Estimation of Parameters
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Title 
Estimation of Parameters

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Part Number 
11

Number of Parts 
16

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CC Attribution  ShareAlike 3.0 Unported:
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Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Addition
Distribution (mathematics)
Multiplication sign
Expression
Moment (mathematics)
Mortality rate
Limit (category theory)
Rule of inference
Open set
Mathematics
Binomial heap
Arithmetic mean
Centralizer and normalizer
Root
Lecture/Conference
Term (mathematics)
Ranking
Moving average
Right angle
Renewal theory
Stability theory
04:30
Functional (mathematics)
Distribution (mathematics)
Dependent and independent variables
Multiplication sign
Normal distribution
Moment (mathematics)
Mortality rate
Numerical analysis
Arithmetic mean
Film editing
Lecture/Conference
Square number
Ranking
Normal (geometry)
Right angle
Asymptotic analysis
07:33
Point (geometry)
Functional (mathematics)
Randomization
Divisor
Multiplication sign
Correspondence (mathematics)
Blind spot (vehicle)
Equaliser (mathematics)
Water vapor
Mereology
Rule of inference
Product (business)
Power (physics)
Fraction (mathematics)
Lecture/Conference
Different (Kate Ryan album)
Term (mathematics)
Square number
Modulform
Analytic continuation
Maß <Mathematik>
Random variable
Area
Potenz <Mathematik>
Distribution (mathematics)
Sigmaalgebra
Quantum state
Expression
Infinity
6 (number)
Line (geometry)
Limit (category theory)
Variable (mathematics)
Numerical analysis
Category of being
Order (biology)
21:17
Point (geometry)
Trail
Process (computing)
Multiplication sign
Expression
Computability
Routing
Division (mathematics)
Mortality rate
Average
Numerical analysis
Arithmetic mean
Lecture/Conference
Term (mathematics)
Calculation
Saddle point
Directed graph
28:10
Area
Point (geometry)
Functional (mathematics)
Process (computing)
Divisor
Multiplication sign
Forcing (mathematics)
Sampling (statistics)
Division (mathematics)
Special unitary group
Flow separation
Rule of inference
Approximation
Differenz <Mathematik>
Lecture/Conference
Square number
Musical ensemble
Table (information)
35:01
Trail
Computer programming
Functional (mathematics)
Beta function
Multiplication sign
Decision theory
1 (number)
Routing
Water vapor
Parameter (computer programming)
Mereology
Event horizon
Expected value
Derivation (linguistics)
Sign (mathematics)
Estimator
Population density
Lecture/Conference
Different (Kate Ryan album)
Natural number
Square number
Mathematical optimization
Distribution (mathematics)
Potenz <Mathematik>
Prisoner's dilemma
Expression
Computability
Special unitary group
Exponential function
Limit (category theory)
Braid
Approximation
Numerical analysis
Arithmetic mean
Film editing
Normal (geometry)
Gravitation
Right angle
Musical ensemble
Table (information)
Family
Thomas Bayes
Directed graph
49:46
Randomization
Functional (mathematics)
Sequel
Equaliser (mathematics)
Multiplication sign
Decision theory
Event horizon
Food energy
Population density
Root
Lecture/Conference
Term (mathematics)
Different (Kate Ryan album)
Square number
Analytic continuation
Fiber (mathematics)
Set theory
Random variable
Area
Standard deviation
Distribution (mathematics)
Expression
Computability
Independence (probability theory)
Approximation
Numerical analysis
Arithmetic mean
Film editing
Symmetry (physics)
Right angle
Asymptotic analysis
Table (information)
Limit of a function
1:09:29
Statistical hypothesis testing
Functional (mathematics)
State of matter
Multiplication sign
Real number
Sheaf (mathematics)
Routing
Mereology
Event horizon
Dimensional analysis
Grothendieck topology
Subset
Product (business)
Expected value
Population density
Degrees of freedom (physics and chemistry)
Causality
Root
Lecture/Conference
Different (Kate Ryan album)
Wellformed formula
Modulform
Ranking
Analytic continuation
Area
Covering space
Distribution (mathematics)
Graph (mathematics)
Uniqueness quantification
Neighbourhood (graph theory)
Moment (mathematics)
Commutator
Independence (probability theory)
Line (geometry)
Numerical analysis
Arithmetic mean
Factory (trading post)
Spherical cap
Order (biology)
Right angle
Object (grammar)
Maß <Mathematik>
1:25:49
Metre
Potenz <Mathematik>
Functional (mathematics)
Distribution (mathematics)
Divisor
Gamma function
Multiplication sign
Moment (mathematics)
Gradient
Infinity
Independence (probability theory)
Line (geometry)
Numerical analysis
Radical (chemistry)
Population density
Degrees of freedom (physics and chemistry)
Manysorted logic
Lecture/Conference
Negative number
Square number
Normal (geometry)
Chisquared distribution
Directed graph
00:05
