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Introduction to Probability and Statistics 131B Lecture 1

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Zgoda number 2 photo number 1 X is uniformly distributed on Mir will from 0 1 given by X Y is used only to rely on it or from 0 to that so we number at random between 0 1 acts that wire some number between 0 next Granneman added said at following their 1st gasses the 1st part a fine time there's a native Texan wife OK do we know will lead initial density of why given tablets is Alexis do because if way duo we did expressly joint density is a conditional 1 currency marginal acts do we know this right that's where teams for Catholics to be uniformly distributed under what has a stance they now quinoa the value of Kappa waxes Eagle Alexi Watson this distribution wife uniformity in often 0 2 X auto what's alike over 0 X X Oh the densities constant and value is 1 over the length of 1 over X Men Water what next year work should be restrictions are white ex rel X is less 1 or less table on where life that's less acts ever it's bigger than 0 otherwise what's stance of equal to 0 occurring OK so the joint density its war erupts times 1 if 0 fossilized next is somewhat and 0 otherwise they started I guess that's part B R I find the marginal decision of Argasidae for why value fine Maazel's by integrating out the other Grabel when your drug just so a severe over there X variable of the joint density now want to be the limits of immigration why states and that's where his ex have to be rolls of Hawaii between Bly and once a center should be from white to and what is this function hits Water Rex DX and there will be a lot of moderates is locked uh log wrote 1 minus Lorna otherwise bachelor 1 is 0 so we met minus slaughter white this might look little strange here where negative it my and work my probably density airbase was positive now lies between 0 1 so blogger is negative that's what mine either rewrite this as 1 white without my act if you're scrimmage auto so that's a density again what loads on my here why is between 0 and 1 person at a time and then find a conditional 1st decision of XTO white he let's just joint Over the bottle of life and this is 1 over
acts and this is why white my why did this no the limits are restrictions on XOY 0 less than white less than that that good as part C R D I would need computer expected value of cap elects given capitalized I was just be relaxed Times e conditional density of acts given 1 definition of it so what are the limits of integration here this that conditional Betsy 0 unless happens of bravery in which verbal why so why should go from 0 to act earlier next time 1 over X or with my assigned D argue White DX answer is yes the EXE and this looks like minus X overwrought whining and solid are so that was a bit of a civilian why states bravery X X could yet some wider 1 Expos from white 1 might really extra canceled so the despite its X over log life is heard from wider 1 so we get 1 we get minus 1 of and track value wives white over or 3 like this that's why my over sir they I think E 3 x 1 show X sub R R & & posts songwriter rare world around Rolando Ed that relaxes the somewhat but they were swastikas Buick b momentarily function for 1 is discrete ran verbal some and some of the sun and the rebels takes on the values 0 2 infinity nonnegative integers brigade the TK tons of probability that's 1 escape that's what you get from moralist definitions but you're the only bodies were this is different from 0 in Kazan on a major and water what it is a sign of its Lambert the or cave factorial Biedermeier slander every early this summer has a factory of Icelanders for out and now of both CUT and lend our race the archaic we provide them off by land at times unity raises the bar tebibyte case for a time start now this series is investors for mental function busy some cake was easy to care backdrop that would be busy so into and will not fight on exponential xli at exponents both landing gear is planned needed minus 1 Ito and best Auger function Posada next part was gave moment Joey function for X this becomes a product of experts also these are all in the pen the venerable sound regime he expected Ira product of an apparent rebels becomes a product of expected values all those expected orders would be the same equal to this we have that by itself are times we just get this race R B to the land our leaders minus 1 so what's sadistic and also asked What's the distribution of acts as well its post on private land are excess probably landlocked Texas bosonic land that is smaller generate function this is defined miserable containing origin any time you have a moment what looks like this has to come from with distribution real momentary like that would not the but land the times are excess Santos tremor land and finally resolved
approximations find numbers Easter products as fast Posey what point 8 5
