Random Variables
Formal Metadata
Title 
Random Variables

Title of Series  
Part Number 
3

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
Metre
Greatest element
Sequel
Closed set
Multiplication sign
Sheaf (mathematics)
Water vapor
Open set
Event horizon
Grothendieck topology
Product (business)
Explosion
Ranking
Circle
Körper <Algebra>
Set theory
Physical system
Closed set
Independence (probability theory)
Mortality rate
Open set
Numerical analysis
Mathematics
Right angle
Maß <Mathematik>
07:07
Beat (acoustics)
Randomization
Functional (mathematics)
Multiplication sign
Connectivity (graph theory)
Real number
Sampling (statistics)
Physicalism
Parameter (computer programming)
Line (geometry)
Variable (mathematics)
Event horizon
Sequence
Numerical analysis
Product (business)
Probability theory
Explosion
Genetic programming
Spacetime
Random variable
14:10
Point (geometry)
Functional (mathematics)
Decision theory
Event horizon
Hand fan
Subset
Different (Kate Ryan album)
Modulform
Lie group
Analytic continuation
Arc (geometry)
Set theory
Random variable
Social class
Distribution (mathematics)
Sampling (statistics)
Counting
Limit (category theory)
Sequence
Numerical analysis
Category of being
Arithmetic mean
Right angle
Freezing
Spacetime
22:34
Point (geometry)
Functional (mathematics)
Group action
Observational study
Sequel
Length
Decision theory
Multiplication sign
Equaliser (mathematics)
Connectivity (graph theory)
1 (number)
Chaos (cosmogony)
Parameter (computer programming)
Rule of inference
Event horizon
Food energy
Grothendieck topology
19 (number)
Cumulant
Spherical cap
Causality
Term (mathematics)
Cuboid
Circle
Integer
Analytic continuation
Hydraulic jump
Position operator
Chisquared distribution
Distribution (mathematics)
Process (computing)
Graph (mathematics)
Theory of relativity
Interior (topology)
Sampling (statistics)
Independence (probability theory)
Line (geometry)
Sequence
Numerical analysis
Category of being
Curvature
Binomial heap
Factory (trading post)
Order (biology)
Right angle
Wahrscheinlichkeitsfunktion
Spacetime
Directed graph
42:24
Geometry
Free group
Beat (acoustics)
Sequel
Divisor
LAN party
Multiplication sign
Range (statistics)
Variable (mathematics)
Sequence
Numerical analysis
2 (number)
Network topology
Geometric series
Right angle
Series (mathematics)
Summierbarkeit
Game theory
Nearring
Set theory
52:39
Point (geometry)
Process (computing)
Multiplication sign
Real number
Dreizehn
Mereology
Event horizon
Expected value
Term (mathematics)
Natural number
Cuboid
Integer
Position operator
Hydraulic jump
Area
Noise (electronics)
Distribution (mathematics)
Theory of relativity
Process (computing)
Block (periodic table)
Chemical equation
Infinity
Binomial distribution
Exponential function
Calculus
Limit (category theory)
Sequence
Numerical analysis
Curvature
Binomial heap
Factory (trading post)
Thermal radiation
Order (biology)
Vertex (graph theory)
Right angle
Summierbarkeit
Figurate number
Table (information)
Family
Maß <Mathematik>
1:07:12
Standard error
Group action
Free group
Divisor
State of matter
Multiplication sign
Direction (geometry)
Decision theory
Routing
Mereology
Rule of inference
Event horizon
Explosion
Population density
Spherical cap
Oval
Lie group
Analytic continuation
Area
Model theory
Independence (probability theory)
Staff (military)
Limit (category theory)
Lace
Cartesian coordinate system
Numerical analysis
Network topology
Object (grammar)
Arithmetic progression
Resultant
1:21:25
Functional (mathematics)
Density functional theory
Randomization
Identifiability
Decision theory
Parameter (computer programming)
Event horizon
Rule of inference
Expected value
Population density
Spherical cap
Arithmetic mean
Lecture/Conference
Term (mathematics)
Area
Graph (mathematics)
Theory of relativity
Concentric
Line (geometry)
Rectangle
Variable (mathematics)
Numerical analysis
Category of being
Figurate number
Probability density function
1:31:25
Point (geometry)
Functional (mathematics)
Group action
Divisor
Multiplication sign
Mereology
Explosion
Mathematics
Centralizer and normalizer
Sign (mathematics)
Population density
Manysorted logic
Root
Lecture/Conference
Term (mathematics)
Square number
Arrow of time
Position operator
Area
Addition
Distribution (mathematics)
Gradient
Mortality rate
Twodimensional space
Calculus
Variable (mathematics)
Limit (category theory)
Numerical analysis
Substitute good
Mathematical singularity
Family
Resultant
Relief
1:41:25
Open set
00:05
Still every questions on doing homework Material You do all the more problems Rate Botswana which was lost on thing is still are what numbers but what number 4 34 OK so on and problems only 4 I think you have to have a maybe like Food problem of Ozal circles is being Fossett or baby wipes their opened with a probability Probably all you need is 1 pass from the left side of the right side became so on But The church was From 74 Argus your realized of each unit fails in the heavily with probability The The question is was probably following system works so I think that means the being down um pipes or something There have been opened at the site That's so you pop watering year mark their meters 1 opening To get through So what's a probability that its operational or water it through this 1 is almost probably 1 be dozens or more probably oneliners from probably 1 They might ask what the probability that Everyone might probability that it works For I hawkers The Well from Paul free these passengers must be closed or so of 3 things must happen the top Middle bottom must all be close what's of And their independent So it's problem with Serbia problem with Koppers closed funds probably Miller's closed 4 times problem a bottomless cost and what's the reason for that quiet quiet the sequel to that Krebs Right Well of course we might That Independents or leasing of a circus urine and that was Partly that they also fail at the intersection of this fails the fills the sales probably intersection of independent events is a product of their ability so it's probably Tapas close romp that Squared is not only 1 of those The report Well public this Which is easier to deal the probably tapas closer probably tops How probably field Both things have your rank what's probably the top open So I'd be a probably tapas closed 1 by a set of 3 1 minus 1 minus D squared and what's probably most close offers only 1 Foster wherever there and that would be probability He's right and then But a lot of Miklos outside the top so square at the ritzy regulates units In the same as the start The disturbance 1st OK so right here Is Maybe just to be excruciating details Over 4 Or the I don't know if I will for What's this event section of your Iraq so that's that's independence
