Limit Theorems
Formal Metadata
Title 
Limit Theorems

Title of Series  
Part Number 
7

Number of Parts 
16

Author 

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. 
Identifiers 

Publisher 

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Greatest element
Ordnungsstatistik
Observational study
Decision theory
Forcing (mathematics)
Sampling (statistics)
Sheaf (mathematics)
Insertion loss
Price index
Cartesian coordinate system
Sequence
Open set
Numerical analysis
Mathematics
Plane (geometry)
Uniformer Raum
Order (biology)
Modulform
Set theory
05:32
Point (geometry)
Randomization
Functional (mathematics)
Decision theory
Multiplication sign
1 (number)
Similarity (geometry)
Water vapor
Event horizon
Rule of inference
Order of magnitude
Grothendieck topology
Product (business)
Vortex
Goodness of fit
Lecture/Conference
Term (mathematics)
Cuboid
Set theory
Social class
Random variable
Distribution (mathematics)
Gamma function
Sampling (statistics)
Independence (probability theory)
Price index
Sequence
19 (number)
Numerical analysis
Category of being
Arithmetic mean
Voting
Exponential distribution
Factory (trading post)
Order (biology)
Right angle
Fiber bundle
14:35
Logical constant
Functional (mathematics)
Statistics
Beat (acoustics)
Group action
Ordnungsstatistik
Divisor
State of matter
Decision theory
Multiplication sign
Decimal
Water vapor
Open set
Student's ttest
Rule of inference
Product (business)
Power (physics)
Group representation
Sign (mathematics)
Population density
Lecture/Conference
Wellformed formula
Different (Kate Ryan album)
Descriptive statistics
Social class
Random variable
Area
Distribution (mathematics)
Potenz <Mathematik>
Cohen's kappa
Model theory
Projective plane
Sampling (statistics)
Independence (probability theory)
Median
Mortality rate
Line (geometry)
Cartesian coordinate system
Numerical analysis
Arithmetic mean
Exponential distribution
Uniformer Raum
Order (biology)
Gleichverteilung
Right angle
Game theory
Freezing
Directed graph
32:58
Metre
Point (geometry)
Functional (mathematics)
Density functional theory
Divisor
Multiplication sign
Real number
1 (number)
Open set
Mereology
Event horizon
Rule of inference
Grothendieck topology
Frequency
Population density
Lecture/Conference
Wellformed formula
Square number
Cuboid
Energy level
Area
Distribution (mathematics)
Scaling (geometry)
Expression
Moment (mathematics)
Sampling (statistics)
Median
Mortality rate
Lattice (order)
Limit (category theory)
Affine space
Stirling's approximation
Numerical analysis
Uniformer Raum
Factory (trading post)
Order (biology)
Gleichverteilung
Right angle
Object (grammar)
Figurate number
Pressure
Maß <Mathematik>
51:20
Point (geometry)
Statistics
Divisor
INTEGRAL
State of matter
Direction (geometry)
Multiplication sign
Range (statistics)
Multinomial distribution
Parameter (computer programming)
Drop (liquid)
Mass
Inequality (mathematics)
Event horizon
Power (physics)
Prime ideal
Derivation (linguistics)
Mathematics
Population density
Lecture/Conference
Different (Kate Ryan album)
Wellformed formula
Series (mathematics)
Set theory
Area
Distribution (mathematics)
Sampling (statistics)
Independence (probability theory)
Line (geometry)
Limit (category theory)
Numerical analysis
Uniformer Raum
Factory (trading post)
Order (biology)
Charge carrier
Right angle
1:07:28
Trail
Beat (acoustics)
Group action
Divisor
Differential (mechanical device)
Equaliser (mathematics)
Multiplication sign
Range (statistics)
Water vapor
Parameter (computer programming)
Mereology
Grothendieck topology
Expected value
Frequency
Mathematics
Population density
Spherical cap
Lecture/Conference
Average
Natural number
Term (mathematics)
Geometric series
Energy level
Integer
Series (mathematics)
Area
Shift operator
Matching (graph theory)
Theory of relativity
Forcing (mathematics)
Algebraic structure
Line (geometry)
Price index
Flow separation
Numerical analysis
Uniformer Raum
Order (biology)
Right angle
Summierbarkeit
Spectrum (functional analysis)
Wahrscheinlichkeitsfunktion
1:23:35
Group action
Regulator gene
Range (statistics)
Numerical analysis
Population density
Lecture/Conference
Term (mathematics)
Uniformer Raum
Average
Different (Kate Ryan album)
Oval
Order (biology)
Energy level
Right angle
Figurate number
Family
Set theory
Condition number
1:28:40
Functional (mathematics)
Divisor
Multiplication sign
Kontraktion <Mathematik>
Insertion loss
Ext functor
Mereology
Power (physics)
Frequency
Mathematics
Population density
Manysorted logic
Lecture/Conference
Gammaverteilung
Moving average
Energy level
Alpha (investment)
Potenz <Mathematik>
Gamma function
Computability
Infinity
Numerical analysis
Category of being
Factory (trading post)
Right angle
Musical ensemble
Asymmetry
1:42:13
Lecture/Conference
Open set
00:06