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if we subtract the young expected IUX from Max and divide by this warily variants we got something it's a properly normal so what's expected Ivax proposed honorable of the value of land and its variants is also a member of Saudi it that offer you expect divided by you could start here OK there and do that another way is here where the moment I functions for different and evaluate the revived 0 we could be expected value we French twice the virus 0 get 2nd moment dropped the 2nd such squares 1st on the variants of those ways that they waited on the short of it is that they expect live lambda its its parameter and its primary would be land at times which is a 100 And if we divide by the square of its various strains that also meets Premier which is again this is approximately normal is approximately normally distributed means of Swat at central at E so starry with the Polish Apple Exs or that policy 4 we shed subtract a hundred from both sides and abide by 10 for but and this is about equal to the probability that Kaposi's is less Woolsey minus Sunday over 10 Zia's industries which is normal means Iran's what we want that to be equal to appoint 8 5 0 you go to the table which lost faith and find that the trial of 4 . 8 5 in here it's about on 1 . 0 4 Z my asunder Over 10 should be called 1 . 0 4 assault resist choir by 10 that honored mother what I status because 10 . 4 added and 10 . 4 questions from member force may be a way to do number 4 after a review Chapter with review of Chapter 6 South forwards from 7 a are doing now because some of the students are newcomers and haven't seen made it may not have seen the fact that they are likely to have get so it's got a number 5 2 X and are independent Xpress drama 1 at 70 is that their Ma told and Caesar even by the and the joint density would be what or in the Panorama rebels a joint density is a product of the barge also and thank have fears was a finely joint density of expos wireline of such a list of products was lighter X or Y Y Syria we have you as a function GE 1 of ex-wife equal to X or Y those is function of X and Y and it's actually just like to invert these acts as equal function of you and be 1 course auto idiot exit window you and me you times his acts but and why it is another function of X and off by you and me get why when you Andy was just knowing a vivid Jacoby G have but cause she hoped for well being won the Axis 1 white dg Lundy why is minus acts of wives Square 2 DX 0 and DG 2 Y is 1 of the several years won over water and the change of area former Merrill formula for the density says that the density of U and V O U and movies it is the joint density for X and Y evaluated each 1 of you V H 2 of you mean Annan
while rap survivor Jacoby and evaluate 1 H 2 and that's a change of rural farmers OK well here's a joint density will act miserly evaluate their wares a each 1 of its 2 . 6 1 2 times to its being the miners to me must and then won over a J at a 22 2 so this is being what is a wide at the ex still would be won over age to overwrite wherever survivor aides who was won over f solidly while or forward this as a B 1 over aged 2 and is not becomes 2 in the numerator aviculare comrades to hear was aides to its me time and this is what they us a new lessons and reading and their lessons these sets a joint density simple distilled little bit Kish but I think we find the Maazel starts fired a R B find marginal density of you'll see they which is carried out there I knew that of oil was racial reduced from 0 to infinitely Brooks and what is this look like cyber gamma density With premier Alfred to and land equal to 1 plus you is Reagan-era gamma density wears a gamut as they look like member that was extremely has landed the awful download Belfour Baxter the ophthalmitis want Eli Islam that could also expresses views Barbie's haggis news media make me in the box here but like this by proper choice of Elf and land that I really veto the 1st from all their probably made a ophthalmitis warning of what would it yourself to the office too and awkward Hollywood glamor to get this month plus you deserve would become gamma 1 plus 2 over Elf is so absurd Gamma Gamma Belfour that's too and other offers to over lenders want us to Tooley Alpha which is to and what scam of to its 1 camera to lose 1 and so this 1 or want us square the top and then fine Media artsy what's probably acts is less a line for wise lesson 1 these are continuous honorary boats and have the same distribution so I'd be the difference between this and the probably wires lesson abuse saying what public wise equally their independent 0 so at this point this probably be happy because this plus probably wise last night's adds up to 100 people half on the eve the the density of the but if you this from 0 2 1 a to 1 more for the break number 6 NATO a questions a vast area a lot of rain rare also did bone was out of God rose number of off rules but sustains that stuff probably it is 1 of 3 which is 1 minds probably 0 and empty here it is to over tender the 23 when they spot but peak times the number around I will say is about to to act so How would you use a lot rare events E. says that we add up all those killed but of rocks bubbly for Sondra drummer too but it it was all over and Romania recession session we talked about the atoms of