My notes I've written here CLT as and Center with their arms we do the they is a very people today are that additions there still proving central appearance in various contexts evenly I paper recently in the head on the subject I guess the EIA words central to give you an idea that this is free important our classical us said but there was room for binomial and rebels um We do want to use a half But We do a little more generally and that is so it's take of the that's 1 directs IID January rolls and maybe they say the list goes on and on and on For all of us were Back at new New was mean and sings critters a so I said Let of X 1 is new in the very next 1 is spread were rocked the meandering threats to Because right there the same distribution and distribution determines the dean and right then They get where bat or We add up the 1st and ran a rare also I hope I have ever deliver probably this expression as stable X Watson mean Bessette what's expected S & Partner and new what's expected value a summer and rules of the some of these expected values right so we add up The expected values of these guys all them renewal and there and terms of END so a new is Minot expected by what's variants of Quotes the very some of independent ran rebels members Some Some limits on ranks squared so the very best would be and times Things were so this is the square root of the soul of the expected value this trend rate bearable What's expected by 5 Subtracted the expected value from SAN truck mean from ran a rare moment they expected value would get 0 expected I 0 of the brains of this 1 with the reins
04:33
80 times why is a constant writes a squared y 80 square Kobe rates so the ranks of theirs would be 1 overseeing the squared and Times the ranks of the numerator what's right away Word and phrase this thing is 1 of friend Ruelas mean 0 and variants 1 and the remarkable thing is that as long as it's in this happened In their independent They serve it doesn't matter what the distribution as the merge 2 0 4 4 4 That I see some response on markets Oh I see why puzzle X K OK this is distribution function for the normal venerable means Andreas 1 other words this guy Asymptotically has a normal distribution would mean 0 rates 1 OK R O Let's try to see what is true I would save us through this The enough right panic it scared or think you Kadir Center suffered 2 recalled exist on top us That's true duty moment Jan earning function And see what happens so that I'm doing or the momentary functions for the draw means Iran's won its EU that she's heard over
07:30
But save CUT Sperber to right
07:49
But With But I think this is legitimate Think of having and then over this number and mines and new over this Member And that means I need to a difference in the life of 80 miners being that seemed to be a dance you might be Where beaters this part and this is a But now expected values of this and this 1 is random but this 1 is not Sorry Poland nonrandom 1 obvious I don't know what they are Now Are centers of some of the axes and again I use property of exponential viewers saw product Individual some Now butts use the fact that these are independent of all these random the rules even these things early Expected value products In ran rules becomes a product of the expected values so I get expected value of over rude and times X wander in and get the same thing with the next to next 3 and and all those factors would be identical because redistributed I'm not by missing times itself in times like this raises to the park But Don't But for An hour put this back inside It's something raised to the amphora what is this thing Also raised They are so I put it back inside and foreign years just put this insight Red For us That So positive OK Now Tom what is Ito something But Sacks and would Exs very small Look CDs is approximately 1 plus Expo sex Ferber took us Because what happens to powers and really small numbers being by 10 the minus 3 Cuba that the miners 9 which is a lot smaller than 10 minus 6 so the rigidity North terms passes for next is released Let's do that in here what yet We expected value of Poland Katie is what we do expect this thing where we substitute destined for The left side of the goal line have a T over Sigma rude and times X 1 my and then plus a squared over 2 stigma squared and X 1 my New Square This is a body on the summit as a ghost Finally we get the same things both here OK Now say they expected value this expression expected I wondered why expect 1 1 like divide this year's around awoke from which i've subtracted its expected so expected by this difference would be 0 list goes away and they expect about oneliners New squared Selects 1 and is a very selects 1 down here so when they do this Cancel the Sigma square the denominator Leading Tsquare squared over to an Ann Arbor says races power and came close at these tour same but is is is Endo to fraternity
14:47