So the exam will take place in a discussion sections A pot colleague defeat Friday Due on him Chapters 1 through 4 chapters were free They source for uniform but not very loud I like Some ruled defeated a colloid choosing between 2 forms of execution chapters 1 through back with Tiger Woods probably bought 3 force who USITC Russian With probably about threefourths of feelings The 5th Needed 1 Well yeah furor discussions in the the other room you meet in Pick Sir OK so what's been each chapter 3 a ahead The last topic called order statistics of share so cause we're a sequence a random variable studies are outcomes of some random number alike World guy Burnley trials 1 application would be Insurance claims X 1 is above The amount that The client number 1 planes a year from his interest is not tied to frame up by 3 kinds of our and my lawyer be of interest to interest companies is the decision of the largest claim they get in 1 year Why would they be interested how large what I need to switch of the largest what What is in your company want Happened But it was probably the largest kind these Small big probably the largest big know they'll have to to charge more money for that Premiums so their into this vision of the size of claims and particularly the in the disposition of the size of the largest so they might is reorder the sample X was the largest sonant next lodges socalled um X 2 of them bring parentheses around indices subscripts Because of the but but but but but but but but but but but but but but but but but but were We still have the same set of values industry orders from top to bottom of the largest of the vendor was here the 2nd 3rd And then the loss 1st tour of couples of all things But 1st through the following day These are independent And identically distributed so well often have to write this independent and identically distributed and census comes up so often we use IID
05:38
For that independent increased With distribution function after The cases a restatement of identically distributed they all have the same distribution function Was What Here beside just means that I'm taking the same survives by reordered Indicate that this is a reordering of the set aside by the same numbers It is Maybe the order in which they arrived This is their ordering by their magnitudes sites that lesson Is Not identical means they'll have the same half saying distribution agrees to return property could be exponential gamma normal as long as it's same overall trend rubles Which is often no reasonable assumption you like Bolivia certain classes of up from events and l forward annexing class Dollar things like the role of a guy roller died 10 times the distribution beach role with the same problem wonders What's that To answer this doesn't matter which role you're making the same on the 1st or 2nd order tossing a right and then you have got to Occam's each time probably heads or tails these terms perhaps they all have the same station options on same point Talks 40 might be testing lifetime of white box and maybe like folks are often the same manufacturer which all have the same exponential distribution pockets as chemical distribution means sequence around the rebels that all of the same distribution what would but is independently E It is Back Get exactly what to buy back stock or appears a joint distribution function What is that at this was probably the independence It is at this joint decision function butts in the Product of the individual once Texas Definition of independent of it So now found where that But All but of the old of Civilian say what their decision bidders for the largest of these sample or goods around rules and they lost and never water or water UBS forewarned gas distribution of random rural areas for distribution our thoughts start with the largest Ms. says that The largest in the sample and random variables has to be But 2 X
11:02
So what were vortex 1 cannot be bigger than extra next Our which which X 4 I where like this what this is less Glaxo That's also Austin biggest warns Lester Glaxo this 1 has to be where votes to although realestate acts of the largest ones less neglects all although if the tallest person as rumors Larson some feet tall them more or less the tallest person but it does matter if the tallest smaller than strawberries and we all are so this would say I think This is true of words This event the largest disaster lacks is the same as All of them are less than that of the same events The same as all the rights and now what you do with that Right because independent security that way but the same thing appears every time right here and XIX to attend so I have died X 1 X 2 X 2 X and I've never X 1 year after next year That's and thereby I of acts everywhere Money terms so I ever so there's a bit of their spot so that his decision The largest if they common distribution function raced and hour Oh that's her before lithium examples unsavory say something similar but the smallest 1 thing must And this is 1 of those cases where we use this varies Trivial useful fact probably based on my spouse of a couple of years we've probably a factory in computing the problem a compromise is easier for that Met they complement the Office's there Is the smallest Bigger next so Mr. excellent and where the height of the people misrule Be summoned Aguirre statement the shortest person the room is taller than final 4 feet They now Whom we use independence and the in this region of the Urals product express that Up here Yeah we said Tallest must go through X means all of individuals you're saying the shortest is bigger than next summer statement