living alpha-particles particles but 2 the 23 out of the blocks of any substance Rick whether individual items in itself
part or not for newly random rebel and if it does it within our playing with some primary he is very small something like this Adams acting independently some means all these things would be independent this would be 1 of the 1st item is now part of their otherwise we wanted so was sample found on a for soul and this is kept blacks so then the problem acts last it to would be well probably X is 1 0 was probably acts as 1 us probably access to probably Texas 0 4 0 what's probably Texas cave Kate Exs was on most of to the case over case factory the mites to advocate 0 here would minus 2 . 4 K equal 1 2 or 1 of these mines to duplicate what to get to over 2 factorial times you might be 1 us 2 plus 2 or 5 times my charm what expected Ivax while census is brought song to the city but to me it was like being evasive acts again or post on the variance in the both the parameters of the possible at stake attended break which is what will always do do they can avert what the staff region in the world and up and start through review they were let's approximately a 10 minutes prime number 7 here's
the density of Jew and rebels it is done by his demise when axis between 0 1 4 figure the next thing and it's of course 0 otherwise so it's difficult ways of ex-wife which is expected by next time times wife bias expected Ivax fans expected so but these 3 things Budapest they need to marginal density for acts to complete that we need a marginal for white and is making do with which I don't speak for life says we have battery let's do this 1st visit me double winner role of Alexei times a life Times a joint density not what are the limits of integration what region in the plane is described by 0 works a but there's no Lexa light satisfied this is in the 1st quarter and obviously and we where X is equal limelight like now where were the Of all charter for the 2nd quarter to be bigger than the 1st both sides this region up here and we won a over that read sort of described that well what does why do it starts at their own ghost To infinity period 0 turned now offer expire why what is acts to worry that Expos 0 2 expired why like this 1 x values go where we process line here right 1 of the 1st quarter net on the hours are lying do go from 0 to hero as were wise people Alexei otherwise excellent have that ability litigation ballots substitute value for advancing it seems my his wife did they have winner ATX 1st Ballwin yet x squared over to make illegal acts d acts is that where over to be evaluated between lively didn't have thought frontier in and they get a Y square times why would be wise to why do want and know what setting too period redeem be part of a dam that events again I with healthy for the 4 and led people to 1 so what what city that's movies Jamil Over lenders of 4 4 or 1 of the 4 ship right this is member the evidence in an from 0 to infinitely y the Alpha minds 1 minds lambda y is equal to gamble Delta over led to the Elf in that Ottorino Myers 1 3 Elf should be formed and I we had planned a wider White members what so what's 1 the 4th its Aswan Dam of 4 is like the 3 factorial 3 5 over 2 3 but it actually I think in this whole tests you never had to do with a by snow was there I do want or loss part lasagna radiative is 1 of Rex you Tom I had dinner in excess of 50 in attacks 1 I take it back up case so are
over what elsewhere which it expected Ivax expected by wives modified track From here so they get a sector buybacks we need be marginal agreed to agree so let's get the module for acts
get vase joint and whether the limits of life going to be axis why then as what rose from 0 Melbourne Knights 0 but accident Friday Selena great next affinity Myers Why do I see you might why that way of life for accident earlier this year 0 truck the value at X subtracting lines to my sex life marginal before acts sexes were next is positive so that's an exponential venerable right so what's expected by vexed by an exponential From around this year 1 here sir if you have dinner ready light of integrating acts times you the mind-set right X times the density and what's is hurdle what you use gamut because there would look to level equal 1 says began to or what ballots could be marginal density for why that means will integrate the joint density in the X-ray want and what should be the limits of integration here for acts biased sex acts goes from 0 to 1 great from 0 to Y minus why DX this doesn't depend on a roll of 1 from 0 YDX why is my presidency that so it's expected either white he again this is it like the the Bok of born part gamma density with Prada L equals free and equal 1 as a demo 3 and these villagers never ever vendors and my aunt process meat to doctoral work To expected Ivax