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Random Sampling

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Automatisierte Medienanalyse

Erkannte Entitäten
Updates Discussing Chapter 7
The last time we considered a simple case were population have
Assigned to it values minus 1 0 or 1 according to whether the individual in question was a favorite candidate B had no preference or candidate a the computed be almost before variants up to 1 hour step to you
Trapping the expected by of excise turned XGA our let's review of it on there is a sum subpopulation oxides capelan individuals in this population have our values assigned to them And the list of values would be given by Small Exs with subscripts sway list of capital and values
Example we did last time the values were all the former minus 1 0 or 1 but they could be on heights so they could be be some measurement inches could be wait some measurement and kilograms or could be total wealth that these dollars
Many others Possibilities and the book there's a running example by Hospitals and these values could be the number patients discharge in a month or so of their many many situations that cover this could be scores on exam for a class for example I printed out CR Sister exam want comedies have seen it a good so um meters sir reproduce what it looks like on the board This is I think I know
Printer 1 out from under the facts but still below the luster Example
Aeroflot all these eggs and you probably can't read these from the back of her own But And now I am the histogram for this particular classic like this and there's a number for above that 4 7 9 5 8 Chang 8 8 What I 9 9 3 Rule at 0 0 s I sects 2 0 6 again Joe 4 0 0 what these numbers mean a means for be buzzword 395 and For 7 at his former trimmed 98 94 So of Where they were round down The scores of other words just recorded things I'd 95 per cent 98 will report 95 person at 86 will report 85 some lists the numbers that we see the population so ritzy 95 4 types Books And Edward C. 90 7th and Edward C. 85 5 times a month And ritzy 18 8 tabs I We keep going like this ritzy um um 15 twice and then 10 4 times And that would be a list that would be this Leszek slump through acts travel
And there is a lot of repetition and this list so we might District Court the numbers you see receiver spores 95 90
85 EDT among 75 70 Sutter of 15 of the attack And they require Army Times those but Appear So we saw 95 4 times we saw 90 7 times recite a 5 5 tie 8 times signed 5 10 times saw 78 times 15 we sought twice can we saw 4 times and saw appears is the complete list of the numbers you you you see in the population and here's the number of times those numbers appeared
So have sometimes rewrite C-1 through a C Torode George C. am as a complete list stuff The distinct values that you see here So there be no repetitions in this list this would be the slowest here readers recorded missing values occurred Population without repetition but then we also record-high 3 times each those values occurs
Song Little and 1 would be the number of times see 1 that occurs when 2 or be the number of times
See occurs cetera bill and am would be the number of times See M. occurs
Don't know em as the number of distinct values and has less
So in Osaka For example here there is B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 guys think now Interested in sampling to try to Determined things like what population means so the population being removed again is given the name new and it's exactly The average of the values of their current population where all these numbers abide by the numbers So in the example the scores we have 95 With 95 I was Of Here they would abide by a later Scores there were things that would be divided by 4 4 7 plus 5 plus a toast and being population now there's another way to computer population means It here You would be what Well we have 95 5 times in another way of doing that is Modifying 5 times 95 right and then we multiplied 4 times but not for 7 7 times like wrecked 19 in there sometimes Well I get a big victory for time 5 reserved for 95 7 times 90 plants Army 5 times 85 etc. must either Then we get found that 2 times 15 and we divide by capital and which I didn't from former students Soccer we formulate that in terms of a general case for where these distinct values occurring this many times Well we got the 1 or and it with some over the A number of distinct values Jake 1 2 M calmly times we had in the number see 1 And 1 times times we had in the value of CT and two-time Army times we have in the value of c sub J & J type so what do we do here and sub j times subject another way of expressing Back populations means The 3rd statistic that sometimes it is of interest is the tall population 12 For For example I over the years population of Bob 43 students and No calmly I forms They are in this population So I know what numbers were I have this 43 and here I have the value use 1 or 0 according to whether the person protect Labeled 1 has ordered the person 1st number 1 is I phoned