Joint Distribution (1)
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Title 
Joint Distribution (1)

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Part Number 
4

Number of Parts 
16

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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. 
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Publisher 

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Mathematics
Functional (mathematics)
Process (computing)
Spherical cap
Multiplication sign
Open set
Euklidischer Ring
Hydraulic jump
02:09
Functional (mathematics)
Statistics
Sequel
Multiplication sign
1 (number)
Water vapor
Drop (liquid)
Likelihoodratio test
Proper map
Expected value
Exact sequence
Sign (mathematics)
MKS system of units
Spherical cap
Lecture/Conference
Energy level
Analytic continuation
Set theory
Distribution (mathematics)
Process (computing)
Closed set
Normal distribution
Sampling (statistics)
Independence (probability theory)
Mass
Mortality rate
Variable (mathematics)
Sequence
Numerical analysis
Category of being
Arithmetic mean
Factory (trading post)
Figurate number
Wahrscheinlichkeitsfunktion
Spacetime
17:43
Geometry
Entropy
Functional (mathematics)
Divisor
Sequel
Multiplication sign
Decision theory
Parameter (computer programming)
Inequality (mathematics)
Event horizon
Rule of inference
Grothendieck topology
Power (physics)
Lecture/Conference
Different (Kate Ryan album)
Term (mathematics)
Geometric series
Cuboid
Physical law
Series (mathematics)
Conditional probability
Distribution (mathematics)
Process (computing)
Commutator
Infinity
Line (geometry)
Numerical analysis
Probability theory
Normal (geometry)
Right angle
Summierbarkeit
27:31
Existential quantification
Group action
Building
Decision theory
Multiplication sign
Parameter (computer programming)
Ext functor
Grothendieck topology
Fraction (mathematics)
Expected value
Duality (mathematics)
Sign (mathematics)
Positional notation
Spherical cap
Different (Kate Ryan album)
Position operator
Social class
Potenz <Mathematik>
Process (computing)
Gamma function
Moment (mathematics)
Infinity
Orbit
Category of being
Order (biology)
Right angle
Resultant
Directed graph
Unitäre Gruppe
Trail
Functional (mathematics)
Divisor
Event horizon
Frequency
Population density
Lecture/Conference
Term (mathematics)
Wellformed formula
Nichtlineares Gleichungssystem
Analytic continuation
Renewal theory
Set theory
Hydraulic jump
Alpha (investment)
Distribution (mathematics)
Physical law
Calculus
Affine space
Cartesian coordinate system
Numerical analysis
Integration by parts
Charge carrier
Marginal distribution
Maß <Mathematik>
46:26
Trail
Functional (mathematics)
Randomization
Group action
Divisor
State of matter
Multiplication sign
Real number
Archaeological field survey
1 (number)
Inverse element
Mereology
Explosion
Expected value
Mathematics
Population density
Spherical cap
Lecture/Conference
Term (mathematics)
Forest
Operator (mathematics)
Square number
Mathematician
Modulform
Circle
Integer
Associative property
Set theory
Alpha (investment)
Random variable
Distribution (mathematics)
Graph (mathematics)
Matching (graph theory)
Cohen's kappa
Gamma function
Physical law
Infinity
Independence (probability theory)
Variable (mathematics)
Limit (category theory)
Numerical analysis
Category of being
Order (biology)
Right angle
Bijection
Table (information)
Marginal distribution
Statistical mechanics
1:04:39
Statistical hypothesis testing
State of matter
Equaliser (mathematics)
Direction (geometry)
Multiplication sign
Water vapor
Fraction (mathematics)
Derivation (linguistics)
Sign (mathematics)
Mathematics
Spherical cap
Square number
Daylight saving time
Series (mathematics)
Physical system
Potenz <Mathematik>
Logarithm
Sigmaalgebra
Normal distribution
Sampling (statistics)
Nominal number
Degree (graph theory)
Arithmetic mean
Vector space
Uniformer Raum
Order (biology)
Normal (geometry)
Right angle
Figurate number
Thomas Bayes
Point (geometry)
Functional (mathematics)
Statistics
Transformation (genetics)
Inequality (mathematics)
Rule of inference
Event horizon
Element (mathematics)
Prime ideal
Population density
Root
Lecture/Conference
Wellformed formula
Term (mathematics)
Genetic programming
Nichtlineares Gleichungssystem
Immersion (album)
Distribution (mathematics)
Independence (probability theory)
Line (geometry)
Mortality rate
Cartesian coordinate system
Numerical analysis
Universe (mathematics)
Object (grammar)
Table (information)
1:22:09
Statistical hypothesis testing
Building
State of matter
Multiplication sign
Equaliser (mathematics)
Decision theory
Parameter (computer programming)
Grothendieck topology
Explosion
Sieve of Eratosthenes
Different (Kate Ryan album)
Circle
Area
Cohen's kappa
Normal distribution
Staff (military)
Price index
Arithmetic mean
Binomial heap
Normal (geometry)
Right angle
Spacetime
Point (geometry)
Standard error
Functional (mathematics)
Supremum
Divisor
Transformation (genetics)
Characteristic polynomial
Distance
4 (number)
Population density
Lecture/Conference
Term (mathematics)
Operator (mathematics)