is 1 of my wives too but directs Times wires 3 so of 4 days of light years 3 miners who put but or case boast River expect directs given capitalize of Of visibly integral part of the times density initial Nancy Baxter why so now we need to compute this initial density and that's the joint over the marginal the joint is Eada mice a marginal is Hawaii minimize fire which is 1 over why and what are the limits here where is this from 0 1 0 is and that so the conditional distribution of acts given capitalize the light is white what you call that uniform money away from 0 to coming back appeared what are the limits of immigration that X Expos on 0 2 Y axis times 1 why the acts relaxed dances x squared over to evaluated at why would give Weisgerber to them we have like 1 or Weiss these fire to about life 0 let you might just written down from here have around rebels uniform on from 0 why what's is suspected by its midpoint while In the other part will see other conditional expectation I think show but but but but but but there we integrate why times a conditional density of white next life so we need this conditional that's that's the joint density divided by the marginal White House acts this is Elias wife where it's different from 0 areas and what was this you minor sex sorry right this is EU the miners why minus purposes and this is 4 0 annexed less son wife quick and so the conditional expectation what are the limits integration here will act suspects was why do goes From next to and say are king key well we could maybe change variables equal why checks this becomes a rope from 0 to mandatory Z class acts in my Aziz pleasing river that Jake so it to a girl's times it easy What's that that's 1 because it's a gamma ray right and then at times in a row you might easily been X the final part here identified Malaysian
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way to do this is computer moments function for geometric which is pretty easy I get the variants more take the log different shapes twice since that a 0 there's no way to compute the PMF of X plus Y but they were here to do 2 things
what's interpretation of a geometric venerable its number right member trial dates to success you're doing independent Bernoulli trials province successes Peter so these are both the number of trials to get a success right so Expos nor a chance to get what to successes
soul what what's a probably that the number of trials to get to his successors is OK was well if from In terms of success and failure imitates Kate to success is the last trial have resulted the kids from result in success Frank well says that in years there have to be a minus 2 failures and 1 so there will be altogether minus 2 failures and successes of iPads wanted dictators sequence like that they asked all absent and ask What's the you'd probably that well for the we get key squared for the failures we hadn't won my speed to these same to did matter actually where this is worth about her you probably have any sequence with 2 asses and minus 2 us would have that building now we have to count how sequences are there where there is an here and only 1 AS there is a choice about the summer choices we have 1 choice tanks Sami forces were here they rest sets you could also use a formula for the he met give up some of our theories of Exxon's plant reveal that their independent we will all of and this is our water repeat squared appease verses water repeal 4th and ovaries of acts and is the same as razor wire expected I've Exs as expected by wire on I'm this the MEDIA variants of acts as expected value of X squared quantities squared to being the same minus 1 repeal 4th and then substitute the value on their parades left at that point and finally numbered I'm mad Texas binomial what primary what's expected by exorcist boats remember our party represented by normal program the sum of an independent movies with that divided newly published years these songs he and times of being but the Razorbacks both races in the the ground rules of some of the various the eyes of the summit and the around rules as what's the rates Bernoulli P compromise so varied so some being this some of the races for now and and we want announced problem is a central limit their what probability that is less than 59 . 8 probably Texas minors Our aim is 50 a hundred years a half so acts Midas and P and B 50 over the variance be squared of 500 times B times 1 already was from moment is less than 59 . 8 minus 50 over square of a hundred times times one-liners and what he did in this case the half time from is a 4th a hundred times a 4 . 5 per providers 5 of is the probability that the text minus 50 over 5 less than 9 . 8 over 5 5 in the 9 . 8 1 1 . 9 6 those probably best thing is lost 1 . 9 6 What a coincidence that cannot be that that's . 9 5 hours at . 5 kinds of what are the chances are that there would be exact numbers in that's 1 Sylvia . 