14:36
Everybody has taller and Airways 40 of the surest person for everybody followers for the probably next 1 public works wonders bigger Texas Who was there the next to x as and now we can use independence here And make a expressed each endorsed germs and the product using a distribution function this is I want my And All of them are 1 might act so the end we get the probability that The smallest is less a is 1 minus 1 Half of acts today and this 1 is that 1 and each of these is 1 might suffer Maxson there and modifying the together sigh get 1 myself the and number but here Now let's suppose that suitable examples abound Forward better yet but suppose or in continuous case and whereby the density the odor densities B for DEC's want excess hiding it to a density via the decision function taken area and are the distribution function so you ever distribution functions of all we need do is different so the density Flora the smallest why don't we just different shake 1 goes away a minus sign a toll on another 1 where different saying something to power so it comes down we get whatever peered inside be and minus 1 and multiply by the workers inside the Jane Roe Remove capital leftists left but with a minus sign and arts out that 1 Soviet little after presidency for the smallest Water buffalo largest rate different tickets and that's a simple application of a jail Me now But Object Was For all the of but the boat But The of all of us find it this ratio of 0 artist Look You have exponential and saw this These something like the following the light bulbs are Commonly models lifetime of light bulbs is calmly model is having an exponential distribution in this room we might me In light of the fixture and 1 2 3 4 I think that an 18 18 times 3 is 52 proper 50 to all case 54 54 like also this is 54 Annex 1 would be the time when the fund that 1 burns up next to a time when the middle of burns next week Times now and burned what would despite the decision next And change this is really misses which like Paul this is the first one burnout is to be when the first one burns out the smallest lifetime chores time would be when the first one up through finding this vision of lifetime of the shortest will like of not least that's what this would represent banners for ODA solar reduce these formulas This 1 year old This 1 what is the distribution function the state's wellness case 1 legacy Kappa As you might slammed uses for X End say his S 2 Kit But The Seoul yeah we just I'm in the formula to give the density for the shortest look and and then we get a this termed today and pop analyze 1st foray and Anwar that looked like this As far as this 1 this early multiply by the left would be Each my Aslam acts and this is for expiry 0 and the fighters and where we get well these 2 are constants right goes in front and Oregon exponential although B minus Tobiah where visitors a land of freeze turned been X X richer than and minus 1 plus 1 is banned And so what's in this region of this render all the smallest of an independent expert rentals
23:53
At leather sex told of Premier and land Should be As duo All the Macs Mom There's a further back here would be a misuse s we get end and then white Elias You demise land X rays me and my 1 and then this is land In my Aslam for experience 0 sources of theaters 0 clever and rules are to be negative And we don't have a name for this So that's how you do this density Florida largest further small was not good Followers to 1 more example of example 1 do example tool For each cheek to cheek at so Capital user 1 all these are uniformly distributed on from 0 1 that means distribution of any 1 of these We each but he It looks like this is For all I think know that's is that uniform distribution and let's right down the for these small snore largest tho the case that's me for largest 1 is here says attire comment is function rice onetime z density soul Will write this down 4 x between 0 1 is a beat end X minus 1 the density this For these minerals our oneday career saw what what I want and of course is densities 0 area from X is not that reasonable this is an Xray my and capital have been my times the left the left is 1 where are smallest despite this formula and on my sex with minors what times the density is 1 misses if zeros between exit between 0 1 and it's Of course 0 Sex is not in Middle Falls early breezy right down Main densities for The largest and smallest in a sample uniform what about something in the middle of other life Largest might found me density for the height orders If you know of his vision And the