That's for the final Lewis from doctors Back For the pure argue that Take the log Start safer Lord of S K So if we write Equal 1 over and is a logger 1 plus times acts over us and taking limit mangoes corresponds in limit as goes to 0 What's Lewis's escorts to 0 what happens in the north Grows to log a 1 0 0 Ray rose too Soros's call indeterminate form limited this is the same as limit of a ratio of areas that call We speak French It will be far so as as Costa 0 this is the same as The real suspect which is what But X over 1 us Sex I differences over 1 over the thing inside times means that ended there The suspect as 1 and there's Best poses Eros goes to X that acts this goes to 1 that's 1 The rabbi 1 driver 1 is so the log about thing goes to acts of that thing must go to orders Remember this lamented the lack of soap What happens here This goes too easily Where were 2 axes to spur Massimo magenta function for Off With be 0 and OK so prove the be momentarily functions for this thing converges to normal so we need something that tells us that happens in the distribution function purchase distribution function for that random variable is converging to another distribution ahead We all this is converting to Photograph water what the distribution of options fathers of Theron that says that and that's called the Cottonwood so it that out The tea There a surrender variables are Zia would be the sky Is another random rebel and Vermont dairy functions momentary functions for Louisiana's converged to a momentary voted frizzy for all tea in some interval continue your Where work Then goes to infinity of the distribution function frizzy and as is equal the distribution function for capital C at Woolsey at all points of continuity of the function of the That was it Some particular Juppe lots of disease continues everywhere In this convergence of everywhere So that Covers our situation Ozzie and momentary functions converged in the general came yards and 2 motor functions for the normal so it says that the dispute functions for C and converged distribution function for
21:26
Z sub SOsub at play So 0 or on what What does is applied to I call on all of us all These are in the where Louie reverie also would probably refuse success He will Not only All that this Renner rebels approximately normal means embrace 1 distributed so I'm saying that can is the expected value of X 1 and that he turns on my skis the rates that which is what we are here for ever for Bernoulli's public X 1 blind is 1 must probably X 1 0 years Expected value 1 is key to raise next 1 is backed by 1 squared minus expected value but X 1 squared is 1 of the same By square 1 or 0 wanna 0 sources and expected that once was key this is key A squared key minus D squared at peak times honesty guided by route and cut their that's approximately normal So if And it's 20 years onefourth of approximate The probability their send is bigger than threeeighths I ever sent bigger than threeeighths But it's a prospect that probably As member successes in an equal 20 trials what only successes would you expect when trials of the province 4 About 5 this number would be what creates terms 20 is a bit more than 5 on watch for At some point 5 Ursal grasp what probably of Ada more successes review this well Wigan actually computers exactly Because we know that The some of an independent yearend rebels as binomial so this could be computed explicitly it's some Katie Equal Us to be precise 3 8 times 20 plus 1 regret injured 3 times 20 and and up to 20 20 twos OK onefourth to the case And then threefourths of the 20 miners K values is computer all these numbers now And creates tyrants 20 years what exactly is at 3 8 some 20 years 3 times 5 and by 2 . 5 . 5 times the years 7 . 5 so the greatest that a 7 so with date when at 13 terms and Soviet 13 numbers Get not impossible can you do it before The break Hank William 12 minutes job returned Maybe if you have a calculator you don't job not by the central there says we don't have to compute as richer proxy despite a normal Instead We get this in the forward news settlement Expression of careers in the saddle attract somewhat track and times mean abide by mood square The best thing so inherent through our computers probability subtract entity in divide by route and oneliners being and
28:22
