Simple Random Sampling
Formal Metadata
Title 
Simple Random Sampling

Title of Series  
Part Number 
15

Number of Parts 
16

Author 

License 
CC Attribution  ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
Identifiers 

Publisher 

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Mathematics
Table (information)
01:16
Lecture/Conference
02:18
Lecture/Conference
Mortality rate
Flow separation
Measurement
05:39
Randomization
Multiplication sign
Content (media)
Sampling (statistics)
Basis <Mathematik>
Mereology
Measurement
Numerical analysis
Estimator
Lecture/Conference
Term (mathematics)
Selectivity (electronic)
Object (grammar)
Random variable
10:37
Lecture/Conference
Meeting/Interview
11:32
Axiom of choice
Area
Estimator
Functional (mathematics)
Randomization
Lecture/Conference
Sampling (statistics)
Gleichverteilung
Parameter (computer programming)
Measurement
12:57
Standard deviation
Estimator
Lecture/Conference
Sampling (statistics)
Independence (probability theory)
Mortality rate
14:19
Sigmaalgebra
Divisor
Lecture/Conference
Term (mathematics)
Multiplication sign
Moment (mathematics)
Square number
Variance
Mortality rate
Mereology
Algebra
19:47
Axiom of choice
Estimator
Sigmaalgebra
Lecture/Conference
Term (mathematics)
Multiplication sign
Forcing (mathematics)
Square number
Sampling (statistics)
Division (mathematics)
Right angle
Numerical analysis
25:05
Estimator
Sigmaalgebra
Lecture/Conference
Multiplication sign
Square number
Right angle
Division (mathematics)
28:19
Lecture/Conference
Multiplication sign
Sampling (statistics)
Selectivity (electronic)
Entire function
30:12
Lecture/Conference
Wellformed formula
Mortality rate
Musical ensemble
31:05
Statistical hypothesis testing
Estimator
Meeting/Interview
Lecture/Conference
Wellformed formula
Multiplication sign
32:30
Area
Vapor barrier
Sigmaalgebra
Lecture/Conference
Closed set
Multiplication sign
35:18
Standard deviation
Sigmaalgebra
Divisor
Multiplication sign
Sampling (statistics)
Mereology
Estimator
Lecture/Conference
Meeting/Interview
Different (Kate Ryan album)
Square number
Normal (geometry)
Set theory
Directed graph
40:26
Point (geometry)
Lecture/Conference
Numerical analysis
41:57
Lecture/Conference
State of matter
Sampling (statistics)
Numerical analysis
44:49
Area
Free group
Block (periodic table)
Forcing (mathematics)
Sampling (statistics)
1 (number)
Numerical analysis
Lecture/Conference
Average
Forest
Oval
Calculation
Phase transition
47:06
Covering space
Force
Standard error
Standard deviation
Arithmetic mean
Voting
Lecture/Conference
Moment (mathematics)
Sampling (statistics)
Lie group
Inequality (mathematics)
Numerical analysis
51:34
Point (geometry)
Area
Standard error
Multiplication sign
Inequality (mathematics)
Theory
Frequency
Mathematics
Population density
Positional notation
Lecture/Conference
Normal (geometry)
Right angle
Game theory
Table (information)
Alpha (investment)
56:24
Area
Point (geometry)
Quantum state
Lecture/Conference
Meeting/Interview
Confidence interval
Series (mathematics)
Table (information)
Associative property
59:27
Lecture/Conference
Meeting/Interview
Multiplication sign
Forest
1:03:39
Lecture/Conference
Meeting/Interview
Expression
Similarity (geometry)
1:07:03
Area
Estimator
Lecture/Conference
Multiplication sign
Variable (mathematics)
Bounded variation
Flow separation
Social class
00:05
The key to it There Monday will have a reduced Table or South Baxter office are that there will be a C 3 3 Fox or its are . created Brewer triggered 2
01:44
But it ever Rice's warriors are words here are they Of course all of my usual office are tombs For
02:25
So review of it
02:28
So far the topic of several Randall suffering a simple rendering sampling years erupted
02:51
Here In the end render rebels Are not independent But on or Bulletin book at Angry computer can call rates of excise And where we get Was a rise want force But In my 1 was is a parenteral sex data and attended by Corey 0 around arose XI next year independent is 0 the says XI dare not independent houses as nearly correlated wire would being new accord to report moved from 1 of the smaller they can't stay away from each other pick XGA 1st means you like something from apartment in some measure of population lives less likely that XI will will have the same value because that values now God and this is reflected in the mike that's why the mice A Sigma scores Reversing threw populations Soviet Red Army
05:44
Tremors again before they population us
06:07
For But He But Content The new That But Of of But Case Eleazar The population means Carlos population tall and whiskers Population Is Put They also for of it But at the bar Co It is The basis On just to make do with talent sickness greatly effectively sold sample and individuals or objects take their measurements these are the values acts of I is a random variables because the randomization is in the selection procedure These numbers elects Ira that true values In the population those around the next reuse Ex parte parts New Why do we use capital and time that's part of parts Top Top Yet we of unbiased estimator this gives unbiased estimator of the new because expect about expires knew what would be expected I TV would be an times expected foreign entirely new and what's talk in terms meal Kaplan And this is an unbiased estimator for Save us work It West
10:39
We didn't say it We haven't covered it why this is unbiased as well let's take a minute
10:46