deaths of at of all of What So IOUs some America B 1 could be and we've done those Nowzari but Probably somewhere middle like 3rd or the 10th or in the cases from 26 There were 50 for light balls in here X 27 would be What that's called be median extra the media of be some airports a description of the media Laura word Bunia scores years for the random variables are what's X 1 X bond of Prince disease I mean X 1 price this would be the score of the vessel or acts the was prices would be the lowest score there were 90 students in class X 45 with France's overseas would be means What might be asking What's the disputed the median is that things will get a lot of new factor often asked me the public off but you will probably Esther presses EU publicist statistics on Tripoli aspect of your North comedian Some ingenuity of the density or something like this that orders were I might be an overt I think so of talk Hollis actions Heidi do this Well our 2 Yes got which are higher So in the back seat at the project buyers or lying years axis the a density Gag order statistic is they limited as epsilon boasts a 0 4 This ratio at What's this whatsis what's a straight mood important Suzuki visit Europe The skull the quota It reminds me of a joke by sample choir classes so quiet life that so Einstein Newton the pastel hours of play a game of hide and seek and Einstein's
33:11
It 1st new Pascal height so I closes eyes cast to 100 Haskell runs way off in this summer stands right of Einstein buddy draws a square meters around himself and stand there and wants a nite opened his eyes abuses as Newton I found you and has no value on Over a square meters at scale composed The I a pocket bird now Rice's under a writer or with OK now on continues and rebels a problem finding 2 independent ones in a very short intervals about like squared finding 3 years More like a flight to in a smaller will you'll find 1 in a sample of so if this happens it ignored the possibility that there are other samples between area where Perhaps a means that Are largest balls in here somewhere and the rest Fallside 11 So where the rest go Are there any any over here Harmony But Well let's suppose I 7 Harmony would have over there the 7th largest made it look over here Is a 7 5 7 Harmony Gold figure This is the 7th largest means that there are only Well beer What am myself services over years dirty and miners by bigger Up to here there are I mean over here there are in minus 5 samples rendered rail and down here calmly smaller ones are the minus 1 All So orders are example remain Oberle South do We have 3 boxes The number We are several has to do what has placed by a minus 1 and the rebels here 1 render it will hear an end Myers I ran a rare will steer now For a particular er Some of them were I minus wonderful here I want 1 policies and balls there What's a probability that event Very particular Wannamaker could be x 2 x 5 x 100 x so I just thought I might as 1 of them a year on here with probability of any 1 of them happening while was probably that I might 1 grand Robles fall below this level their probably 1 Capital of events are probably Who would be squared WI minus 1 Volvo The Everex guidelines won the probability that 1 falls in here Is about Well The limit here so let's say But Every backs what's probably the 1 Fallson here it's Everex times epsilon divided by But what what I should actually probably do this That would be the probability that 1 falls the next subsonic acts and then what's probably that and minus 1 of them are above here well was about any 1 of them is what we're D1 1 minus F O X steps on to the end minus 5 Now let's can't somebody Ways are that history and things in these But 3 boxes where I would My is 1 of the box 1 this box and in my mind that box nursing thinking like that before capital and objects and you're just rudimentary places I might want the 1st place 1 the 2nd basin and my side that's and choose eyes Minus 1 1 and my side multinomial called and witnesses eat probability that now we wanted densities of is divided by London website boasts a 0 this number here is that factorial divided by sartorial times is factorial times at the end Factorial over by minus 1 factorial times 1 factor a which is 1 0 rioted and my I factorial ever get the distribution function at rates that are I minus 1 here we get the density function here we get 1 minus the distribution function and my aside and to get rid of L. Wright appeared a mail plant Open open but At all thank so so that Maybe example of uniform Crew But work Or to give it to
42:10