North Keep things on a switch to do the same thing here we take 3 8 and subtract NYTimes end and divide by word of time times 1 ass The probably A lot of it so that's how we don't need to figure out what this but we do need this is the hour around Ruelas approximately normal so we don't do any competition Here's competition has begun but an eagle 20 people for I think that's do that if sample but where mail this OK so off backdrop a 20 what's 3 8 slightest 1 4 1 8th of 20 years so won for the 20th 5 0 2 . 5 per The case of the new writers 2 . 5 and 20 creates Myers onefourth as 1 8 1 8 cents on his 2 . 5 orderly at 20 . 4 times force What's 20 times a 4th at 5 5 times 3 force 15 It's a provider so that we give off the floor from here Because what happened time there and was out 20 over a square of 50 Right over 10 years and I 1 half of the year by more like 2 types has 20 per container was 22 hours 15th certainly somebody must have thought Mu volunteers to compute that The starving The same day saga with finance death Divided But should be Well this is my 2 times 5 I carry my own writing thank you OK so as to be 10 said 5 but alright 5 Alright I take 5 Sinhala off and that was once for what we had so 1 for the the visitors a 1 . 3 9 . 1 points The thought we find that Now we use a table and solo I'll do that they will to it and we want . 2 9 and I look down the left column forewarned quite true in way until I get to that From under Poynor financed is probably is . 9 0 1 5 And that is I think that Which is a lot faster than doing this Get back the job several but Herbert there appears in other forms But for Now foreign normal approximation occurs Corpus Sandra and rules of bars Both of them all OK so XP for Sun from under than expected value Maxie Member and the areas of X is also found Member the on Jerry functions for Posada
35:11
All of his socks And Press That allows you to compute commune braids quite easily if I take Lock rivers The For the seed derivative of the Lord of the mojo function evaluated 0 Is expected value of around I take me driven suspected TV Stays there and different take this unity the Atlanta unity is evaluating at Eagles 0 gives as me Founder and they 2nd 3rd event gives a very always does not on for this to be true But now we different twice whether we get 1st family of land unity with different Japan again you get family unity valuing it was you get Where 3 so that odd The you That's of itself but not a lot of depth 1 I say what what It said If you take the 2nd rows of Obama them directly If they provide at 0 Work The target 5 So this venerable has what expected I X for Sun with primary lender which attracted me means so expected by missing 0 wire isn't band But quota cuts Wanna rural land from the expectations and have expected by this bias that virtually 0 what about the merits of this trend It's well that Slender but abide by this Becomes 1 of the Means is 1 not The race was be normal or post normal let's completely monitoring functions and if we get beauties were were too was a limit the Gaza war We conclude about acts My slammed over planned its nearly normal Flanders Bay We saw Do the same thing again up all the as are Words nonrandom part They now . I know it says a broad thoroughfare but whereby a nite tea but edgy over prove that I know so perverse to ride around the room Banda He preferred be useful and we have this from being to the land She overrode Lambda minus 1
39:57
As now land is really really big so what about T lender scurvy really small 0 gravity So really small number em when we're beta really small not what what approximation we will use for yellowtail banks 0 our Mary off throughout the 1st turned 18 Times you land And that tireless I will use the approximation that this It is going to be like 1 plus 2 euros and then he squared over to wrap and minus 1 warehouses minus 1 What the This 1 in this Cancel leaving just the linear Germany hard right That means that the land and sea over route and then plus Tsquare over 2 and there is a real 1 went by there's no 1 there were alright combined the exponential so by adding in the export of water we get Well you're Simitis land Here's a plus 2 this canceled cannot by land at times is what I get A tease were Araujo Sources as saying that all of that as a lander goes to infinity from Omar Jerry function for Posada from randomized slammed overrule Banda Converges Jerry functions for Nor I can't naughty fairly And this calls for all acts Because the distribution function for the normal is continuous everywhere But So in prison A great example X is for song with parameter Gay while for Further Track Landon Alonso or 72 Last May A placid wicket computers explicitly for 4 4 The new that's so it is computed these 73 numbers and then added together and we get the answer And you would face by the end of the summer session of the We could use a normal approximation in which case we faced by break saw how to we convert this so so that we newsy Nishimoto subtract abandoned abide by square of land So it's it's subtract 81 and abide by scores of 81 which is nite and with this Now should be really impressed because I read of these numbers at the board and I can't find 1 So this is about like the probability of normal minus 1 and as a table have Entries like this Now has probably say your us will do a positive numbers yet to convert this to probably that for now it's normal So this is approximately the same as Probably the normal disaster delights From now on if you see is being Granbury with nor which is normal means a race so you have to convert This is to say something but soon to steps It is a step cracked and wires cracked if it's gap The distribution for Aziz symmetric respectively origin Barry under the density for Z to optimize ones equalarea densities precede the right of what would be the best even from an awkward convert this to an expression evolved probably easy being and didn't I tell you long time ago that you use this being made times even 1st and now we look this up out there for you just look enough column under 1 hand encoder 0 it's . 