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Fitting of Probability Distributions
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Title  Fitting of Probability Distributions 
Title of Series  Introduction to Probability and Statistics 131A 
Part Number  12 
Number of Parts  16 
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  10.5446/12882 
Publisher  University of California Irvine (UCI) 
Release Date  2013 
Language  English 
Content Metadata
Subject Area  Mathematics 
Series
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Transcript
00:05
OK there's 1 exercise it was more difficult than the rest of us That I don't think I area sign this 1
00:28
Q. What is the best hope maps best for .
00:54
F uh say up or what
01:13
For favorite be limit of a NASA It Given epsilon bigger than 0 years a capital and so that aliens between a biceps on Biceps Bob Crowley who have bigger than what to do with that statement at serving out it Right because that is the limit will treat made in there so let's replace a 1 on 1 side by a biceps on their side by a concept Where was What But But was Drew that
02:25
And what is a side
02:38
As The sky mergers to something that's what UTA my Osub slot and converters to Peterlee A tossup Thank God
03:10
So debut Rembert do you know the terms limit insolent soup OK well I if this
03:39
If this limit exists what is never to be between You Right Between this and that so the limits but soon limit exists and this is true for every epsilon bigger than 0 Letter went up so I pick this holds limits A lot to do with us or not I can up cyber 0 8 . 4 Because a tour squeezed onto eatery
05:00
Right
05:06
Erin request on this technically speaking I should say for those who would do no oversight But with the when all but but but but but but but Assaults and then you up upside 0 include the limited physical so that means limit exists in their common value which passed itself for more rigorous you have argued that these terms I think he might have had them in of sequences but anyway I think ideas from here hand This was forced to use them they never exercise on these Extreme order statistics for Tom uniformity is a really bad ever Factory which Number that was 29 never 29 it's so we take you 1 to renowned from 0 1 and then After taker Sappho you Call the largest when use Apprentices and Max at largest Observation And the exercises to find these CDs 1st financier this fine Oceania for that I was easy part of their designs I now with the stance or pick you moved a series of boxing A Practice He will The CDs for a venerable as city with random earlier the probability that Iran's rules must be backed of functional At the That's her interest this says what US West OXU accused the largest of all the observations of the largess is lost it works well the largest Lewis Black Sea if and only if all of them are
08:42
Apply These are independent Those becomes Thomas Maine And intersections becomes a product of the probabilities of you us act You to us success as I could but probably You to us what's here in the budget talks probably said By floods is assigned me and I II Identically distributed have the same distribution so that you repeat the same thing over and over again but House NYTimes repeated and time so we get back to the end And what is this well at depends on X effects is bigger than 1 hits 1 that with Cecelia for a uniformly this Iran a rare loyal officer on like that 0 Italy 2 0 its function ex Article X that's what wiser 1 because that's forward is to return rural on officer while ran a verbal asset value Westrick 1 probably this article a member bigger 1 is 1 is lesson 0 and this probability is 0 all the numbers are between 0 1 so they can be less than 0 Maxim kept 0 otherwise effect is between him and saying is acts rays and Thanks to a crime
11:15
I did OK let's find they have
11:28
Book Expected value of U.N Well I officer 1 there because I know the density will vanish off Will 0 1 white what's the density here's a acedia density is driven up what rural constant function was Roberto of the stars of the PDF 0 guys Texas 0 ever rise next bigger than 1 You should have years in a row for months review the X times a density of U.S. but the density vanishes off sort of their what and A Between 0 1 drove that would be by And that's And so inside he reacts to the and hero Baxter the end is ecstasy and plus 1 plus 1 and we evaluate between 1 by 1 as 1 over and plus 1 times and analyze so is expected value Max How's finally various acts while ever the expected value over the from square bias the square of the expected value bridges he argued this year as part of it appeared there so why are computing expected I would buy back serve all week but before going square cracks squared They of 0 4 0 1 end That's what are X squared period Lee and minus 1 next to these and fast while the other OK so our hero Z CDF Anthony PDF is Is was was We think back So we exit and plus 1 or more bodies And this and this alone OK and then minus And divided by 1 squares and this becomes and over And for us too Bias Over the past 1 square off at