But the took But 0 4 4 4 4 0 that's what they now yes say look site for the ice largest at Or 4 But tastes 0 is a Mike MSA fragile rulers but so that it can you that was Say it Well must be really is talking about as I just dislike about up here Why is this Related to rats in I suppose because there's an accident is the 1 might enable hours This is our 15 there are 17 20 twos and 9 15 17 here Well this must be fire minus 1 So I must be 16 16 And 13 33 so I was 16 and is 33 What is Yes there says is alive But what were once what's word on when and how the density aside the best what What happens in a greater density In greater so there'll This is what so what Cicero The court As it was What if Give back for free more less I think this duration is easier than going out interval There is a This is I have defied bird This number of over here that the a density of period and want is using a fact that real there's over 0 1 1 and that's true whatever and I are so by a 16 NDB 33 would get the stack of Also on let's think for just a moment of R What these Densities look like let's say a and over 2 Argentines stake and even some of the fires manager Vendor A says That's a comedian Did he that she was with which he is What she is He When that looks like a wedding gets bigger and bigger bigger He bidding more more points in the early New following me away from 0 1 to think they're hiding at those points would look at pictures of community unit yearold maybe 10 thousand points in the press and the history of uniform distribution but clustering somewhere 1st they have diesel following struck Ramiro tribute from spread so where's median bought half so was a new are the density the densely reflect that a thought that means a meeting is Likely be 1 place as any other so this will not be like functions 1 but rather the is going to be more more focused near perhaps what should the densely be doing me a small away from half and it really be it will be normal but a 0 0 1 is a great guy gets maybe Look something like that war or is a reaI therapy Agnos affinity with 2 or more concentrated near it X is a number between 0 1 what happens next year or 2 At Gross to their house number lesson 1 race I part rose 0 busses for what prevents the whole thing from going to 0 This stuff off from here Will do this later there's some of the important formula called Sterling's formula that gives asymptotic expression for a factorial She walked I think there's a scholar of amazed by a reversal of As of Costa I think it's a sigh saw All Parliament's and factor looks like this The and what half and news that in here here and here you can deduce that advanced against By this very high peak around 1 half very narrow as is for the other wants these lodges in the smallest the largest won the density of Cyprus and for the smallest won the best they will look like pressure on them our not so this year over to its end Here Bird None piano over to watch a B minus what is always said there were 2 temporary might want 0 1 1 last little love Flourish they rate Suppose I is lessened Day
51:35
What would be and little X unless little white or other joint density of the ice orders And they Jake We might be interested in court files like I might be in a Foreign J. might be 3 in a row for the media from our core the 4 persons asked 3rd quartile markers distributed Over this it's not like that Their rich their way up the Take our sample size and would place 1 sample here and have the probably say Well after next year's bid but 1 here and have probably will ever wine To gone and an altogether life largest goes here somebody over here is there's I will go Hours army over here than minus 1 army over here This is the ability barges and minus J so far we've used up and minus J was Karzai's minus 1 plus To I might as well go their 1 year 1 year and Wednesday That's and minus J plus I was 1 0 in here So the probability of a particular sampled limits would be While the probably I minus 1 down here Cabler Amax minus 1 probably getting 1 theirs Little FOX Following getting this many In here Would be probably getting 1 Uribe's baffled why miners and relax That's a problem getting 1 venerable here following that many in there were there and that it would be this number to that power Probably getting 1 euro via left and then we have In my stay out there public anyone Bearden Why was 1 minus What we get this many of them their independence Now it is up to count Tommy wizard what I might respond in that are on this 1 and Myers J. I minus 1 year 1 year and my still their finances multinomial vision and to my mind 1 1 I'm running out of room here but the should be and miners J plus I 1 and here on 1 Evans Next year were Dole and biased Jagger cerebral that Finally will be and factory I Myers 1 Vaccaro 1 factor of the structural 1 factor so this could be used on the example with back but to kitchen but it's a lot like The previous derivation before we decide that I was here I want to go there and now we have to think of it and because his life largest going here today fires going here we go on Eagle years The probabilities of each 1 of those is the probably having highlights 1 in here Rather the having that many in there as a public having that many of their going and then this would be so public planning exactly here from landing Yeah That Polish that this would mean that 1st the smallest X was a small largest sorry