Conditional probability
Random variable
Pairwise comparison
Distribution (mathematics)
Weight
Forcing (mathematics)
Independence (probability theory)
Mortality rate
Cartesian coordinate system
Numerical analysis
Radius
Moment <Mathematik>
Table (information)
Wahrscheinlichkeitsfunktion
00:05
That Capital I Alexis is equal to that 0 it relaxes less than 0 It's
00:30
1 minus 3 0 disaster Glaxo's less than 1 that's 1 effects as big a very poor 1 Apt At function looks like this Do That for the 1st time in 0 Up to but not including didactical 0 attempts to 1 At 0 stays there and tell you to 1 minute jumps to 1 and stays there from this scrap debris of the following season The nation's the probability that cap 0 It is the job Eds Euro A job there 0 as 1 might as P Probably Exs 1
02:09
It is a job that 1 in that size he see why this is true this captors every aspect they need to know but discreet Rand Robles is generals are ones Feature they have jumps and between the dumpster flocked called the You look at this function here and You know why Less than X then But And Texas My several why would be the probability that 0 why strictly lesson cap Alexis last So Exs is a young functions on this 2 . space Calmly values Mexicana that's a function to hobby about it take that only 1 have only 1 X may only if died on bike put and what could goes to values be well if I put some number here bigger than 0 it's son of rigor less than 0 for example Of drop picture like just whatsis probably in this case Death Well it's At FedEx minus otherwise we did this on Friday what's at FedEx or my ski with that of why it's thereof It doesn't matter how close to my heart 0 well look that X can be over here as long as acts is near 0 right Wiesner 0 this will be 1 might He by the wide collapsed on water include about the value of X What worries include but probably the next sequel 0 Yeah it's well what is this collapsed to 1 Expos 2 0 on white Collapsed to to the . 0 worker next week as going 2 Possible I use 1 of 0 and the probably being when I'm on my feet and if I put acts over years and YEAR For whatever Max myself for quite a while VAXes 1 is 1 minus 3 1 might as well as he so this would be the job here Which would be key and Nikon let X and get arbitrary close to 1 another in the public axes won his heat Thank you The review found really ready rebels led the whole bunch of other wants back probably all or almost all the ones you will study their discrete from her newly renovated A guy shunned this bird a rural edits distribution function I guess as 1 last thing to say the prob dilly Ness function They end otherwise The Probert X is equal to a value of Alexa 0 And where don't sign values to a probably has functioned to still their 0 and will use abbreviation for probably best functions Key ship But all of a sober till you an array a and a rare low size value IUX success I say want success 0 failure Back final or an array will you do And trials Which are for Nollie quiet day And these are are solid equally likely but the probability and that sought to juniors XL an outcome It is a number of Asses And the outcome of be sequences of of apps you know any 20 counter number of successes that's X and the Probability of any outcome It is CD Following its feet of a number of S's our appeal to the young number messes animator The And then oneliners the number of apps thing so they would be a sequence of S's next Oprah probably measure on the sample space which assigns this amount this probability to a air from 8 years They said Katie busses and then minus a sleepy most people in my and here a binomial ran right will of primer and But But Which will abbreviate binomial and he has properly probably Exs equally came butacaine on my skis and let's I know and revise interpretation of a number of successes in In the trials of An independent Bernoulli trials I'm sorry I forgot some ghetto times an cheesecake Brill a also led to a geometric of he But he or she is is key pumped up
11:33
Forming the Beverly trial set is different from Rory experiment talk on successive failure probably successes he probably The others on my speed on that Intel the 1st success happens at render it will call a geometric venerable last time we said that probability that act case For this friend of variable bidders 0 1 might as he became minus 1 times he has call 1 2 There was probably for a after Grand Prix distribution function here probably cap Alexis But say these figures The necessary Would be a song J. equal 1 decay 1 less to the J minus 1 times he be distributed function from the probably mass function by act Bernoulli also led to suicide All of that 0 4 4 4 4 4 4 or perform rendered said trials but the probability of success depends I Maybe biological examples also the example of recognition of alphaparticles From us Blob of radioactive substance that The probability that acts equally case is approximately equal to land To the K overcame a factorial he's level and a friend a rebel with this Fiji But who is called for somber But Could And then finally The Bernoulli