15:32
And Combine this with find common operator cannot come up to me and
15:40
Us to and plus 1 squared but not like this by this The right and squared by Mr. monitor how A Ortiz's become 0 or what On the 1st term of and squared Plus 2 and plus 1 by multiply that by Igor and plus 2 end square miles and irrigate liars and killed to and squared For grand tour of are what At a soft K There was the variants of you But but but I object of our said Now the exercises a The distribution of being standardized That's what's the standard normal distribution we use that term has a book use that term but eager standard normal would be 0 rates like standardized venerable means you some transformer has me 0 rates 1 of transformer reports has been 0
18:06
The truck me so it's track and over a vast 1 now hopping maker render will have various Exactly like I swear still take you and you parenthesis and the fact that by Spurs
18:26
I don't
18:35
So if ever
18:40
Try do it I could It all and less Westrick auto X He It's a thing For works simplicity Lemley Dulles see where squared or It was it Broke thank you Don't Well done If this number is blasts between 0 1 notices What's that number to the poor Story of But It is He is And has been rewritten 0 sigh List But OK a foot back you know this forest statements books This should not be sick scripts are to be square root of that square roots But said I do that because I get a racer 2 on the board of the June race to hear notes All of us out of my But was its too Area Ferrero Farrell or a lot of K Australia's OK so I sit out of us See wary of end over end plus 2 0 and then X over and Botswana plus an array of us Thank
23:26
I just thought of as a major shift to sue us
23:54
What It is too That On the way to get from here to here It's an matter 1 here in the numerator and 1 Fianna 1 and Botswana of us want as 1 factor 1 that gives me minus 1 over And plus 1 whatever over here playing back Exercise reduces long ago As if 1 they Angola say a friend month plus a a rented van Gogh Wheeler severed here Mr. and was a converts The way conversing What is this race and over and passed to do is Costa 1 so noria goes to X minus 1 rareroasted X minus Want end Readers Not quite Equivalent side but we can't accept that's replaces would But we wanna be honest or keep same had before and You're and up and an array of puts and Oriental swan song a rewrite the says 1st somewhere the 1 because over there for 1 1st overran today and and they'll output End over end plus 1 near Times Square Root end over end plus 2 x minus 1 and that's equal that this season plus 1 In the operator of mean the same as being done here And we will end up here and then there were they canceled sectors are now this is the year And what is that Lewis an ghost In rebels 1 goes What an array us to goes to what this whole numerator goes to experts is expressed poet who then what is the probability converts converters to eatery X minus 1 so long as this is true This in the limit but see what the says new areas An array boss wants us to say that acts as a disaster area equal to 1 biased view and over state where and what does this is endless 1 way It is What's 1 that's converging to 1 right so 1 rescuer was converted to a 0 . 1 yuan Would be and plus 1 over and plus 1 miners and already plus 1 is 1 over and want Next Fish or 2 This was 1 and this 1 on here will cancel its want squares Being an and passed to swear route and what is a stew is ghost proving goes to 1 of those SBA's long Exs last more than a CD of 4 x than that would be what so Olivier CDs or whether standardized backs It was also clear or But what is is do an X is equal 1 Yeager 0 or 1 the CDF looks like what our when exposed to Myerson viscosa 0 guys are expressly because up to 1 at 1 and that's 5 Turns out you're going through insurance This kind of friend River comes up a lot the the maximum mentioned Earlier why would lose interest in the back almost sequence of random variables of the claims they receive on their policies are random variables
30:38
And the maximum would be the largest payout have to make Oh they 1 charge of money so they can cover the largest payout if they want to know of the suspicion of the largest and his a number of claims it received so they probably thing about the large number of claims over a period of years among on states so what they do is there some distribution for the claims may not be uniform could be something of a maze of track means and abide by where the rates it turns out that