so he notes servers that inequality LLC detained on here we don't write X 1 bit density Virex of 1 4 was this is same right or 1 and there And and 1 arguments Were intercepted change labels by what that acts of apprentices and is the largest advance the largest this before I said that would be at the front of the plant So you but presses and here as before I said this was the largest but That An but that's XAX 1 that's the smallest fitted with changes And the 1 And then I brought in nearly year I put the wrong already this was This This was a public bond between carriers I can't tell you were in there I got nobody words in there there're I might my might 1 over here and my stay here 1 year In 1 here That meant the remainder here this is nominee used so far and minus J psi minus 1 plus 1 plus 1 2 as some of the newest commenting the news and miners that in mind this should be And minuses The become J. minus I might want a life again I wrote the inequalities wrong direction I thought that this would be the largest that was the opposite called arguments Stiller through this change a label here Before you would have expert as this 1 and this would have had sex practices and changes At the end wants which And then again either Jaime Isiah So another Another statistic bits of interest is that for that That's a larger slice a smaller sets call the range
59:43
Harvey find vision A difference of 2 render a you know there a joint distribution erase froze accumulate I reverse the order I got the order wrong X sub Prime is the largest exit as 1 of the smallest So that means you have to reverse the labels here there for the densities of Seoul on Area B. We have joint density for the largest small simply take what's here near 1 and and But if you have a joint densities what's the probability that explains why less of acts But I can't speak for these 2 Over this set of stairs ST that's less biased his Lester Galax maps of exwife of S. They S The joint density of probability that the pair exwife business Saturday There'll over 80 of the joint density Saturday is a set here reiterated density over the Sept described in that event They About the only thing you have to give my areas set up this So is case Drop picture what appears St were asses us go the tee times acts as Gallegos as my sees acts so that's a line it's aligned rear is what line she equal to as my sex Rees is where the line of slope 1 wind is equal to X 0 when Exs egos is what masses Eagle the 0 2 years by a set of previous line And what size that line interested in where President the set Where 2 years beer ask my sex So right He a miracle at my website that Line is said they were as much us Sample 1 . 1 side or the other half what the point as he was 0 0 that satisfies this inequality Texas positive it does So it decide Soccer we describe that hero of what limits integration should we have well a looks like a Wigan let s go from 0 and trading Our And then offer particular of vast Weathers Why do start on heroes too And so what would the quarters of this point it's on this line firstquarter The 2nd Quartet is or as sex so why would go from whatever The why quarters you're up to and when they do I caught areas and my sex of us my sex and then we just put Cup of tea And we My 1st and then Yes with Solana so state with sad example here was that we're uniform Sample Independence Day asserted the density dry gas for the rumor the smallest And the largest Use this formula here with equal 1 end date will But Now what is this cuts out there that's Already done here and allies is 1 so I idea 0 and then 1 and then Jada's I am right On his wrong years and analyzes right So in Never I can't in the And minds the army has left us and lies or might decide 1 0 on Syria And fury of 1 0 and minus 1 plus 1 is for My mind just as C & J O minus 1 they fresh should have a ways to write
1:07:29
But good wiser hungry between the sponsor largest and Rice to and then 0 both Sosa beat And factorial Over and my But at And that's the end times in minus 1 0 fact Torrijos 1 or fact rose 1 Soviet and federal Over 0 Cockerill times 1 factor of the spectral times at in times and biased what and minus 1 Wales Found Where the uniforms so long Capel effort is Kappa X 81 my 0 that be want this As for the of 1 period so why minor sex right out of white line level exit Why when Sexton what's this number here Found bets and my look right And then we get finally density at why that's 1 and here we get this Turned to the end miners and were 0 that's what again against so is best for the range and here's what should be the restrictions on Malaxis force Capital acts apprentices 1 little wires for tablets of dances and so this is worthy of this venerable this that venerable water we know what the order of which is 1 so that should be lessened and They should be between 2 0 0 1 That's a Density further terror and done of exercise I think it is users applied to Catholics equal acts of apprentices and capitalize people acts apprentices What they So it is time to move on to 1 the more fort Chapters in the book said The author book all the Jason so that was being 0 rebels 4 But it is with this list to venerable supposed The Texas State venerable with Probably mass functions looking at the finite expected value baccy acts wearing this as I started Ivax that's a weighted average of the values X that times a problem has I value Right next to have times probably takes on that So I suppose example If Is 1 6 4 values that go 1 2 3 4 5 6 or and ran What really looking at their overall that I what's the expected size of the role as witnesses the size of the role before we even we before good that's what do you think it should be heard the right answer somewhere 3 . 