To do that The book and Mbytes must suffer from Green
11:43
Which did it give But again Watson unbiased estimator me and by an estimator estimates some parameter from the population like being on the floor of bear Use a sample of the sample you want some function of the data from the sample and use that destiny worries parameters be estimate is unbiased of its expected value is equal to The parameters and was expected over it's over Randomness in the area of little land Individuals from the Population began It is as likely as any other choice of a uniform distribution or measure on the choices OK
13:03
So will start with this start with being mean square deviation of a sample Cope For more This is not B sample Marriott's wears a sample variants of like this and what wise in my when you're This makes a and the independent case case of independent Renner rebels with this It is an unbiased estimator or Rates
14:12
Foul on a simple twostep
14:29
The manipulation brings you do this to steps to get from here
14:41
1st step expand the square It is right I swear minors to excise tax bar a sex parts of freedom wise to excite expire sexpot when I was a solid becomes this nearly double plus acts bars Great White Way of miners here but what won the next 2 terms minus I X bar and employers that bar where it would really some that we get when I was always on this to occurs in every term DEC's Parker's character of factors that out someone the excise where some of their size and do what divided by the some size and by when you get but says it give rise to a light is to expire squared the way of past that expires with Sui add up this term hungry times well in time but then we do and time that bars where But I would abide by and white separatist expire spurts whatever's well combined these 2 together if that OK so allows a sector value say that's great The It And for rather rebel with finance sector moment the various wife is expected value of y minus means square which up by almost same sentencing thing is what we just said This the scars inside out so the 2nd moment of wine It is its variants doesn't mean square solid victory here for quite so excited I UXI squared But Is he buried select Expected value XI but we've done this before the Ms. Bergen react because of because of simple rent is true population variance The true population of a but dance or expected buybacks bar squared It is a very select spa must expected Ivax far square I was wearing Fire was Sigma squared over and 1 my the landmines 1 or Kaplan writes on Anders This is the expected so it was a really fine population correction came from the fact that we call rates of excise XJ this bias English Where you do evasive XRO 88
20:14
Here these all Sigma squared over and Myers 1 comedy terms are there summer With 4 out Yeah I did run from 1 to the and this isn't quite all the eyes and somebody will terms of some by didn't restrict I differ from Jack II goes 1 NJ 1 of modification principles says other And how it is I therefore And together there are and spread choices harmony are there were harboring of those forces of all I equal to end of the Derby and squared minus and terms in the summer and when you combine this in civil why you get this turned out so we have to is found for these 2 Things where we get well 2nd you ready I don't need this 1 and because all these are the same right side and times a common value and divide by and I just expected by 1 of them squared These things were so this becomes where we were and what is a speaker as becomes Light squared over low and 1 minus the Linn 1 over capital minus 1 and then my For I But And that is equal to 0 We could that The doctors square here Now he said A becomes says XyWrite That And I guess we have to find a common enough laic combined these terms As it Oh Carrying and we stuff here or not Wearing Zeus's simple Ozick yet It But The ship Now it looks I rigors of ice on this book canceled this will cancel However and Kaplan minus capital and that looks to me like capital times land mines 1 nowhere and capital and minus 1 times 11
24:56
So let me as Sigma hats squared this way it's expected value is us numbers almost 1 of the population size begin a sample size but never equaled 1 is signal squares and unbiased estimator of sickness
25:51
Not hokum we use cigarettes square modified to get unbiased estimator of sickness Divide by dispatcher right so this implies that Capital and minus 1 time 11 over travel times The 1 Singer squared hats and that's where it is an unbiased estimator our Sigma squared off OK Well our signal that Square has a 1 already here and here's a 1 0 years now so let us but the sale and pseudo yet But we we will For But They bombed This would be for Ms. zest squares times Kaplan runs 1 or or any right the definition arrest square
28:27
Get from here to here would wouldn't walk I'm putting 1 over and times us but I remain here like cancels and I just put the 1 relies on his arms argues Soviet that And minus 1 over and squared It is bound by says Mary for our say Where Gay problem What about the Razorbacks What was a equal to the assignor squared over 11 times 1 and minus 1 That is what voided on vise mayor of various sex partly to various next far involves Cygnus where do we know what that is not to sample entire population of what's Cygnus where he like to know the hit ideas Idea about how big are very select Spartacus Kansas
30:05
