statistics)
01:33
Covering space
Standard deviation
Divisor
Multiplication sign
Sampling (statistics)
Analytic set
Mortality rate
Mereology
Summation
Lecture/Conference
Term (mathematics)
Square number
Dependent and independent variables
Right angle
Subtraction
06:56
Point (geometry)
Decision theory
Multiplication sign
Distribution (mathematics)
Insertion loss
Mereology
Theory
Number
Frequency
Mathematics
Population density
Positional notation
Arithmetic mean
Lecture/Conference
Circle
Absolute value
5 (number)
Alpha (investment)
Area
Normal distribution
Sampling (statistics)
Mortality rate
Measurement
Functional (mathematics)
Approximation
Local Group
Flow separation
Arithmetic mean
Normal (geometry)
Right angle
Arithmetic progression
Bounded variation
15:36
Sigmaalgebra
Multiplication sign
Expression
Sampling (statistics)
Mortality rate
Inequality (mathematics)
Hand fan
Spherical cap
Meeting/Interview
Term (mathematics)
Ranking
Lie group
Table (information)
Subtraction
Resultant
23:50
Point (geometry)
Group action
Standard deviation
Sigmaalgebra
Sampling (statistics)
Mereology
Number
Estimator
Arithmetic mean
Lecture/Conference
Average
Square number
Decimal
27:13
Flow separation
Area
Lecture/Conference
Term (mathematics)
Multiplication sign
Square number
Water vapor
Uniform space
30:07
Trail
Multiplication
Sigmaalgebra
Multiplication sign
Moment (mathematics)
Expression
Sampling (statistics)
Variance
Water vapor
Set (mathematics)
Proper map
Number
Estimator
2 (number)
Numeral (linguistics)
Manysorted logic
Lecture/Conference
Term (mathematics)
Square number
Right angle
Units of measurement
37:54
Point (geometry)
Divisor
State of matter
Multiplication sign
Water vapor
Dichotomy
Solid geometry
Grothendieck topology
Number
19 (number)
Positional notation
Spherical cap
Operator (mathematics)
Square number
Algebra
Area
Sampling (statistics)
Staff (military)
Line (geometry)
Mortality rate
Estimator
Voting
Commutator
Right angle
Table (information)
Nearring
49:39
Lecture/Conference
Multiplication sign
Order (biology)
Directed graph
51:01
Root
Lecture/Conference
Drop (liquid)
Resultant
53:36
Lecture/Conference
Multiplication sign
Sampling (statistics)
Cuboid
Associative property
Wave packet
58:06
Sequel
Lecture/Conference
State of matter
Physical law
Object (grammar)
Units of measurement
Number
1:00:09
Area
Multiplication sign
Total S.A.
Mereology
Vibration
Number
Goodness of fit
Positional notation
Lecture/Conference
Order (biology)
Supremum
Normal (geometry)
Right angle
Table (information)
Pressure
Family
1:04:03
Point (geometry)
Lecture/Conference
Network topology
Square number
Sampling (statistics)
Mortality rate
Number
1:07:11
Geometry
Observational study
Multiplication sign
1 (number)
Mereology
Variance
Number
Prime ideal
Coefficient of determination
Mathematics
Goodness of fit
Spherical cap
Term (mathematics)
Square number
Cuboid
Perimeter
Statistical hypothesis testing
Process (computing)
Closed set
Sampling (statistics)
Perturbation theory
Cartesian coordinate system
Measurement
Functional (mathematics)
Approximation
Estimator
Arithmetic mean
Doubling the cube
Physicist
Differential equation
Right angle
Pressure
Family
1:20:23
Geometry
Divisor
Sequel
Wage labour
Multiplication sign
Grothendieck topology
Open set
Number
Spherical cap
Lecture/Conference
Term (mathematics)
Square number
Lie group
Area
Process (computing)
Thermal expansion
Variable (mathematics)
Functional (mathematics)
Approximation
Vector space
Order (biology)
Right angle
Figurate number
Nearring
Directed graph
1:28:52
Area
Series (mathematics)
Divisor
Multiplication sign
Valuation (algebra)
Mortality rate
Functional (mathematics)
2 (number)
Mixture model
Sign (mathematics)
Spherical cap
Manysorted logic
Lecture/Conference
Wellformed formula
Oval
Order (biology)
Cuboid
Renewal theory
1:36:47
Lecture/Conference
Right angle
Open set
Grothendieck topology