5 because that's what that's the average role was that in this case For am What's a sum lasers from 1 280 particular a wand and somewhat from 1 and as an times and plus 1 or 2 You're and sixtenths of our 7 Do another 1 Exs Personify parameter Alagna distributed While 4 sons and rural Compte Nonnative integers natural numbers It was a An area And here Times FedEx TX proposed Sunday is landed to the X over X Factor oil you mind slammed
1:15:32
He Show that while we're times x 0 we started 0 so we could just as well start 1 because Can't be sure From the correctable 0 0 midway of this splendid reacts Allport Biedermeier slammed a hazard Doesn't depend on the index of summation and XRX structural with that X finds 1 fact trial no You might recall From near talk just days and this summer I 4 this summer's not taxable But it's not far That Of saying far under because that beat matters as part of that are want our land of experts 1 left so far away And then let by shift but White minus 1 8 works fires 1 effects is 1 J 0 and Jesuit entity Because Does it landed The today over factorial this year the lander I see demise slammed so dancers land expected diaper son travel and this land 1 more example of its as to geometric Where they Kia math of Axel cap blacks It is P is now reviewing 0 1 so here we want a computer this summer She went on sorry You're restart 1 . 0 He was I think that like if our truck He because every term as But but The but 8 German air is minor sister Redux Right But Differentiate their site next coming down various track want from this In the name of our by your minus 1 This aged trust me that you exchange Some career but that actually in the previous step The a changing if I do that change next summer's from 1 0 what's the term here 1 0 a year on my user witches Want what's 1 with respect that doesn't change a thing That Sublet here too Because now I nodded evaluate this Series using a geometric as a geometric series is 1 over 1 minus 1 might be The The Schmidt Pierre at their respective The but Which is my esteemed drove respectively 1 minus 1 might be Expected of 1 over key that's 1 or minds P. squared so Europe as expected to match that make Sends Related die until you get a 1 the Roma junior first one that'd geometric random variable what's he in a case 1 6 how long you expect to wait and see the 1 1 over key is 1 6 6 . 6 times larger tossing a coin and probably Kansas have sales as have to wait until you get your 1st heads That venerable the While much of the 1st set to beat director of people have you expect to wait 30 1st said 1 over onehalf or to make sense Or what's a chance of winning the lottery he has evolved a miasma 1 billion or 1 year depicts back 6 numbers was probably match Several works and numbers are what to what To Underwent a hundred a very that the library on 200 ever more daughter went 80 OK so the probability of matching to be won over 80 the 6th day of the wedding will be won over 80 The 6 was to convict 80 numbers any the match also sets is 1 of 82 6 army trials do have to have a expect have before you and 82 the 6 OK
1:23:51
Well my lottery again OK so that a lot of trials The you knew that a lifetime of which will come 1st And your life for when orders well I guess That figure By 6 tickets probably have an even chance of winning OK so Some of these things in this course I hope you take on light is a good idea the lottery you gamble at Vegas like family had Try lose your money it's always possible and have fun OK so those are couple examples of this group expect expert advice discrete Renner rebels of the continuous when A kit now serves as the COX terms Adair overall I've provided this is 5 Sir At all But also She came as Dr. we need it over the whole a row from eyes and very different in this case of advance easily nonzero from 0 once disintegrate over the range for the set where the densities different from 0 4 0 1 3 need to worry about this condition in this case are satisfied It says that because as number less than 0 1 right or a Wanerie 0 1 and then we get X year he acts and what is identical to blacks were to evaluate between 0 1 gives you have as I make sense average value over a number picked at random from 0 1 would be half Now Look at At He he will be That's fine expected the smallest comedian and me Largest A sample from uniform now always a There's a need for the EU largest memory although the meant to be go general formulas as so for uniform is a B and visibly acts This is 1 provided eggs is between 0 and 1 here what would be the regulations for uniform this astronomer of between 0 1 we take acts and by the density of the sky which is an act B and minus 1 and then level Max density for performers 1 under your answer 1 Soviet and hero from 0 1 X P & G