31:19
This thing always has a limit and there are 3 kinds of limits condemn the 3 different limiting city of Birmingham work Just before the start of extreme value is just 1 example of what think could start with another hour underlying decisions of uniform you would do differently but and in the limit relief free possible limits so the Raiders in the disposition of the largest claim they get it turns out that Growing couple different kinds of limited will get these there was a very famous they're summer called extreme value
32:04
And this is All in the area of risk management people are riskaverse something of a risk averse to using heuristic of our review go on a rollercoaster ride a great ghosts at the bottom of the you're not restored or perhaps to invest your money Yes unwise companies or perhaps Australia singer away and I knew there some people a riskaverse they want to reduce their arrests they sell somewhere else in there the whole industry and this whole industry of risk management or helping people a riskaverse uses a lot of public or so that's that's it for the exercises this is probably harder than would enable debris from nobody
33:12
So there will be a new set of exercises posted today they'll be due Friday chapters 6 of 7 men think that'll be in the course of our what the to think of the success of the last time
33:38
We discussed chi squared just and if Zia's normal with mean 0 1 man on a final view knew it was squared A scarlet high squared 1 degree frail If he won a seat to CDs are independent from other 1 venerable so that use of equals 1 squared fuzzy to squared Pazienza where and price for it With and degrees of these cop and of our on Or some other common decisions arising from the or more are what war
35:48
It Or We But But with the Effeminate are negative illiteracy and view is that guy square with em degrees of freedom meters high squared with and degrees of freedom
36:39
And you and your independence All of The As F Tremendously raise Sosa a Useful statistics to analyze data
37:27
Could 0 0 last time we did that meant Lithuania price where is actually a
37:46
For gamma 4 or 4 or 4 or 4 Dellavedova half for that means Zell flats Alam now How does or or All of which were or was off If I haven't Daiwa competitions worry computes so he UFSAR CDs for ratio so let's do that now With this what back A lot of it Of change thank back So That would be the CDF Differentiated different Jake this sum is Richard chartered the author says he or rather than writer drew retire underskirt computers because 1st all fresh from It's back a spotlight true be over and desired seems a sign or What were you and me Chi squares with mn ended Grise of free respectively work I sums of squares of normal so 0 Keisker admirals or that negative or positive so what off 2 I'll around I don't change And number moblike through by the way lamb Over And V. X. Now amusingly independence of you and me If He I can't get to
42:24
That's this maybe I should take props There's a saying they
42:41
The pair UV is a certain set Basel II between below the pair has a lie below the line in UV space has slow em over and That's it Exercise USA go that means of what may I draw are you last April that means I guess worry named above the like the 1st rebel has to be smaller than the spot for the 2nd So the probability that viewers less over and over and X would be the probability that the parent you he is and that set a baby doll indexes by And over an exodus of the His at 2 quick this that Well if the period UV is up here is a show that you was less a L R & B as excitedly along this line here horrors are lined with constant corn be where star out here it is You bigger than a month Emil ran Texas We're smaller When you zeroed Smaller smaller on the way up until I get them This is the right thing and to Kit computer probability like this you integrate A joint density over that region but there independent the thing So the joint is a product of the individual that's not what we should do is set rigorous Describe wearing a rating plant Soap I RV can go from 0 and 4 of its study of EU goes from you goes from here to em red X Lewis 0 Going from 0 and varying you go from 0 to over an X V F sub capital you will have capital little DU was theater Aero devious OK now let me check the sky And what is this Inter Federal at sea World density Capel you from 0 to something What that call 3 letters and CDs Cecelia foryou evaluated at the upper limit Some were right that 1st as this is Oceania for use of probability that you use less that nite The fish or the Project Sets
47:33
Brent
47:38