8 4 1 3 All right And that's what But . 1 5 7 Kegg sold more as a free approximation this is a horrible thing Greta computer are new program is found but it is much easier would ignore did a pretty good team There is there Off a lot yet that Gas Natural book has it but there call There are 3 That gives estimate for the air or our decisions or it was normal than that there will be for
49:47
Some things I finally looks quite good if they Be federal have heads I can't tell you that 9 0 Trinity that tells us good so that guests may coming You get better us for some rather rare Wilson OK back that's too was Approximation we just covered Delia from approximation of Posada estate this But South by the year Fritz worth West a explicitly What's a ovaries Air If CSX But it with Louise The X X is finally or prairie Energy Suitably standard and scaled random variables Asymptotically oldest However We essentially give this on restoring some of Bernoulli some of the Vernal Utah Finally We prove that We did how would you prove that was I shows some of that compute momentary do that by putting checked for this and then take an independent Louise Adam up all that tests and launch a bachelor equal than that to her parents and be giving you knew that I'll give you tell Wednesday spectators went A beauty tell Friday can't do that by Friday of Ford That E The need for all of us Wheat Arrange in our lawyers her own case of 0 . 6 from rivers Breaks And stroll 3 thousand 600 fighters We must obey the probability that yeah between 513 650 Ollie 6 is really expectant payrolls sixunder whether or not there And I have probably very crazy but let let's visited open prominent because By nice numbers so of course you could computers explicitly this probability the probability that acts as the number of sexist But What kind of random sack While you can't as success and not a success and failure And then back to be numbered successes in 3 thousand 600 trials where are probably successes 160 finally over an area with predators 3 thousand 600 and sex On the A lawyer and all that but what's a sequel to while where did Right probably expose of wiggle And this a floral right a 100 terms services fight As always terrible numbers to compute Computer could do a pretty quickly but then ducked programmer computer or use mobile approximations Why would end times equally an auto outscored event he won lies came at C and 600 Mrs. Watt 6 600 5 6 Never square 500 vary so it 550 minus 600 over square of 500 subtracting ANP from a reading and abiding by a square root and he won rights in that expression over there Playing actually so this is It's not parks were able to say exactly delighted with a legitimate Nicholas Of the approximately The properly the northern rebels between these 2 numbers so what to we take the it maybe fibers and shut out of Inc Mister better charged in the But 6 5 cut Some Leslie get a minus 50 over the squared of 500 right we get 50 over the score 500 Daisy is a nor honorable means 1
1:00:04
So this looks like a fun lefthand side probability that does as become squared 5 Western Aziz molested bicycles 5 Where 5 others 5 times 10 reply were 5 marked 5 saving your skirt 500 is 10 times 5 5 Spurs 5 or squared 5 And against where fibers lots of broccoli make look Calvary that is calculated in the meantime or Thank you But now this we go got this no because Only things of this former and table so it to convert this into some some expression has trouble easy less over something so the 1st thing we do is a remake it probably bigger eagle 2 plus 2 . 2 4 by the symmetry of the distribution of cash for the age of all day and then Wickenburg adding to the that thing again using probably a size public makeup And Johnson called twice probably Zia's arsenical 2 . 2 4 miners want it so we get out And look at 2 . 2 Angora under . 0 4 in 2 . 9 8 7 5 tho that all But That's why guys owned by 0 But I'm quite so I go back from all this stuff from here to here frail amusing probability is equal 1 mines wobbly may compromise where 80 Izzy event Z bigger nickel to 2 . 2 4 so this should be the probability that Z lowincome heartbeat Z less than 2 . 