this would be 1 9 0 1st number 2 as lifelong everyone if not be 0 but would tell area 1 every time that person as I phoned 0 1 not miss a beautiful number of Eiffel or could be number of cars or where it It doesn't have to be back Artemis actually I could count to which you have to like 3 3 out of 4 my computer Sosebee the population 12 but could be like the total wealth so anyway this is capital in times and because its capital Times new we also have this way of computing it fears meal by multiply by Kaplan stir races 1 over and over there But what the that Then there's ATR population barriers In with old how Which can also be expressed Of it And dump XI occurs Humbert XI square Kerr somebody times when I'm adding up well again you I use as saying that they are yes of its backside is equal to workers can take time to rewrite the says
NJ times The vise CJ square For but And finally on auto College of the dike Artemis cases This'll set design or maybe car X-ray When 1 analyze appears on the list is 0 On the other side is appears on is 1 and that's all that because This is a number of times 0 appears is number of times 1 appears and by those together I get all the members of a dichotomy case and this is used determining whether Or not you like something Chocolate ice cream sells everywhere you look dry like chocolate ice cream or not so Raise your hands if you like chopper that you could raise a higher if you want OK all of you people with Ray hands you get wants to air the rest of you get assigned the value 0 and now there's some true populations proportion that likes this population ice-cream depopulation abortion a life-size eyestrain would be key equal to get to the number who Hands times C 2 gorgeous and to a divided by capital and I think this is number people have wanna assigned by by the 0 populations such as called me troupe of course some of So I think that would be new but we give a special name in the fact guy that guy Calamus cases also used in opinion polls elections OK now legal usually used to try to estimated knew or sickness word or deed he might be on show on the example of that what we just talk about might be of some companies and resident preferences of population products this could also be applied to weather a certain medications works or not a population of individuals of this size are given no medications and you want to know whether works not so each valued be 1 4 0 according to whether the medication worker 91 often medications work OK so what What you do with 2 s may face death is a sample of population All Is We must face a stark capelin is a lot bigger than the letter E At that What work Of OK we say aboard our replaced them easily reaching grab over group of sisal land from this group of sites cap but as I said last time think of this as being an urn with capital and Bosnian region in gravel and and retreat these is being random brave the randomness comes such a procedure
And they're not independent these are not Which doesn't provide much of a problem of the layover cap on a small and all of us could you Beira Mar till joint decision
Bake they RAI daiquiri Sturbridge I call on all
And the only guy user can take R C 1 to C 3 up to see him as was going orders of here in population and no matter which 1 you take the probability is equal the CJ is saying there's no preference for
X 1 being CJD as opposed to being seated as you have finally reached sample A select another words are decorator Sturbridge or I don't equate Asturias but not in suds compute what the summer as Robert X 1 single are aimed at Brown
You reach and grab up Individual random what's probably that that individual has value CJ speedy portion of the population has seated Comedy individuals have value I raced with land Jay and now they are in the population capital and says Some place And J. billions of over Capital the number of individuals having his value by by the told him
Now let's compute The probability that And this be true then for any of public to hear a free ever Show So Q. scorbutus probably Probably Alice J. given XML CI And their 2 cases here 1 is when I is equal a day Now there's when I is not equal the shit With But the Consider the 1st equal doing so we reached in and grabbed an individual that individual had value CI Nouri but that's what the probably that this 1 has value CIA also warned this happens hungry Rating But harmony I remain the population And minus 1 and what's talk population size A so and I minus 1 over Capital and minus 1
But However allies differ from J. well homily remain elements
There are individuals population have this volume of protect are different but we still have NJ but individual during the operation Kaplan my sponsors BNJ over Capital letters the surmise over here using move salt which of my mother laugh at me once Michael of 5 was sitting in a tree in new 1 hungrier left for his speak English when might be stupid Michael every none left followed by way of a good thing if it were
Thai army of objects and ITC more Alert OK so and remind Acevedo things I knew we were never saw estimator for new