It's always remember this view on a computer probably of something a lot of terror random variables you need a joint Your vision or probably Mask option any expressed wherever this restriction is The And integrate being CDF over that that or used some of the probably mass function over that period settlers That's us Automatic every time alright so it get to this point And we wanted to different 6 so it's different that For us and for the trip While which on ice ax appears frantic this this is these CDs for use different which media but we have to use each chain different reflect Axel will get this thing off site was found in a row from 0 infinity It's pedia at em over and X is at the root of this function of that All but written off by by rumor of a suspect acts which reveal them over and and PDF review that substituting all right this is this is a cap of us of U. S Am over and acts so of we want different shape that with respect to acts Capital after you Prime em over and These acts times a program what appeared inside suspect access Em over and I was kid As OK And we have to make this really uh but You will be 1 of many areas in that sub suit would be idiots are now I wrote them on the board to Constance out front 1st fund where bias will be Emil France From here and there we take evaluated media for you Em over and value has these constants Up front but bows out and then He will have 1 half the end over again have and we take the value of this We raise that The emir over to my 1 And there were veto the Andover to minus 1 Bays says I promise you it's not as bad as it looks OK I know what You're doesn't give has never been never The Doesn't have support said Last The dollars but with have a M over a policy sticker perhaps 1st where half of these books or 2 here where half employers and over 2 Where Gallo whatever He Here's and em over and we also an over and lead them over to minus 1 That is chain Work All right No But it's here You're right and included At that level of these I never thought I forgot to put this D . here OK so air more and Over 2 months 1 hears in them over and the 1st part Soviet altogether Am oriented motto took And what's the designee there's also a constants 0 0 off practice when x 30 am to minus 1 then times Ariel 0 infinity Lead to some our what It is the 1st years over to minus 1 hears in over 2 months 1 and all that 1 them over to minus 1 plus ever to my fund that is Peter Nick am plus an hour to buyers want And then he The minus V Each or for what he did
55:02
But OK so it's Late said break back but base so let's continue but Our amend your notes were down a half years to be able to relieve down against Islam the awful or am of the offer minus 1 Eden minus Land acts as 3 damage em over to hear them over and over to their so that shows up here MOM were 2 of them over and over 2 and hours evaluating be density for U. S
56:01
Thus I did I put that in an already acts Over to minus 1 For the farright forgot To that end the exponential part so this should not be listed be already acts I forgot would be I would be a pretty expensive are set in be evaluating this Em all over and XVT that's going here lots going the extra That Britain network It is the best for you that evaluated here I do their truck We are progress with the export of battle show up when I do me exponents of Irish EU or 2 and then there's so at the Expo opponents I'll at minus over to end over and Acts and minus your to got the miners viewer to Iet 1 plus em over and acts The overt or your Israeli minus 1 plus over and over 2 times we think that combined these so once again I forgot to put em already X and the Expo a part of the Benson for Europe where heart Are we also pertinent X for the and corrected Densities for unity tavern dam of em to ever back here and from an overt and that brings us to this year and the last part at carryover from there's even this far He obtained sorry do this in a row for use a fact said
58:44
This is advancing right As a matter What is the alpha L 4 years and there were 2 ambiguous 1 half 1 Am Laura next Do At 2 Their offices and and over to Lambert leaders half time on what our next And solve this becomes a but we put Down here Chic And here I did land that they often the denominator 1 him 1 plus over an X rays to the Pollard Alpha right which is said or 2 as Lambert they offer The saying this year is a hero from 0 the offer minus 1 EU minus land X is is scam of all over land But On the off with Web equal half Times quantity 1 or annexed Alfie over 2 years go down L 4 Well you combine the but that's so there a couple of steps he steps 1 is out of your computer probably distribution function for racial You right back here We now always a them off by through I'm back and not change about the quality and then you have to express this As probability that they're UV lies in some regions in the states above all I and near integrate the that's for the air over the region of all the light