led to center Drive to talk normal distribution of sewer but we want And the proper XRO Uscio number well X is approximately given by this Distribution function and this is a decision for normal ran verbal mean 0 rates 1 0 Bernoulli let all these different and artist will study all them If we spend some time on week that spend little time on continuous I would like to do 1 accommodation with a the geometric before going on to continuous himself continuous means that the distribution function and ruble it has no jobs as Continues on Cell by getting here it back Obtaining acts to be geometric appear so when I say that I don't see what the value of X is I say something about being statistical properties or problems Property and the only trouble circuit originally thought that would be
17:48
Or equivalently its distribution acts as a geometric venerable I'm saying its distribution functions that whatever I identify around rebel axes something like normal I'm saying what the distribution function if I say Exs Bernoulli and saying what the distribution MCX exit geometric and broke with that should say what parameters are
18:18
What that means I don't know what the probability that acts smaller was somebody case sequel bullets information really do a conditional probability the probability that what what's interpretation attacks again it's a trial on which the 1st success appears stores like he is a 6 this is same as rolling it died and tell the first one appears in number roles of takes number rule were numbered rolled on which the first one appeared that the value acts So what's a probability that the 1st success occurs after this trial given that it didn't occur in the 1st and minus 1 what's probably success Success doesn't occur in the 1st and last played minus Charles Taylor's when Charles given that it did not occur in the 1st and Phillips arrears and wife what I'm saying is Contained in this line here acts as a trial which 1st success occurs visitors you bend Trying where we're trying growing diagnostic owing waiting for success you've done it and minus 1 times and you didn't succeed with the probability that If you do it came more times still succeed Africa's probably 90 recall a definition of conditional probability public aid given are 2 events this an event that so look at probably a given be That's a problem a sector be Survived by But the probability of will be right So you do that here the event a event It was just a cup All of you Right So it's both things happen now 1 of those inequalities is structured and the other in the numerator which 1 stricter or which runs gives a smaller events right now because it Acts is bigger than is automatically bigger than that were taking KTB 1 2 3 So that means I just would do what triggered the process out a doesn't adding more to Right now it's computer what's a probability theory and probably Exeter something we know the probably Texas smaller than something sorry but to a distribution function as a storm water if you want to compute that right this 1 might suffer back it's just 3 things that I told you before probably of a copilot is 1 minus probability of 8 8 here is this event X lasted do little acts what's a complement acts figured elects there's a compliment to be a problem And so we can compute these things because what we know that this vision or sold Howard returned this around what would 1 minus as ever Here What's 1 might suffer a case Well what happens they add this up want to infinity Agate Trinity witches 1 1 my KEB the some plus 1 to infinity I do This summer This 1 is some J. closed 0 in friendly 1 minus V J minus 1 times disorders some Jake Cozart decay 1 minus V J minus 1 times This is The decided this last time wisest is wide as this 1 If that's what 1 rise right is the geometric series Box outside to be 1 here that's 1 I started based on what get ordered other way savers is evident Kennedy and decision functions as an is always equal to 1 earlier subtract this from this or you have the terms from Cape us want If OK so sofa end Saving more specific about that I am guy like that with well wearing Joey make it simpler The spice it without using answers While there is a factor that multiply time every term here key right that doesn't site that out and what do we know what series of look like this We do not The sum J. equal 0 2 infinity ardor Vijay was 1 over 1 are as long as have Is less than 1 And here we're 1 my speed retains a whatsoever to 1 most is lesson 1 The difference between this and this is what Well August 1 differences here's a day and there's a day Myers rivaling that's about we could just change variables right So 1st well maybe we do that sex but that was the difference they restarted Cape us 1 here we start at 0 so we'd like to start at 0 and have a J O maybe commute to tweak factor out What's a firstterm here if they escape us 1 what appears be chased us 1 workers here right This is Kate Plus 1 because of the 1st 2 years 1 might lead to the case all the others will have higher powers of 1 mind Diesel oil factor out 1 might be OK Bill occurred every term soapy 1 lies Peter K. some people something to infinity 1 mostly to be quite a now that we've taking out there 1 might be the case we start with what