This tells a gives information about Hobgood X bars as mayor of
30:20
If there's vex far 0 or there is over a to receive that we've X bars always knew race are as rates fall of X partisan reverse for very much from New
30:59
Raised explores big music be quite ex parte could be quite far from the farm with this formula for race expires we go nosing was where
31:12
So have decimated what Do we used estimates The sex all right But it is In a E So this is true formula for the Razorbacks far beyond estimated that we don't tests may go and or capital and about times in Lewin
32:39
And rob you have a good idea what capital and they make you may not know exactly as they are desperate Sigma squared will use this so we just put this in there and you back and I think this might simplify especially if we rewrite Combine these 2 beers and mine Capitalized on there than they can cancel out so that as a 1st step this would be capital and minus over Capital and my If I come on barrier is Kaplan minds 1 over Capital lights once we get the Kaplan minus 1 minus the live plus 1 wants cancel Kaplan Notice thus canceled and so we get mirror this way Squared over and times Kaplan My slowly and over affluent Maybe 1 Warsaw evaluation squared over blue and white might as well as a recap or close areas coalesced X far square think
35:08
Farright 0
35:22
So that's next buyers probably bids that standard bearer Scholars air and to make coffin also Where place missing which we don't know biasing which we do it all from a sample
36:11
But But So severe Cox from a normal FON as they are Back to think back several were fairly plant source for the spot here on Earth XI as part of normal if I fail to my top my life But a rude and fight at top my life and website by despite an idea X barred by despite an ideal meal by despite a signal over food and Were not IID case moreover we don't in the case but were false not the ID case that Wikinews normal but we have replaced a signal rude and by this they asked where is as if we were in the Yankees he says square Which was This is an unbiased estimator for sigma square in the center of Riga notes Sigma spread in this setting we replace stigma by s Spurs squad in a not and a simple random sampling setting we have to modify whereby by That other factors to give a unbiased estimator for signal overreact and reuse it says so we treat this as being And allrounder rare so for example if they are an example in the book of are yes as exercise its exercise 3rd Yeah No The humor wears exercise had the hospital 13 in the 30 They we're a copy the 3rd edition of the 2nd act 13 also but I have a 2nd is looked at it wasn't so this was due to his copy what I do not actually are alright found a problem is Laura on the full not means move difference between what is written and what will do so of time
40:55
It's quarter to Dellroy the probability of break going back at OK so Each He did it All of us All day so this is the runny example target Martone All that is The broader story some information from example a of some point through to to do this and the 3rd quarter with and this is what the number of patients discharged here where an Eagles 393
42:36
Hospitals Yeah XI head of a set little excise patients discharged from hospital I it for what we in January 1968 And then Arango sample 50 ask those in state and then his continuing just f f So while a meal somewhere in the book here they give the act acts are things I saw a lot of suffering break down your flight of the I thought the numbers in this I highly recommend to video runny example on the hospitals and over discharge faces generating here but several things with
44:49
This exercise uses data from that example a sample size 50 years a collected from 393 hospitals or the average number of phases discharge in January 1968 in those hospitals
45:14
His by a 38 . 5 The SX Parker me using the data all areas as Where is this this is computable from the data cracked and sold where its forests futile The data and knowledge of the sample size and population Melendez 50 Kaplan fair and free But the data entered them in your calculator harboring you have Captors old compute this summer I use it or not Reminds me of a joke 3 0 walkin block bartender asked you all want a drink 1st one's air forces Merrill And secular Irwin said yes But at a basal what happened By persons Enron Oil Docket Gardener you always takes away so that me As well seasonal beaten 1 of inquiries Egg You say you would you would say no but he say that I don't know what the exact sex means he was very good there was a guest seem so I asked somewhere you have Doctors akin to listen he said not like now The salaries of its riddle I get updates another that vibe
47:10
Will bet on interest there's some very fascinating numbers sample means and a sample standard sold 1st let's find their competence were ex parte defined comprehensive role for capital for aristocratic are visible from new use
47:37
As it actually asked for conference For top which Its was fined covers you 1st Plant I That But Citing but squared error of durability skirt by phosphorus that is that does probability that minus Z disaster X bar New over X bar must is approximately equal to the probably the miners little seeing his last a capital C Staples Inc where capital C is a normal means 0 Reds 1 and the No votes of from moment our we don't on you but we do know and not from the sample these numbers we agree right It In a colliery say never knew lies between 2 value Is This parody of all users across this by You just solve this inequality from you what's 1st step multiplied by the number it gives you might Founder Tanzi and foster worthy However that might here Richards attract extra from Mozart summary of the Sept . 1 we get miners as suspects Ozzie lest would cap elects a new Western Auto S X party next step Jack debts from both sides Thank