1:01:50
The Independent Democrats density factors and the rest was collecting turned As you work using the fact that you know that the Democrats season
1:02:05
And they don't do any leverage I It's got Aubrey a dozen regards What it so how about other ah decision a comes up is cold we teach sometimes referred to to a C student leader distribution S Is but is it it is As This is a color student
1:03:39
A distribution sometimes on student doesn't refer to people like yourselves refers to pen name of a statistician who work for Guinness and get to work with small samples and who are analyzed data from small samples What it will arms argued she was a challenge to compute But That would follow the same steps with just under 40 computer density write down the decision
1:04:22
What like to have a lot of this racially you never see here and a route over and near long by to by the route you over and they don't see less lets you overhead This is built Perry and that means appears EU must lie a certain region space down roll over that region of the site density what's eject density before seeing you scurry product of individual densities and end summer and then there will be 1 But I want do it That is Britain book but see they're going to writers of so
1:05:20
Although saw 0 What some consider the following stores Exxon
1:06:00
Through accent innovator and rules for now I don't End and up kid who did Several meters just this their average and assemble various the hours for years where Richards Warren 1 here Now Because the end my son goes here The reason for that is as CEO of the X is our independence are but seems a IID with stuff variance found ranks Seamus where man Expected value of ask where is swear this is supposed to be an estimate for Sigma square If I ever wanna Rainier here I would get there I dips and miners were rent types It s squared is boss made some parameters Was where the expected value of the estimator is equal to True value than recall that an unbiased so renormalize our water reminds 1 here to get unbiased up here on what would be expected of ex parte were in this situation again please identically distributed Expected Ivax parte lies that well what's expected somewhat random sampling expected not sordid it in some it and times view with and abide by a new get me so vastly nest mayor from you and it's expected value when you expect expectation of animus get you that's column on bias as later It's Expected value is equal to the parameters for CBS so only its let's examine the case for we are normal land the rebels It was in their normal means a rates Which is often the case Because of the settlement there many samples and applications can To be normal and also will be back that On distinction when properly Saturday as close to a normal inoperable And I know the Japanese divide by grew rates that because so a lot of the samples you get our Assumed to be normal and revels in that case on X bar is independent Of the friend of vector x 1 might say expire next to my sex Everest And might Critics sir Scott strange X bar appears in both places have their independence But So 1 way approving the users and vendors as the joint density enjoyed factors on other ways to look at the moment Chattering functions And so that it factors in the product if it does Member of the Musee uniqueness property of omerta options Along with folks can only come from 1 dissolution of Council this vision where that Ex parte part factors away from this part of the new overturned and the moment Jenner function for for the vector value case we have and plus 1 random variables here so we need and past 1 real variables here's what we do with the eatery not plus 3 1 X 1 by sexpot plus 2 acts to that And bar and or hitters will show 2 But this factors until he was or he Never be enough to show Independence Day I don't know And All of the 4 of recall struck And that start with the left hand side Each Get over For us to do OK And what's expired For all of old old today
1:15:05
Yet
1:15:10
T So who What we did here It was coefficient of there's there's a there but Rex ones America was cooperative X wantonness expression that's what What we get for the voters next on from here Well X was 1st terminus some small might buy And the remote but also by TI Aretha Somebody work retreat Axewood for motor Truong But the key if a Period she not and Tom here I will get a idea for the profit of exwife He now right There a whole here the next term would be 2 x 2 miners set are soldered minus to Overend Times X 1 from here and 3 over and etc. and minus Jeanne over and alltime sacks 1 a lawyer for the cultures led to the idea get that he knocked over an hour from here I get a minus won over and from here are getting through times 1 minus itemized 3 over and etc. have to minus of an Oregon times next to keep going like that and I get down as 1 If But Thinking on the diagonal I get 1 Tires 1 rice and to retire from ice water always don't let's recombined