27:35
All 1 UK was here pulled out so what's left for the 1st time when carriers budget escapist 1 factor as this becomes 1 what's next term would take us to get on my speed to the wall wonder what's next 1 where to Where we get 1 0 past 1 must 1st pass from might be squared unless you know is we get some day was owed affinity 1 last Tuesday And this would evaluate using the back of the year be times when Lansky silicate times 1 0 or 1 minus 1 Myers p And 1 might as well as he is key From 10 years of fee Listen this canceled leading 1 Myers Peter K. sought summarize what readers to the probably X is bigger than K Origin enter granted right parameter he is 1 might be the case Fire so ordered we want a computer compute this ratio to redo it yes we Can we Up Know what things like also like a more things like that look quite so it's fiery back at all Period 1 mice Peter what are they never yet and this is 1 less Peter J But Which was the probably of wake tryouts are you start waving Schumacher probability that you don't get a success in the 1st A trial So the probably have to wait keyboard trials even if you're gone even if you've gone in minus 1 trousers the same old you're starting from the beginning So if you're a Rowley a you've of a thousand times you get 1 you didn't get a 1 hour doesn't mean that you're do they should be more likely to get 1 next door in the next few trust not you're not do it's just like you're starting again as you have role that I think sometimes you hear people say that's In the lottery some numbers be higher because I'm here for a while well that mean there it appears not Keep this lesson mine rearing us remember that and does it make sets to life the quieter diarrhea going with not with Memory no way of controlling outcomes is that a do about Frank Orbit So now Zgoda continuous China rare Alsace again I think I did a mania continuous should 1st alright of the case that means distribution functions it to use function of X decision margins I did earlier were all had But spots interspersed jumps interspersed 1st class years continuous increase those making these functions can have black spots but no jobs We did 1 last time uniform ran a rural area for what is called exponential runnerup with parameter lab he From my Fabio more care fall The Excon take on negative values probably cap Alexis negative 0 the probability assassin Alexis like this that this is the case war the probability recap Alexa Vere lexical As But Well what's a complement of this event Small If your life is complement of this event Catholics Bill Lexus complement of tablets lack of this probabilities oneliners that probably what's oneliners is probably right you might so that probably dies off exponentially fast and relaxed But they know sometimes East functions are different so will miss a What Severo of this function would be And the EU the demise slammed Rex positive and 0 Brecht's and it's a not French law Then But we call this so user given nod Notation little left that's called the density and what's a Dreier function That is given by being Inter 0 calculus member the welfare of targets be integrated drew revoke want him when you get you get the function back again all that time laugh then will left from YTX skiers ever Cap effort attacks my wife and these are distribution functions and this But that they forgive
37:06
This formula might be 1 of the top Robert probability like this if you know the distribution functions take a difference of the disputed by Nova density unitary cadets from White Seoul This is where rebels exponential and arose from there are used to model waiting times at the time you wait a time you wait for our current for you to start up After like turned red to green Time to wait for a phone call time for lightning strike time Someone Customer 1st customer come into a store of kinds of things like that Time you wait for like burnout time you wait until the 1st edition of from For once 1 is admitted the tiny wait till next Still many mania Applications of this and they have also The same peculiar property here that She measure venerable had And that is what if you're Gerberding this in terms of like Bob's annexes is the time when the light bulb burns out Michael been To keep track of Holliston burning When I 1st moment abroad Burnedout Capital says that this is the event that the light bulb has not burned not by time t still wear burns later than what the probability that it lasts longer than s past moments given that its Lassiter key moments says Probably Last moments words it forgets that it's been braver tee time units are ready in its probabilistic behavior result is you just wouldn't check to see that stroke I mean it this equation is true know that's definitely true but light bulbs if that is true love Light bulbs I think I'm pretty big My home I've always going to the grass unilateral burning in light of