2 4 I wrote Lester it'll do But Does it matter whether I've used strictly calls here are not quite out of war The The People that That Take a right quite Right it's a continuous venerable African stranded rebels probably would be able to list is value is 0 for all And when we see that probably new single will you would be less stable The probability that a U Mya steps on this bus that capital you always unstable you are set 1 and the of the distribution That view The epsilon distribution function that You will you might as epsilon and what happens this is on goes to 0 This goes The capital 0 0 you might sets of capital you although Hawaiian decision functions continuous and this differences 0 0 and this is bigger than a quota 0 and holes for every epsilon so we conclude probably capital you use 0 The I But the height of the the court They take a couple examples was B is Lily minerals what values to be had 1 0 Saudi The answer is that What's probably was 0 0 what's you was white But probably use any fixed value of 0 what's probably usable a 0 0 what's probably was equal to 1 0 so it's probably Uzi Bolivia 3 Bernoulli 0 where he is finally the predator and and I don't care what you but that is 0 through And but probably that you is 0 There was probably was want but probably was equally these to be 0 so what's probably using the YOV is a discrete random variable The suit be 0 because it is a spate of what's a joint density over these 2 guys big and Seguin right this display right where I got here Bissonnette Capel you Eagle Capel B is a union of these events
1:09:44
These events for different little br disjoint because capital began To a different movies at the same time so the probability of the Union of these events as a summer probabilities each 1 of these can be written what you would be a independent right so Here 1st step 1 is as saying that they died of capital its little being so Alexis A Nunney said that net and And Lexus charm there 0 Backed up here this probability is less the problem you was equally His ever be less restrictive Watts is probably weary no it's 0 Think of 0 What planned Dallas was Is continuous backs a hero by these continuous but will With density absolutely But absent due note the density of than the probability that you would be fallen some set 8 days a subset of our 2 years over a of their joint density another independent saw their dike density is a product of their individual that's that's what densities to for Sole Joey's breasts You will V has an the form the pair UV is set a date for that Alike so I knew you Gulati it's this But So is the probability of a parent really is I underline L and by this formula over L tests of you You have some be of little value you you know what's interpretation of this as a B area under the graph the function the stances over the line L but that area What's waiting over a line in 2 dimensions 0 0 0 0 the problem using will be is 0 you will beer this doesn't require section just by had a joint density I'd like Tanzania SAR sulfur for example There Yuan beer independent Earth Continuous rather rebels from us Where the same distribution and identically distributed Legos I could upset ID What's a cover you as I say Chief Well is a strong But So do Sexual Why would that Cho was a visiting be statistically speaking nothing the same rank 0 base to should be the same because you would be of the same distribution factory label them tho we get back I will above the probability that You is less Plus a probability that you would begin with that What What about the probably the EU is less poverty was probably you upside do is bigger what's article Why is it while I was there is 1 of want This has to equal to what the proper use of added in Europe and the probabilities of these 2 problems are the same still want So these 2 numbers add up to 1 2 numbers are cold So they must be cause of aft They went Of I What's is probably I tell whether roots of Apollo real use quite right formula and see if the socalled discovered it is very goes 0 this career being its you squared minus 4 times the size of this bill is commander discriminatory Cricket But way Foreigners use spots the probability that use where it is material to be
1:19:27