9 7 5 sets in the final questions and leaving in the killer problem was number 8 had ordered applications like that for those who just came across as a kind of a good reference about what was learned In the last 5 weeks and for those by going on this is the stuff of mastered if you haven't over again amassed a question it was a long just give on test I give if you do well use it so great it you don't don't despair of there's always a chance Group updates so let's review of bets we are finding All-Star would Chapter 6 Oh I highly recommend it didn't take 131 a last read out by what the sent does abusing them frequently but they can't Chapter 6 starts out with user will use each of a normal run rural and word Donota but only to see 1 of the Sabine normal mean 0 that's 1 in there we define you to be a squared this is a follow-up high squared venerable . 1 degrees but the square of a normal and these arrays 1 expert and a precise that Zia on all means their own ranks 1 means that ain't deaths of at all but market which means said it's probably easier said any sets me is payroll being of the best have OK if I were but all but would not say key she said could can't that's the definition any memorable same density is this the St. over Terry voters will recall widespread agrees show he now so this symbol here means say distribution of you a sky expert and reason that means as St. Pierre as the of Vermont as saying density if you have the same density is this news called Keisker there's reason U.S. ties were In other words like some Of the squares of an independent normal means referenda rebels and Zia's normal with means 0 rates want a new NCR independent auto her there's Z divided by the square of where does was called 18 GE end dissertation at sea statistic banned agrees or so will be where scatter around the rebel look in Chapter 5 for the best means for chi squared and answer I was on Sept 6 2 6 4 the densities don't to memorize that could be that you work with a lot of stuff that you do without intending rise of another our common distribution is following ties fertile and degrees of freedom skies where with and degrees of freedom and you and appended call for better you over and divide by B over am doesn't have and it's I must ordered and enters the number now you don't 0 0 OK maybe I should the folly his wife and you can look up and see for that are we did have a problem the final but the density for racial on 1 of the exercises in the book is terrify me this vision for a water white or that being take wonder why this pose a greater this in so there would be F mn they have OK so that however a review Chapter 6 Carter recommend doing some of exercises distributions that we use in analyzing data From samples of alone suppose that don't and X 1 through are I IDE isn't it abbreviation will use commonly independent identically distributed the normal be numerics Sigma squared Bari equal water and some might go want end of exile as what decision well we know the sounds of normalcy is normal again and you establish that what what tools we have for identifying distributions of random rebels only functions would take a momentary function over some of its but about of independent rebels of the product of a which functions what's a momentary function of XI so what's expected West Samoa Jerry function for X buyer I did 2 3 Sept Sarah what steps erode ex parte as 1 and summer and I put the wanna ran with the team that I needed you over and times as some of its allies where I'd be the products units urine X 1 time unity your next to times EU foreign accent that expected by their products but these are independents be the product of their expected values and they're all the same so I could put 1 areas NATO and number theory and things like this what by the of the sink to the end so what is assigned crime that is yielded knew she overran plus stigma squared over to be over and squared thing inside the parenthesis power and now we multiplied excellent by and when you do that the becomes the new team boss saying most square Over To our baby can I just changes so that rewrite the same thing idea but the 2 under the T spread because only caucus in the cheeseburger to Izzy various things under the the same me here there among this by again it's isn't squared actually and or else I get a cheeseburger too and must Sukova shifty square or to over and so that means that X bars oral with mean new and variants they was burned over and thanks I think a still Chapter 6 part of the sample variances his best In this case several variants by multiply by and minus 1 and abide by Sigma squared this is chi squared with and my 1 reason car OK and important additional factor but X partner squared with novels X far AS bird areas offenders auto auto a so 0 or almost in that situation there where you was now being an well rare forcing whispered and Z or we can use that bar Aziz normal means Iran's wants we have turned expire to a normal and we don't want you never nor a me new abrasive whispered party converted to normal means of track right we would abide by they should take are biased means which found was new divide by experienced wherever there is a means bus being signal over rude and this is normal with means no want his squared our so X minus new overstatement abide by rude and divided by the square root that's our you that and now it to divide by number degrees of freedom this is going to be a teacher statistic with an minus 1 degree of freedom but civil fighters this and my is 1 might on canceled also there is a segment of an hour later in the numerator there's a stigma and the denominator means they canceled and so we get X bar my new over Road and asked it is a team for ago they died Perry agreed so be typical will this in the future a lot of times we should assume were sampling from normal that the samples are independent and metabolites are sampling is using this ratio