For busy Sample means Frank What's expected value of X Pa E above spectator those over all possible saplings Well of course at doesn't change and we take expected by over some samplings I should be more precise samplings of little and individuals what's expected XI Well The some Ali called wanton and watch the news out of camp here sorry skater members reserved for being told a number of different values against forever
So definition of expectations this Some or all that But this and rural XI cannot be by EGY by the probably taking on and what's probably take the value L But for the sack
As we observer over there and active backdrop a capital and
And this is meal that it true or population the expected value Not yards moved meal so this up here would be what I have new here this many times so I form that some ideas and Times New divide by and you get me so they expected Ivax far is new soul were using X parte to predict or approximate overestimated you have the nice feature here is passed on average it's equaled SOX parts scholar not unbiased us All s because It's expected value is equal to the parameter for using
Were you they aspire to approximate her predict expected that is equal to the Prowler reusing it predict were drug use EX barred estimated annual and is expected values musical an unbiased estimator OK 1 way of telling how good and estimators might also be spread out the institution of that Yeah
He left with The various acts are small then rates Inc X parser get S Mayor from you make music usually values that are very far from its expected value it brings sort thing that means that there are a lot of times when x Pa It is far from its would like this to be small so we should try to conclude that the various means what is expected value of X bar squared Bias expected life of ex parte and spraying that and expect Asian means with respect to be random selection of individuals and now so computer vexed by arm is the very itself normalized something like that and whether revoke variants of a multiple of a random variable whatever working to that constant Comes out with a square right Look Earlier Brazeau some becomes in this farmer before and so we need to commute the covariance of XI mixture Is up But while the 1st step To some simplify matters right over its this way and we know expected I've expert state those are or we'll still be expected value of times XGA miners New Square here That leaves us through forbidding guests At The kid XII my BCL XJ Mike B. C Casey and never model by buying a joint decision for its job He amassed I am retains a letters or The But with it or have their bare There's a court order Again number when that means 1 individual type with the number See elves and take out 1 lap 1 nite last left so it was probably Wales differ from case still and surveillance rituals with that
Value of problems as I do that because dear I'm going to do In the shop robber waiting for Now Take probability intersect B is part of a given Fans probably beat And I know it reaches I know a conditional probability now and they marginal all of us in the plant But now all this event asked whether Elise equal the carrier not sigh should break up this sum into L differ from K and L equally K Frail differ from getting Texas case So the conditional probabilities and Isabel over capital and minus 1 and marginal probability is ends Case over Kaplan and and for L equal a case While these 2 things are the same See elsewhere and them Make initial public notice and Sydelle minus 1 over capelin minus 1 when the marginal probabilities and At End The media Difference here between The and this is minus 1 suffering that part out take this far here and myriad control be and down here every control see on fire There are located here that your pay attention and then plus a half-acre fire here with This is the minus 1 hard near and then they This article on gay now I look at this and then I guess But we still I give written by I put this back in here this gives me what's missing here the died long-term right term Ellie bouquet that's missing over the term L. equal to look like have here Squared there A mail reminds 1 or and over And what's exactly what you're here as the missing died diagonal from The call Were The thing tho OK on crew savored make sense Alves a racist
8 on par or somewhat I think that can rewrite this says Purcell also my case
The friend then Here are some L And these Torre votes CYF found Siam right from Mort When I always term but a 2nd but some freed from all I put the on-site visitors like When you integrate integral to it a double after Baxter GYD XTY you can or 1 variable 1st hand over the right so this is becomes a double somewhat you're going to be going from Monday understand this But that's what you have here Most of that part There is this Mr. Oleg Sapporo What you see case where and NK over and over and minus 1 that sustains us but with King said about I'm using the summation index It's exactly the same stuff Gaviria S . 5 . be enzymes and less want and what would be laughter this part would beat house where the Agate