51:34
Final step All right by minus 1 reverses these inequalities period this time might on Times is bigger than New was bigger minds want answers
51:48
Which is the of the composer becomes X bar standard error privacy ex parte plus center there and the probability new license interval is before that arborical us
52:23
Now the question is if you wanna required Probabilities they say . 9 5 or something it finds easy so this is . 9 5 She was The cake Now in the book uses a notation that convention I think is a little confusing he calls These are things 100 Times 1 myself up per cent conference that uses Adolfo this way so it for 95 per cent composer will ward off after be . 0 5 thing and then They also uses this audition Here's a normal density Game And imports A shaded region here and the area Shaded regions It is I offer And if area yourself a calls us Point Zia Alvalle I don't like this All that much because And the table to New York Brings right Is an normal He all of There's a the Lord And this area years called And this point years callers Aesop Sorry sorry my theory over here On his ZEL selfawareness is out of the area and a table laid out whether Syria called anarchy and Point of these I think he should just stuck with Abell all the cereal which is why I did last time passed yours I would that labeled a self label that Alpha but year and these 100 L 4 per cent of all 4 of the 5 sodas as slight confusing change course for a change of notation between his convention here and a convention that table went so as to prefer you can't it with 101 myself for Percent is over
56:36
100 off you knew Newark good we wanted this is a good example of how we do it this way how reminder that we are capable of lawyer sewer let's see what we wanna find here will ever disease so this is true I guess we call this a hundred
57:08
L 4 per cent of got key person and not a L 4 percent covers As The 100 L 4 cent CI were office might so as to give you a 95 per cent confidence I used myself so powerfully finders east of the movie was probably like 95 so in this picture At the We want find those ease of this is capturing area size of doing so if This series . 9 5 watts a stereo 0 2 5 because this area Was this area was add up to party gap . 0 5 and they are the same so this ears Going 0 2 5 Soviet What's a probably then the capital Z is icicles . 9 7 5 . 9 7 5 solidifying visit be then but a summer here in association or findings Aesop Dewar Peters . 9 7 5 period till after this place is quite may 5 vary between here here is . 95 So in the case of table to defines of new work years . 9 7 5 0 in Table so there's EPA there's a point I certify moved near a spot in the vault here for
59:47
. 9 7 5 minutes right there that's in the role with 1 . 9 and the left side and the column under . 0 6 Aziz of his 1 . 9 They are now let's go back to what if here that's are 95 per cent covers there will be of Zia's Z . 9 7 5
1:00:37
Abstract for meal for NX forests 938 . 5 SX is 81 . 1 9 endeavor Who as a chopper Kaka 81 . 1 9 times The . 9 6 4 5 8 8 I think he'll there Or But I'm OK I'm 30 a bias 89 938 38 plus 89 This Allison The 27 In a related and if so sorry 9 to 1001 Bayboro might any 8 but fight And the other 2 Lyall is a year or so or where like about where we are seeing it summing up 95 per cent of the time when you try it and see if it works that lockers A mail that expected can expect 72 95 per cent profits over ex parte What about 40 Assured for top whereby conference for top quality That However say yes 1st We started with a X are Myers new over S X bar is above normal when we use decimate topped an ex parte so what if we multiply cotton and then this becomes capital T minus and knew was what
1:04:10
Top over Sex sexpot So we want the probability that minus Z similar Capel T minus talk or and Tests X far less Posey to be equal to about 12 . 9 5 different now what is this expression in years I exactly X biased SX far right and that was approximately normal sodas and give the same values of z right because as this is no different from what we just did disease 1 . 9 6 what Conference oversight For top with the solve this inequality for top 2 But Half of it she to St. sets as before I give this all ears Cast that Co Thank CEO like that it off
1:07:09
But the Always alike available for new For me off But At Why severe world for seed Tommy so much bigger than they all for others more variability in 2 years I knew we divided by 30 T 50 would modify new by capital and so whatever variation area was in the estimate for New gets passed by buying and OK so here's a here's an announcement we to racial there's only narrowly 17 minutes left while 22 minutes left till the end the class don't think I can explain racial stew and try to itself as I'm sure some you're disappointed with But all I do is take 131 B and will so or stop yeartodate a give you little break out run over past maybe I think I run over 2 and a half minutes 8 times and use and they will resume Monday with the reviews