Offene Menge
Vorzeichen <Mathematik>
Mathematisierung
Vorlesung/Konferenz
Term
Frequenz
Klasse <Mathematik>
Vorlesung/Konferenz
Drei
Lineares Funktional
Momentenproblem
Exakter Test
Gammaverteilung
Gammafunktion
Dichte <Physik>
Umwandlungsenthalpie
Parametersystem
Subtraktion
Mathematik
Sterbeziffer
Momentenproblem
Relativitätstheorie
Term
Dichte <Physik>
Konstante
Negative Zahl
Quadratzahl
Flächeninhalt
Menge
Dichtefunktional
Momenterzeugende Funktion
Gruppe <Mathematik>
Mereologie
Jensen-Maß
Vorlesung/Konferenz
Faktor <Algebra>
Gammafunktion
Analytische Fortsetzung
Feuchteleitung
Randverteilung
Distributionstheorie
Länge
Momentenproblem
Natürliche Zahl
Wasserdampftafel
Zahlenbereich
Kappa-Koeffizient
Eins
Weg <Topologie>
Vorzeichen <Mathematik>
Uniforme Struktur
Endogene Variable
Randomisierung
Inverser Limes
Vorlesung/Konferenz
Gleitendes Mittel
Lineares Funktional
Exponent
Tabelle
Reihe
Biprodukt
Integral
Kugelkappe
Unendlichkeit
Entscheidungstheorie
Dichte <Physik>
Konstante
Erzeugende
Last
Konditionszahl
Mereologie
Faktor <Algebra>
Ordnung <Mathematik>
Aggregatzustand
Zentralisator
Parametersystem
Lineares Funktional
Approximation
Punkt
Gewichtete Summe
Momentenproblem
Mathematik
Tabelle
Stochastische Abhängigkeit
Wasserdampftafel
t-Test
Zahlenbereich
Kartesische Koordinaten
Biprodukt
Division
Ausdruck <Logik>
Dichte <Physik>
Arithmetisches Mittel
Erwartungswert
Quadratzahl
Differenzkern
Flächeninhalt
Forcing
Vorlesung/Konferenz
Randverteilung
Distributionstheorie
Subtraktion
Punkt
Quader
Mathematik
Zahlenbereich
Schlussregel
Kardinalzahl
Ereignishorizont
Dichte <Physik>
Menge
Flächeninhalt
Eigentliche Abbildung
Gammafunktion
Auswahlaxiom
Gerade
Parametersystem
Primzahl
Stab
Stichprobenumfang
Mereologie
Vorlesung/Konferenz
Faktor <Algebra>
p-Block
Varianz
Randverteilung
Ebene
Einfügungsdämpfung
Gewicht <Mathematik>
Kartesische Koordinaten
Temperaturstrahlung
Weg <Topologie>
Exakter Test
Fächer <Mathematik>
Jensen-Maß
Inverser Limes
Vorlesung/Konferenz
Delisches Problem
Figurierte Zahl
Gerade
Frequenz
Modul
Ereignishorizont
Integral
Dichte <Physik>
Unendlichkeit
Quadratzahl
Sortierte Logik
Mereologie
Faktor <Algebra>
Randverteilung
Distributionstheorie
Subtraktion
Wasserdampftafel
Klasse <Mathematik>
Euklidischer Ring
Derivation <Algebra>
Bedingter Erwartungswert
Variable
Differential
Erwartungswert
Inverser Limes
Vorlesung/Konferenz
Affiner Raum
Gleitendes Mittel
Gerade
Parametersystem
Lineares Funktional
Exponent
Gebäude <Mathematik>
Reihe
Ereignishorizont
Dichte <Physik>
Integral
Entscheidungstheorie
Geometrische Reihe
Quadratzahl
Flächeninhalt
Rechter Winkel
Konditionszahl
Mereologie
Gammafunktion
Subtraktion
Wellenpaket
Mathematik
Wasserdampftafel
Reihe
Term
Teilbarkeit
Unendlichkeit
Weg <Topologie>
Rechter Winkel
Vorlesung/Konferenz
Indexberechnung
Innerer Punkt
Gerade
Aggregatzustand
Resultante
Distributionstheorie
Abstimmung <Frequenz>
Binomialbaum
Gewichtete Summe
Punkt
Momentenproblem
Gruppenkeim
Kartesische Koordinaten
Baumechanik
Kardinalzahl
Gerichteter Graph
Eins
Vier
Einheit <Mathematik>
Exakter Test
Randomisierung
Vorlesung/Konferenz
Wurzel <Mathematik>
Auswahlaxiom
Chi-Quadrat-Verteilung
Addition
Bruchrechnung
Lineares Funktional
Statistik
Gebäude <Mathematik>
Wahrscheinlichkeitsfunktion
Biprodukt
Teilbarkeit
Entscheidungstheorie
Dichte <Physik>
Arithmetisches Mittel
Forcing
Menge
Rechter Winkel
Ablöseblase
Folge <Mathematik>
Sterbeziffer
Wasserdampftafel
Besprechung/Interview
Zahlenbereich
Term
Physikalische Theorie
Division
Ausdruck <Logik>
Freiheitsgrad
Weg <Topologie>
Erwartungswert
Multiplikation
Rangstatistik
Stichprobenumfang
Inverser Limes
Optimierung
Varianz
Leistung <Physik>
Erweiterung
Stochastische Abhängigkeit
Streuung
Schlussregel
Elementare Zahlentheorie
Quadratzahl
Differenzkern
Flächeninhalt
Mereologie
Normalvektor

Metadaten

Formale Metadaten

Titel Introduction to Probability and Statistics 131B Lecture 1
Serientitel Introduction to Probability and Statistics 131B
Teil 1
Anzahl der Teile 15
Autor Cranston, Michael C.
Lizenz CC-Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nicht-kommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben.
DOI 10.5446/13213
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2013
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik

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