And case seek a script for the 2nd top member was like this I guess I right The Karl use notation talipot en tire sexpot Tom Rick expected by say it's affected by tops by square this thing and that's what our if if you're OK
And then Dom I don't by Parent firm Using this relation from which a replace aspire And New Square over and minus 1 and this thing here is expected died 2 of the square It But Because I They expect that but you take the values squared Times approbative taking on the site B and over so on this thing here is 10 times expected I've squared which would be to be a mind that there's a certain minus 1 here this and this and cancel and expected by rhinorrhea will swear is its variants squared plus its mean square For I'm sorry So I expected by Rexford every Sigler square work A soap Finally Combined new squared terms IAEA and you lose squared minus 1 news program minus 1 that's new squared minus Cygnus squared over and minus 1 The last thing the computation of expected by next
I X J and so we have to put in Last year we do that we get a new squared
My Sigma squared over capital minus 1 New Square Which is minus Mosquero or capelan White what So the answer for once a Kobe rates exchange with a simple random sampling its miners in Mosquero Rand that's the thing to remember here at the end of the next step after the break is we have to write down because the wearing of variants of ex parte object is to finish the race that's part is Seoul every 1 of these terms is this might singers were 1 Kaplan but that in here every time probably times of firms earned the Simitis Jake want and a the and squared terms with the lands where time this divided by Capsules and as become segments Where'd over Kaplan wants what exudate X Clark variants of the sample lean But But at I think During the Byram data TWO must take somewhere along the way but we fix it after the break kisses the Tuzla others quite right this is correct but I W a 6 Overall forced from so this is correct but stop result is the only apply equal check and at a somebody's head lice different from Jay and spurred might so here we have an answer yes and squared minus and over the same And where times this minus Sigma squared over capelan minus 1 mentally down plus 1 over and squared The lands where some I equal 1 2 and call variants of XI XII that's also called variants of excise At the very core of rates of excise
Famously variants of excise what's a evasive of XI
But Well this is just doing what Around of all the values squared at times there were times it appears as B 1 Iran's times a summer I equal 1 2 capital and Exor by squared minus New Square Right and That's equal to 1 over capital and some light 1 capital and acts by squared minus 1 over some light Equal once the capital and Going afterward The Newell and this is just 1 or and some Equal 1 too Kaplan acts by minus Square Which is segments So the rates of excise duties population rates of excise the population in the very size population of this term here is Sigma squared off terms and the sort of say that the areas of ex parte of this simplifies that I think minus and minus 1 Overland and capital stigma Smyrna capelan buyers 1 and then plus with little in terms were divided by the lens so 1 Overland sickness Where factoring out said Ms. where we had Cygnus squared over all Sakharov the land as well And then 1 minus 11 West 1 or Kaplan writes 1 thing the very excelled Pa But both of which are broke So contrasts this would be a case of IID We did this dish for best was just saying squared over the land And what was a reason well what's variants of a sum Of independent ran rebels did see some OB who races or who did good That appear what CERCLA rates of excise next day when exterior independent It's 0 so this term is there this terms their merits of each 1 sigma squared times enough little times we get from the south and tabs swear divided by where you get Cygnus flared over the less so the independent case You get When you're sampling without replacement from our planet population you get this extra term here and Foley finite population correction She This is due to be for dependence between around the very well are from the Senate thoughts because the comments of XIX Friday traders and manage The strong strongly dependents in Brandenburg in a random sample why do I say finite population fraction of the population there were sample from Internet cafe and what would that number 1 miners What could be 1 my 0 1 egg would be no correction There's a little bit of a correction for the sex part of what you would have a independence but times so if Kaplan is a lot bigger and small and this isn't very big numbers proposed to 1 of the chapel esophagus fallen so viewer population of from 100 million voters we probably don't have a 100 million voters will say we do any sample of 5 thousand of them by this would be summit 5 thousand over 100 million but every 4 thousand 990