lender must be large like all buying but let's take soccer we do this Was Definition Nichelle Bob building came ARS Antioch posit didn't say that But let me say now that means as fast he's bigger she and needs at this event has no effect because of Exeter automatically bigger than tea and are doing order completely numerator denominator or what What verbal this Businesses Accidental Mandela how serious probably vessels bigger than the site would be you mines Banda times at nite so what's acts numerator as fast he Pearcy demise slander and that utilize lambaste which is in fact the probably cap Exs So is Of a renewal property if something's been going on for teatime units and nothing's happened yet probably have to wait as more time saying that you just started Wait for the event at times 0 wait as plant a prop I ran rail they were they it 2 0 ext edulis called the young gamma rays pursues a gamma function It is interesting function if using functions can be interesting and this is 1 of them and this is for Alpha welldefined for Alpha bigger 0 because when after 0 1 over acts years and nearly origin that would not have it in my head in his own itself as Biggins But Tom Dugan integrators by parts The bigger signed there again and that would say the gamma Alpha his what new times each of the 8 IOA between 0 and intraday my 0 From 0 threatening VDU what as a minus sign my side the past year the acts That's the D you is a minus 1 put that out for Velva from front tonight expiry of minus 2 The 1st thing here is what an eternity it's 0 because of 0 0 because of the sky was firmer 0 so we offer ways to euro from 0 infinity next week right offline steward of the reverse way about maybe where else minus 1 minus 1 Because y The former gamma function of number minus wanted exporters were back Press Arroyo a number minus 1 in export practice so what is the goal here But Gamma alpha Midas what But 0 8 source as This no Idaho I Ralph Meister itself 1 here I was was 1 of 4 is a safe secure racist But she with And what scam 1 When wanders off Forex Cicero from 0 infinity even less XTX What's that Well we look back to be exponential ran Roble that the density of exponential Akram rely people want and asked be what I think you all on their minds you might expect from gals lawyers 1 of these 2 together
46:28
Applied it gamma of integer end is what and my is 1 factor real way of representing the factorial function wiser Why is it Why is it would end here bloody and my onetime gamut mice what repeat this with Kevin rise 1 galvanize wonders my 2 times down miners to be going down until we get to 1 want what they saw this as if I were a here this thing would be And my artwork 1 Leicester Well they shunned that the but strike give this before the break Now we got a computer visit land is want so that suggest what operation airport We do try to get the variable immigration here change variables Flanders 1 we know this is their valve but why people to plan acts what's DY indicates it slammed the DX think how would this change a variable affected limits of immigration when x 0 which lies 0 when Exs infinity wires and that doesn't change we get our you demise you're scared for DX we put in landed the minus 1 D Y And now for acts we put in Why overland Tracks we wide over land with y overland We get wider do they offer my Aswan what are lender would we get its wife all Orlando sweet landed at 0 1 minus offer Not erase this and this gives landed the myself and what's what's is enrollment at gamma alpha so this is equal to gamma of Alpha Orlando to lay off right and that says That following the density of just made is not negative and integrates 2 1 and like embattled talk about 30 venerable so that density the circle of gamma and turtles and these muddled things were yet law Wake Forest's successor of success tax like maybe you wait fell 5 light bulbs were not part of my public tell burns out another 1 this identical Widowed burns out 3rd 1 which burns for the because resort when when the 5th 1 burns out that would be a gamma honorary or mentioned waiting at a traffic light the light turns red to green nearer the 5th car back the waiting time for the 1st part of take office probably exponential after that 1 takes off another exponential wanted expense of some of these experts run rebels of gamma of waiting time problems are modeled using gamma rays of a break back tho I don't care But The kid or downright a rural censored by that I will workers sets of Davao by Peter lives the form is rooted in the British may drop also rich at a lower world price 0 2 4 4 4 feet deep deep deep Each bulls This bill of rights and death was fast said The squares It's not No yet but it's not the numbers The botulism 1st where single where they are The Made using Oregon Yeah The rest of the year And Graf this function More as Rita 4 The state of things that next year's 1 or I wary You were or where Raw text this is Yeah The better Respected you need a 0 centered over here Here A year and Mark Knowles choose to currency injury for EU and Ryan year Alice Just like list with petitions on press as a great country was a surveyor service arrange on back is also want you Introduce that Density and so a graph there on that and Mark got pass around here is on the front I'm waiting for the day when they have some pretty gives was a great match their mathematicians the things statistical mechanics they will put me under 100 dollars will someday You're a run for president Mark debut every great idea of or so that survey category over for a catalog random variables