1:18:43
Their terms was just like She wanted to its our side Some I will want in TI times Sir But see Watauga times Everyone has a T not over and everyone has a T 0 4 and all Our Everyone has a 4 x 1 I get a 1 corrects to Haggerty Rex tragedy 3 frets identity and so I did a frosty I and I get a minus our are of Iowa Oh about what Some of the some For 1 day and DJ or at right that this quarter and some J. equal want and teacher But for So but this 1 1st 5 deodorant times excise and add up I'm going from 1 day and I get a 2nd oddity and worried times their size and exit Last summer I will 1 day and XI And minus What This thing recall to a bar It is the will to each Or is it select Bridget rear a a This is not far by It's an times expire sigh combine that with us At that Actually that's And sizes I would like to know of this A stock users so you don't these what I wrote was right but for Dallas aside whatever random rebels as well as some of the normal run rebels book render revelers 280 not glory and plus might he XI that's a normal or inoperable What's Maine 0 and its is not over and SGI identity square Thank you sir I'm oral and rule axes Normal is normal means 0 rates wonder what can around arose 8 times experts expect the virus 0 still what's expected about what's there and leave it by the square a square
1:24:05
And so we'd escapist So what kind of rendered of this whole some their independent normalcy some of independent or Is normal Is a and rebel what's expected Each summer and as occurred adviser also the some would have expected value 0 and very use of the bases some is the sum of the races for independent venerable so the of some of these things I think does exam what's but this Races But all of that for all of the but ally but but but but But but the But But but But but but but but but but but Poor But with the butt of but The never made a these where a spare Us to 18 spacecraft that Think The 1st career all these are the same size as Despite and be seen not squared over Aid and what orders went up the Siluria wherever key allies I get And Tbar 1 I have these were yet While they're all the same and times is About attracting Mr. Mr. Watters is what is a stick out 0 as by 0 Each The base so this random variable affair is normal with this basin 0 so that's goes in the sex for this venerable is normal with mean 0 and rents that of this is equal to eat knew is 0 a where that thing over there and done so this is all I have 1 here 1 since grand rare this is his my is now my acts taking legal 1 side yet Just 3 half the race she not squared over and Or to and an entire easily won have some by all 1 and TLI Myers bar where Chasing I find that expected value of missing the momentary functions for this complicated vector form is this love what is expected value eta that she not XYR Can I get that from this Is he not ex party but the way I see there were some choice of 202 2
1:29:23
Yeah what choice Technology eyes to be 0 0 than of 0 0 0 years
1:29:33
0 So this a and what is as part that's if I take I take to not to be 0 like that There are to not to be so I just give us so what's the moral story the motor function for for This is part of the small function and that what was mean means The brand relaxed bar and the vector X 1 writer said Bart through acts in ways that are independent Key I'm gay and America Long was right here The lawyer function for normal looks like this has particular form so when were computing the variants what happened to the tea not part separated from the CIA minus Tbar part Emerg taking exponential this music doctors and that's why the market because this Cancel so a X bar is independent of this would have been the normal cell so this Very important uh results Each rapid it is for the eat it but X Va AS squared are independent
1:32:09
I As squared remember was 1 over and minus 1 some my people want and XI by sex bar square as a function of G of Annex 1 might sexpot to expire and my right depends on what these differences as Spurs a function of these differences bar is independent
1:32:54
Of this factor is a function of the vector that's independent audits are so to render rebels y and acts independent buys why and Geof access and things stake a function of these things in there in front of a sparse so when you're dealing with sample means a sample raises their independent and if you're samples such through
1:33:32
Where so it stop there today have a good weekend