Over a minus 1 that's a 99 million 999 thousand ahead 99 that's very close to what so it's essentially students where it comes in the play when this is like a
. 2 were some it so the meat summarized However they got more computations hollow these Corrections coming when you're doing it Sampling sometimes is a base next fires call the standard error itself are off you might be from the in your Each The
So standard Arab you square root Of the estimated to sell for a withstand where the Razorbacks far we just a few the days of that bar so scores various would be Sigma over the rude and square root 1 minus the landmines what it indicates how far Ex parte is on average from so here you'd want a standard is small so you'd probably wanted sample size big enough comparatively Population variance so that the standard bearers and dates of the ex parte isn't very much from new bar this is just Billion times ex parte this was Kaplan Times New sold would take the brains of T and squared times a variance X bar imitates Beirut's just gets rid of This thing so world Here we did a on the end of case so this what would what would We should to put capelin here or Kaplan RSA from you is an ex Fla IRS River Kaplan Times should be Capital-intensive expire at but the right as they missed with X just make this will end That's far and then we get a stigma square root capital and over 11 times 1 Myers the limo want in this proportion case this segment is It is a key times on similar birders so we just replace said here and you get From back here did she won ski over land and the population crept fine Population structure so Still But my bees are now zeros were once so this would be what you can read off from this start
Whoa A the fact But I at Kate recalled The sample variants is defined this way that
A survey of several random rebels Exxon Tarek send the sample rates is defined as way in the case when What X 1 through and are independent and identically distributed As squares non biased as of sickness The that is expected value of our square meters over unbiased estimator of a parameter has a rather arose expected value is equal to that crown this is where the virus 1st For us on and sampling Albert I spent hours called simple random sampling There's this dependence is not We ran arose after you pay more in this case We have to correct by following means squared exp are to be less Where over and times 1 minus And over capital and and this becomes an unbiased estimator
Over Offer population birds of
And this uses a competition we did a motor robot be buried far but I will go through So we take this thing by by Bill and all Barber 1 minus the lever capital and so on He wasn't
On At all So
But you can always use Give up we don't give up points estimates were on you as you do with that are sometimes you can't say that with high probability new lies in a certain interval and we use an all approximation part state so on X bars Nell not
Average Of in the Peres rural as in the sent on a pair of there's new added up An independent venerable subtracted new divided by a single abroad and said Maria and this is approximately normal when these were independent were no longer in the pending case but When large now The land and And pray Schulte little in or capitalist small For more than this is a product of a normal wear Signetics bar is the various with this population car for Pittsburgh direct popular so central midterm still holds if this is big enough You need the space in the interbank case to be this big enough for the approximation true but you also need this To be small minority give up independence trainer and avert at that both these told vendors apart from a normal know now here I'm sorry ibex bar select has divided by airing by end here at 5 . 6 bar my new book it so far When S mania we give a confidence interval for that premise This means we select a number I offer between 0 1 at close to 1 . 9 5 4 . 9 and find they randomly located in a I was such that the probability that new is I hear their editors is and I never knew me was that population Brimer that's a real fixed number but I is random
And we want the probability news 90 Alpha So we don't say exactly what we'll do exactly a point as from you will be given in a and where preacher L 4 times a 100 per cent of the time You will be an This is called a L 4 per cent conference at all I'm sorry 100 L 5 perceptive Carpenter As co-owner of operas at covered
So lets a user