That probability When apps where no there's a ran a rare woods continuous use red arose continues their sale distribution what's probably 1 of the nearly onehalf Think So I think summaries said that 38 for the answer was quantities for the answers for half Soviet a half on the exam Ogata Mark wrong they bring about things OK well done so it does If that's but let's use this leads into Chapter 6 was you as normal means operates 1 of the reputation of you square This was all planned as a segue from chapter by chapter for non chapter 6 distributions derived from the normal but they do not warrant a rare reward museum Raceway where that happens often enough that has a name Call chi squared with 1 degree of freedom of that bound for the year to assist comes up and sampling and nest Illustrations of various units Is an or memorable means owners want and use weird is called upper oneyear sometimes wasn't there and that Maybe it's understood the Mariners is called Hi squared orders 1 degree of freedom And actually this is not going by an alias sexier different at distribution ART Noel And how do review of suspicions of federal sweet computer apologetic functions see free recognizes fortunately rather quick to side because we all in all a few motor functions of the state of computer moments and function for you square But It is our function is to use I'm using the density of you so this is a function of ran rebel site evaluate that function at them off my body density On route to buy that The function was expectations gyrating now where you're doing expectations you should check suggest that heroes and occurred somewhere there is as always we find that But if she is what is is to use 1 Where you're going to use 1 here but the product is what BVU squared over to and a hearing from eyes friend to and what You you square to do when you go Those entities city as a fine not so is 1 this is not a work of art can be had for values to you would be fine Well exceed if these negative it's fine but can we get bigger than 0 that's the that's the big question can you bigger 0 because make these conclusions about the uniqueness of the distribution that gives the object Fontanini motor function to be defined in the neighborhood of 0 has been defined as some terrible containing 0 would take part a passerby have that been Yes up to of 4 for example than that EX 1 is still That is for EU Mize squared over 4 Right and that would be fine so this is visited converge neighborhood contain or but not for tea equal bigger equal to half so where visitors In order to would commute followed I guess 1st ever February next For us I think it is our right Chen hurried to visit Stop What is a look like A senior girls vaguely remember resemble list OK density is like or what generator with Saiga normal What is a normal that they like
1:25:55
General normal density Is the rubble Maine 0 Minnewil embracing sleeveless where she that would like this Not exactly but not too far Now I tainted eating well I've cosmetically chase on me but this is different is assigning for is a nun equal or start Not a lot like that That would see what might Minus to equal to 1 lines Judy and new equal to 0 Steelview Stuart Harper how would you you square here must be But now it's signal itemized to is 1 Were missing something promising Ms. But you put that Don here It Can't much itemized who is this basic square meters of minus want that Don here but that's not what I started with 5 wracked by putting in that Then somewhat what Cyril this from 0 to mice Trinity it's what I so 1 over this times at a role would be 1 leading that are If K On 1 Myers to Tito back that's the momentary function at for a team purity on gamma momentary conduits will feel it doesn't it's OK 4 4 4 4 And this federal members as long as he is our somewhere it something negative and X foreign infinite sort could hear as combined the exponential so he complained Now there's plenty of for about 4 times that we offer 120 most of acts a density means that agree this stuff I 1 that's not to say that So I know that it'll be equal to Belfour over whether demise Tito the offer from the back of the former gamma density here but primarily undermines he Kirk normalizing constant would be won over this But Can office canceled and so the moment functions for this Slammed overlap demise Tito El the look like that and also the mightiest esteemed signed forward land they have to be 1 as we wonder what we all have to be onehalf Craig so scissor 0 8 Islam legal baby not maybe letters I want but strike over there would there's less cooperative T minus 1 hears to Let's hear it at the factor that out by factor that our you're buying yet Script to write It For crept starch There a far the numerator becomes 1 half 2 1 half over onehalf minus 2 you on
1:32:22
At Now lenders a half also act as a high squared with 1 degree of freedom is equal to a gamma with grammar tremors L Crevalle You want to show you N R I D normal beamed 0 grades 1 then you 1 square cross due to squared must you where is called chi squared with and degrees of freedom and that has another name for the moment at a function for that body that we've done many times before Because of independence and radical distribution of this Their we computer this curious and that's a gamma would like primaries An hour to his Zell file and land a half or so in August is rotisserie source top bearing chapter said Friday