56:12
With various distributions on at times we do manipulations on rebels because we don't like the ones we started with so we try transformed them in some way For how we do it situation purposes under our tables they do list Of independent copies of uniformly surrender so there be tables the numbers There's a number it's picked at random between 0 1 Next 1 neither 1 picked at random between their want you can use these tools Dodd giving effect are copies of a friend of rebels on others distribution so we take functions Aretina reports for a couple of reasons but with But but All 3 of They also will start around a rare will has given distribution function capital could be any 1 of the ones we've written down before and we take a function of that render Let's say increasing margins lower are decreasing profit also work but I want the function of a onetoone so maybe I should say strictly want what makes So it's you strictly increasing or could be strictly decreasing and that we take GUX what's in this region functional GOX to ask other random rebel function Aranda Ruiz a random variable and what's the distribution function around the world defined fight ahead of the insist that the problem is that ran a rebel smaller elects its this function of collects with strike The computer terms of capital L Where's Kappa capelan is probably Cadillacs England's them expresses in terms of capital Exs lasted some Well she is strictly increasing so it's onetoone it has an adverse President burst and numerous would be increased or decreased to use increasing whereby its inverse increasing also sought by in burst both sides of this numbers less that 1 of our whereby Jean merciless number Be that poverty in of that never never words he inverse will Would preserve this order of strictly increasing If I obliging immersed to hear what I get Capital acts and then never be less recorded Jean worse off little extra but this is the 1st functioning capital F evaluated Yeah I think so that would be a distribution function for JOX FS Jia Mercer Let's example Exposed But axis It is uniformly asserted on from 0 1 who She had with with or But was But we When I say where the distribution out of what is the distribution but association breakdown probably Geof exercise Alexis and try to do that so let's Rick by ourselves what this means that cap Alexis uniformly restaurateur Nunavut 0 1 this means It 0 all 0 thank Now As a graph of capital At the history disputes at the yeah ever means making a point at random from your user 1 and there's no bias A particular place that will likely come from 1 side is near OK so that strike distribution function for G of capital Where that's key or 4 0 by around maybe I should say without the is decreasing
1:04:50
We want change here But Jeter's would then be decreasing system be reversed For of the And that would be 1 Out of the Think of what has that so is as much an increasing acts goes from where where Brazilian capped values of evaporite between 0 and 1 0 0 or of me at x between 0 1 here is a sergeant increasing water my sex increasing decreasing L elements Mexico might increase decrees but that the line white mice square that goes closed down right but all 1 my sex increase in secret decrees brought a lot of 1 sex logs increasing function agrees and function of a decrease in Well figure orders may wait a secularist what the That And now yellow my assigned here and when you take a above of his party a minus sign also so they would cancel giving something positive so is increasing is increasing so we do apply that formula for what seer University But 2 Team for July Body of finding versus assault for access so as not byebye Icelander case there's achievers They will be probably cap acts Aegean GM burst That's Sieverson wife G in bursts of acts and immersive axis 1 legacy the mightiest slammed acts and our where is this number 1 minus the Texas X is bigger Aguilar a 0 A but Some but This summer's between 0 So it follows an ear So is just Capital after left evaluated at 1 might might slammed decks that sorry rid But it is safe this is why was FOY outside of that function that why wiring of would put this in here but said that its that value what distribution functions that bears the exponential So I start with the uniform rent rebel leader will consider 1 and I take this function of it I get didn't X venture ran a rare sight mentioned that their tables Lone independent copies of samples of uniform regular also offered you get samples of exponential and that justify this function of the euro will generate