1:29:03
X And this is me what arms Yes that Text Plus 1 over and plus 1 of which is 0 1 and was that bats end over and plus 1 expected value the largest is an or 1 Isis a little bit less than What 1 minus 1 over and past 1 is what's it doing is a ghost of they deserve a sense of larger Swanley would be carving up against 1 what would be expected by the smallest be doing it to do the computation 2 His asymmetry this problem Where fires but Toronto perhaps I take you from granary The 1 being a threefourths of insert but admitted back for Webster we from history and so uniform so expected X 1 Know how Aswan from 1 warrantless onehalf would they must be from 0 1 red 1 NL here weary from 0 1 X what was a density for the us media tho At the Every really I want had density and factorial or minus 1 factorial and my aside factorial contracts today I minus 1 level that's 1 myself next and my hands I hear him so for the case of uniform Was she did she is did The folk With the how was Ever to a Soviet this capital F acts the left 1
1:32:21
So you have period X times at density all these fancy that For ills out front Their backs Many times the density of Hanover to minus 1 1 minor sextillion over 2 acts so this is what the numbers are from don't change and where to find out what's Isiro Over 1 Meyer sextillion or to Auto a computer visitor or were Well we know this a density Foot down Bush I know this is a density evaluators from 0 1 idea 1 so I wanted to do a stake IN AN so that I minus 1 is an over to an and minus by 5 well enough Hollis and m my size art This is so I want integrate this thing over and over 2 years and over to their side that I am so that I might want 2 and my size or means that our by is an hour or 2 Plus 1 And is white 5 this or I get an advance on em is ever to I ever to For center to plus 1 as at Suarez at tell me that tells me material From 0 1 ext to Theodore to online sextillion or to X is and plus 1 doctoral done here I might as 1 of their work to factory and eyes I frozen or 2 That So I just evaluated that nite multiplied by that would get and factorial over and over to minus 1 factorial and my ever to minus 1 and 2 factorial and I divide at pop up and over 2 factorial and auto factorial and endless 1 factor of what's is equal to about here I get an and plus 1 these cancel an up year I get what an or 2 With this over this this number is 1 more than that 1 side is if ever to press the cancels is like it's at half time and over and plus 1 But It's almost a half But Also Right now for my favorite F. B. gamma distribution or all if there's a density that's the big biggest sector dialects At Here we O'Leary over the place of the Dead Sea bearing 0 the Dead 0 4 x negative 0 to infinity acts times a density well the density has some constant stop what was front Daggett accident extra the alpha minus 1 time demise slammed X acts God I'm still story about whether this is fine but perhaps not but we're going to be so I never got finite without right arm is over a finite where we have with something it's going like Apollo Real time something its decaying like an exponential of what The ways And it's not aware of this intervals by revise So let's combined Hours elects yeah they offer And I do do this in a row You got because you don't have to even done for you This the density right of innovators from 0 very idea What that means if you're great the part without the constant from 0 infinitely where you get But If you get 1 over that cost so we know what heroes like this are less is this 0 we want evaluate over there not quite periods of power of X minus 1 So there whatever power of finds 1 we have not yet wait I don't want value Noah Poritz Part of my life with the power Alpha plus 1 Aziz alpha and alpha plus 1 So now I just use that factor but densities NWI get land that Alpha plus 1 and gamma alpha past 1 thing and now remember the property of our down functions there like factorial syntactic villagers its And his and my son Vaccaro generally Delvalle hopeless myself and echoes parts so this over this would just be Alpha and this over this It is a band that Carlisle But But what is gamma 1 planned this is that mental health was 1 of having a right now would be don't demise land backs NATO Lambda mutts gamma wanted 1 exponential sorts of exponential are not exponential exponential so if acts is exponentially distributed
1:42:14
Trevor Lander expected value of X is what we to stay healthy for 1 year 1 It That Mustafa