C X far and about to get a compensable For new specific example The At that Expos array of a population of 8 thousand Us condominiums End Europe Graybill data party not for the people occupied East condominiums 2 armored cars they say sample hundreds of residents and We find it The average number of cars that they have is 1 . 6 Where XI is 1 of Vice-President house car 0 otherwise Well dance or not it's tech side is a number of Karzai's resident has so maybe the ice President as Prius weekdays in enough maverick 80 per cent on average than small sample A resident has 1 . 6 cars full wasn't as good as I did before asked Where's water unless 1 times and some of the wares of XI Wessex part was asses equal . 8 so that as text Va It is . 8 over square of a hundred times a screwed up 1 Songs NO or capital and start of the year The floods a little bit here this summer will be almost the same as eyes water Kaplan was 1 of . 8 over 10 times Izquierdo 1 minus 100 overrate thousand 100 over 8 thousand as what 1 or 8 There were 18 and say that's less serious about 1 says about . 0 8 Here we can is 79 or 80 s Vera neared 1 replaced by 1 . 8 or 10 . 0 8 . 8 or 10 times The upset sell X minus 1 . 6 Over . 0 8 is a properly normal but I think we did say that 1 a radius small and the land 400 is big enough so we want to find
Date but say 95 per cent Brazil for new So Elva here It under Alpha would be 95 . X buyers are estimator from you and the probability which we look for a number of Alpha such that the probability that my of is less do next minus 1 . 6 Over . 0 8 is Lester Bellizzi Velva is evil that Elf where Elfers . 5 and then if we solve a cynical attracts bar we get what I . 0 8 times 1 . 6 miners
But there under left I'm sorry I did over 1 . 6 minus . 0 8 0 4 disaster but are thus able to 1 . 6 Plus . 0 8 times of Alpha is equal to alpha 4 . 5 And then are conference Arab lawyers Barrow from year to year Because well 1st Point bag because The probability that expires in areas but when I 5 probably you in there so that's our 95 per cent copper we still have defined Values development This probability Quebec 5 do that we live in a table at 1st of all that some simplicity right this normal this is about our body will the disease which is a normal ran rebel head of is normal means are over is 1 of the rail defined
The values Makes troupe from looking table we know we can only find bodies of probabilities Of this type probably Illinois and rewards mustered some positive number so I write this probably that capital's use smaller net value mines probably Kaposi's foreigners value Kansas is just using probability a union these public Polegate probably be when AT&T
Destroyed the Sabine Hack AAA as
Be a union a union leaders this and a and B are destroyed because each had simultaneously be between these numbers and was that the summer OK but now I know I can't read off things like this probability from a table would have a negative number on the right-hand side so users symmetry of the normal distribution This is a bold density from minus Z infinity demise internally that Syria under the normal density from EU absurd as the area under the normal best for friend of might developer that would be equal to the area under the rubble best from But 2 and because it's Even function and I can't read this off from a table but I can read this kind of thing off so I use a problem areas will most probably a compliment and then this becomes appear derided twice The probability that Kaposi's Roosevelt minus support They know what they're wanna find our find is a velvet exist throw some solace for probability that disease Lester of Alpha I wanna find Ieave Alpha services to Iceland was sites and divide by 2 this . 9 5 1 was Alpha over 2 is 1 . 9 5 or 2 which would be the point 9 7 5 now I look and table food The will and I look in their defined . 9 7 5 and I find . 9 7 5 1 . 9 6 Ziad offers 1 . makes it outside 81 . 9 and over food problem with . 0 6 . 9 5 so 0 offers . 9 or up 1 . 9 0 1 9 6 finale recounted 95 per cent confidence level For the average number cars A mail said if it's 1 . 6 miners . 0 8 times 1 . 9 6 0 1 . 6 plus 4 . 0 8 times 1 . 9 marriage cars proprietor of the probability that varies a
Cars notable is I and maybe you've heard of margin of error things like that In public opinion polls that for the time being 95 per cent sure that results are correct that means they found a 95 percent office at Daiwa Martin errors fast minus 3 per cent so 30 minute conference call
Statement so they were like
Offene Menge
Gewichtete Summe
Negative Zahl
Vorzeichen <Mathematik>
Gruppe <Mathematik>
Trennschärfe <Statistik>
Vervollständigung <Mathematik>
Güte der Anpassung
Dichte <Physik>
Sortierte Logik
Rechter Winkel
Billard <Mathematik>
Ordnung <Mathematik>
Diagonale <Geometrie>
Klasse <Mathematik>
Überlagerung <Mathematik>
Algebraische Struktur
Fächer <Mathematik>
Stochastische Abhängigkeit
Abstimmung <Frequenz>
Prozess <Physik>
Element <Mathematik>
Wurzel <Mathematik>
Lineares Funktional
Nichtlinearer Operator
Freier Ladungsträger
Klassische Physik
Kommutator <Quantentheorie>
Zusammengesetzte Verteilung
Arithmetisches Mittel
Gewicht <Mathematik>
Objekt <Kategorie>
Numerisches Modell


Formale Metadaten

Titel Random Sampling
Serientitel Introduction to Probability and Statistics 131A
Teil 14
Anzahl der Teile 16
Autor Cranston, Michael C.
Lizenz CC-Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported:
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DOI 10.5446/12884
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2013
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik

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