a list of independent and rebels or examples of innovative and rules that have Accidentally was transforms and rebels of 1 distribution to render rules face another and that's to another example of daylight right this symbol here you'll see the slot Was axes it has a normal distribution of immune various cigar square and I say Why is equal a X was being what's the distribution of why with So what does it mean when they're asked What is this why means you should try a free of what the distribution function status is right the problem wise lacks thinking computer so you're BEST plant of what is Start but this is given some terms as something that's no But what of of but that But Now Weger subtract from both sides these 2 inequalities Arco but not next step My requires amazing the positive or negative which do you prefer on that's a good outlook say if they Esparza we divide will sides by a Bay was negative what would happen ridges right because but the thing at the point is that this inequality because of this event and this event are the same Probabilities were may think how could now we know what that s that's 1 square of I think squared girl hurled from minus infinitely X minus 8 Overby the miners why my new squared over squared Lockyer remember all that well
1:13:36
That receive is so often that you'll wake up in the middle light ahead of you collapsing European a lot for your all Aso that's this vision function of white What's the density of why the density of a distribution function as its derivatives let's take the derivative densely wife ahead I differently than interval especially you have a hero from my innocence for nearly 2 hours 8 of acts the of why why what's the guru of the suspect acts Veronica was its age of exercise state crime of acts that You're right thank you I told him all my vertical version of that Safin again OK so that backs so it is evaluated that they have 8 times 8 per cent 8 vectors explains puree selects 8 prime That's H excise pureed peas priority 1 over 8 either for a little cap light I here Opposed further sir A I like that all that well But so complicated Doesn't it So it's priced quite a bit Thank for all But 80 inside here and that means it becomes a script and then because I don't have bathrooms right next Too That that And then known here I What Let's see combining these 2 guys and this was a fraction of armor add 2 things I have a common nominator so the number should be the become new aid over there and I'll have something over 80 here right but it's square So workers we put that We reported down here would dance and nobody left up here this doesn't have to be changed give X lesbian but then what's left here a America is a new over a combined ATX players USA And we're right this way but thank Crew Series of river that no objections to see wire But OK so what we have That's normal with what's what's the new mule This is normal density this becomes a meal B plus new and that new banks becomes the new singers where becomes famous Bird a script So if we start with The normal means new racing history can we get this transformation which I race to a normal means 0 that's what a Busby we got to this we arrive at normal means 0 grants want to read it the new nudity 0 1 of the Rio from normal means in square to normal means progress what we that always do solve the equation plus 18 you is 0 semis Verde's for equal 1 so what a friendly or 281 over 1 overhang Observe what a city or And new bay I'm Zogby should be But My AS Muir said Then they go from a remote I bought a net be there there will be other ways we go backwards so they start with the normal mean 0 rates 1 can we get to to a normal you squared 2 I would go from here to here said means We start roses 1 0 and this is what I want them to Up with 1 over square root to hide a squared exponential with lined up with what X minus this is 0 so it might be squared over to a square Soccer we get Here And Sigma here the state be equal Mueller and Sick of that is that if exodus Values of faxes Direct normal with mean 0 race want then New acts sorry stigma axis must view is normal with mean new hundreds things where it is legal for normal means room rates went to a normal rates so this is handy because in lot of statistical tests like what is being done to your degree in math statistics and hired by who wants Eminem baby or maybe you're I by necessary make
1:22:44