00:00
Area
Sign (mathematics)
Lecture/Conference
Meeting/Interview
Mathematics
Limit (category theory)
Open set
02:25
Lecture/Conference
Meeting/Interview
Term (mathematics)
Limit (category theory)
Limit of a function
04:56
Series (mathematics)
Ordnungsstatistik
Limit (category theory)
Mereology
Sequence
Rule of inference
Number
Maxima and minima
Lecture/Conference
Term (mathematics)
Factory (trading post)
Right angle
Uniform space
08:34
Group action
Product (category theory)
Lecture/Conference
Multiplication sign
Identical particles
Quantum state
Functional (mathematics)
Number
11:12
Expected value
Cumulative distribution function
Frequency
Population density
Manysorted logic
Lecture/Conference
Meeting/Interview
Multiplication sign
Square number
Mereology
Functional (mathematics)
15:29
Explosion
Standard deviation
Arithmetic mean
Lecture/Conference
Transformation (genetics)
Term (mathematics)
Operator (mathematics)
Distribution (mathematics)
Square number
Right angle
Mortality rate
Normal distribution
18:01
Area
Root
Meeting/Interview
Lecture/Conference
Forest
Number
23:18
Area
Shift operator
Standard deviation
Divisor
State of matter
Orientation (vector space)
Multiplication sign
Routing
Function (mathematics)
Sequence
Maxima and minima
Numeral (linguistics)
Root
Lecture/Conference
Square number
Right angle
Random variable
30:30
Trail
Free group
State of matter
Decision theory
Distribution (mathematics)
Mortality rate
Limit (category theory)
Number
Frequency
Maxima and minima
Arithmetic mean
Meeting/Interview
Lecture/Conference
Uniform space
Subtraction
Relief
31:59
Area
Greatest element
Lecture/Conference
Multiplication sign
Heuristic
Set (mathematics)
33:35
Field extension
Lecture/Conference
Meeting/Interview
Decision theory
Chisquared distribution
35:44
Metre
Statistics
Degrees of freedom (physics and chemistry)
Meeting/Interview
Square number
Negative number
Independence (probability theory)
37:23
Gamma function
Differential (mechanical device)
Multiplication sign
Independence (probability theory)
Number
Mathematics
Sign (mathematics)
Summation
Insertion loss
Lecture/Conference
ChiQuadratTest
Square number
Subtraction
42:24
Spacetime
Product (category theory)
Observational study
Projective plane
Line (geometry)
Set (mathematics)
Mortality rate
Price index
Limit (category theory)
Frequency
Population density
Meeting/Interview
Lie group
47:28
Logical constant
Area
Point (geometry)
Computer programming
Multiplication sign
Infinity
Mereology
Functional (mathematics)
Grothendieck topology
Frequency
Spherical cap
Root
Lecture/Conference
Chain
Energy level
Subtraction
Wahrscheinlichkeitsfunktion
Random variable
55:00
Population density
Lecture/Conference
Multiplication sign
Exponentiation
1 (number)
Mereology
Arithmetic progression
Open set
58:30
Fraction (mathematics)
Lecture/Conference
State of matter
Equaliser (mathematics)
Multiplication sign
Distribution (mathematics)
Right angle
Functional (mathematics)
Alpha (investment)
1:01:46
Population density
Divisor
Graph coloring
Meeting/Interview
Lecture/Conference
Decision theory
Distribution (mathematics)
Independence (probability theory)
Student's ttest
1:03:37
Population density
Product (category theory)
Spacetime
Decision theory
Distribution (mathematics)
Sampling (statistics)
Moving average
Routing
Student's ttest
Gamma function
Grothendieck topology
1:05:10
Metre
Divisor
Multiplication sign
Water vapor
Parameter (computer programming)
Mereology
Rule of inference
Expected value
Population density
Lecture/Conference
Square number
Ranking
Random variable
Product (category theory)
Sigmaalgebra
Uniqueness quantification
Moment (mathematics)
Sampling (statistics)
Independence (probability theory)
Variance
Division (mathematics)
Mortality rate
Multilateration
Cartesian coordinate system
Variable (mathematics)
Functional (mathematics)
Estimator
Category of being
Vector space
Units of measurement
1:14:57
Frequency
Lecture/Conference
Diagonal
Term (mathematics)
Multiplication sign
Expression
1 (number)
Water vapor
Coefficient
1:18:31
Arithmetic mean
Lecture/Conference
Term (mathematics)
Multiplication sign
Square number
Normal (geometry)
Selectivity (electronic)
Right angle
Mortality rate
Identical particles
Rule of inference
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Axiom of choice
Summation
Vector space
Military base
Multiplication sign
Order (biology)
Bilinear form
Functional (mathematics)
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Musical ensemble
Vector space
Square number
Normal (geometry)
Independence (probability theory)
Mereology
Functional (mathematics)
Bilinear form
Subtraction
Resultant
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Sparse matrix
Vector space
Divisor
Sampling (statistics)
Functional (mathematics)