Drive torque but dropped by these truck chips chocolate chips on all have the same way about their weight of a chocolate chip is a random variable and rates have a normal distribution with some mean new some racing's courteous was Find out what is the use things like this for you try to goal from Normal with 0 rates onto to whatever this means weights and rates for the top My user stressed that also there are tables for normal or a number of those things over back Nevada book the table for distribution function of Story so editors are off the back of the book you'll find Values this function attacks for a lot of different exits and it should be table which um yet able to hunt in my boulders and lots of Appendix B Table 2 ill health budget numbers in and right Here's point 4 years . 0 4 sup I go across Europe . 4 4 this numbers are probably Normal rent approval with means a was less . 6 7 0 0 exert that probably right rebel with me 0 rates 1 is a 0 . 4 4 . 6 7 0 0 now if I wanna know a similar probably for this and rebel fighters transformation to a inoperable means rest 1 Me or I might go back so this helps to read off a disk Distribution function for the scanner and rebels from a distance liberal and up later on in the statistical testing are the course will be doing that What day so that's At the end of chapter through tho it's chapter 3 undone Distributions times so comparisons are made for example my oldest son is true size 3 sizes bigger than my size 14 and so that's a random might choose size Renner ruled by you might look at the size of a father and the size of his son these to render it will they be related somehow would expect a Iittle yellow mean for example of son with a size 9 should probably not but gumming sons stool size would be related to his use sites or go the other way who knows whom Messi was soccer player these a soccer players were probably the best player in the world and in factor is spotted him when he was a young boy It was a highly skilled but really small fact they did growth from what pretty still small but expected Sunday of small These are examples of peers around the rebels 2 sides of a father and son or hiding items which are correlated They have some kind of Joint Characteristics Joint distribution of Chapter 3 is on joint to wrecked an error many examples of random variables that come and Paris the drug in Siletz Do a couple of times Maybe there is simple examples of involved but we are ready let's say we take 4 4 4 4 4 4 of or we selected No. Renault from 0 1 At the end of Ripper farm and independent for newly trials Also but for both of my own but but we're all but 4 were problematic view success she was up 0 He was a problem that where fewer than normal boiling case successes and that We knew we picked is a you As is called Joint Distribution of X And you it performs some operations summits were 1st taking a number and that becomes our probability of success and they would probably successfully generator around rebel which is the number of successes in Fernley Charles with that problem Now this is a little ambitious to do a 1st time let's try something Louise you're following that's 80 of Uriel fear of trainees your competition 1st but say they saw the probability that you is a 4th is equal the probability that viewers Reports What we're and rebel takes to values 1 force or threefourths
1:30:55
Yeah with equal problem Harvey do that well toss a coin his thumbs to set you equal 4th Thumbsup tales except for ballots fighters we could look at Mount fact BP PMF a beta jointly I think up for what Ted eyes and Janeva we have consider here This this 1 the Swan so start with this 1 so what we have here on Hi A wish write this in terms of conditional probabilities of like that right now dear lady was a 4th what vision acts have Binomial never had Oh I'm sorry out a areas and make it so given you was a afforded what this region is access Says that it would be with the same kind of thing it's binomial with parameter 1 for binomial proper for silver Societe bench escape 1 4th of the case Threefourths to and my escape times at after afterward from here End of although hero right probably is equal the case and threefourths B. What do the same thing as the public axis equally case giving you his 3 4 times probably use threefourths All It would be this is now Binomial with parameters and an eagle threefourths of the end Through state Threefourths of decaying 1 forces 1 To the and minus cake 4 times at God I I saw generally we say But Of The pair Brenner rebels has advised decision on Capra F if the probably caballus single elects Kappa wisest NY is F of exwife Chase This would look like the best years Ex BY visit point exwife at par building here is probably the prepare exwife Paulson that region At that but but of all of us all but but but but thank a sieve continues Tranter emulsify But at the end of the 3rd Exwife is joined density in the left if the probably lighter rejoined the scan begun by integrating a function at so Give 1 last example of advancing on staff at 4 OK so deal with this means a key indicator of our something space the functions But this wonder if this condition satisfied and 0 that's not But but but but but but but But but but but but but but but but of but So this density is 1 times is number 1 Expert was wise resources gold bars where and it's 0 when its purpose was Spurs bigger cars were so where is this In Edwards words as function differ from 0 inside the circles and the Georgia radius R and wants its value on that or its 1 over these area the circle of pair random variables of joint is said to be selected at random from me from discoveries are is uniformly distributed on of our circle races are or more with that