07:27
It is a statement that will probably be intersection is the product of the problem Case that's overuse Here here the ball I have book 8 at the time of what random variables as a way to quantify 80 of events that we model using probability theory of productive but please Signed values to so if you Toss a coin Colombia had details assign a number to that usually unless you're maybe gambling and if you win a dowry time comes up and lose retirement tale comes up you might think of looking at this sample space and finding a function from the sample space in the real line Such The value of having its is 1 like this function tales is minus 1 represent a simple 1 time trial gambling event where you with a . comes up in the dark of this kind of functions from a sample space to realign scholar random variable Probably isn't a real old subject this was his name was chosen in the 20th century a happen to meet them The guy was involved in the beating this comically random variable he was having an argument with another person of probability theory 2 people were do and willing seller I knew him he told me that he thought they should be called chance variables and he thought They should be called random variables they gave each other their reasons and was convinced by the other 1 I decided by Carson Court E. a feller want so to extend that there you might think you having no longer a game With over 4 And as long as there may be all sequences of and Whose components are either a church She each but could put at it all George to symbols It also think of these symbols is being replaced being replaced by NT being replaced by F P And this comes into a lot of physical problems and analyzing you activists of medicine you minister met perform experiments were you give up certain medications to and patient and reporter wrote the medication succeeds or fails Treating procuring sewer around around rebel here might be the number of 8 acidic currency number pets or a few replace 8 by AS antibiotic as big a number of successes and end trials Are they sell generally work 4 4 4 Arender variables a function on a sample space With real values friend array will it is a function of blood sample space upon
14:36
If The photo plant case so there is a probability on the sample space ever look at me probability of all counts for which the granary will has a value last AOX Robert right that's out as a beaver probably of the event it's a set of all comes address Elvis The sample space America you more details Probably the set of major capital such that the value the functions around rebel at less that a writing all this out Others right Capital last So the 2 examples may in the 2nd examples of you probability of a set of sequences of IBM such that number of successes some number so acts as a function of Probabilities are always between what 2 numbers probabilities or what their 1 this function Kapoor Lawyers in between 0 1 At pulled up he If Alexis less 0 police saying mud The role of the size of these that But This is not can repeat that Where lawmakers recap Alexa makers us lying in the worst Lester attack which is harder be than niner less intense Most Being than restriction right being last nite is more restrictive than being less than 10 of this It is a subset This at a Nov . 1 7 subSaharan other whereby probabilities That Probably Weaver said be be smaller than that prairie at all so of exercise so why capital ever VAXes last Enrico through Kapoor whatever means Kabir It is a lie 90 freezing function The thought of what it was What But But some do agreed that increasing means that you credit quality might also say it's an increasing function but not strictly not necessarily strictly increased Search for but but he will But it's What a think this limit would be when would exists This summer's always bigger than their equal to 0 Also as sex gets smaller and smaller this number this gets smaller by that property so this is Decreasing its bonded both as something creative urges to viable by what 0 He replaces by My Freddy what would be the problem our numbers less than mine but they might 0 Texas summit as early as 11 sex goes surplus and very form as what OK in various 1 other property is that the right For continuous from all 4 OK so 0 5 But for OK so this is the function their captors already statistical or proboscis Coccyzus Capel exercise Delissaville information about their honorable acts as a probably distribution Virender rebels have different distribution function and will identify random variables by their decision functions will be of names distributions will say save that they had surrendered rebels has made like normal or uniform or ports on
22:27
So low Let's see 1st maybe a point out their troop major classes
22:40
Right hurdles See Discrete and continuous Exorcist venerable effects Distribution functions which up T Docket 4 of say that way has jumps interrupted by flat spots so it's flat And jumps up black and jumps out And don't So the graph Have to 0 and then jumps up fight for while their jumps up But for world Jumps up Here's a 1 black and jumps up every jobs to 1 messes tank III of the graph of something like that who indiscriminately 0 Acts is it Contiguous Gennaro Or if its distribution function as continuous or said a graph of that decision function Would have books on like this So that's the decision function like this jumps in Arapiraca hotspots recall a discreet manner revelers because decision function here the decision but overran a rare books like this Colorado rare will continue continuous or discrete refers to properties of the distribution function But so did examples of the sweet red arose out of my way I book would have would call distribution costs cumulative distribution of I I will often dropped the word Q Just used s may reveal CDs Say So saw for all over the place So it's 1st examine examples of how to ski random rural most basic example scholar Bernoulli this region or ran a rare All of the So date some number between them 0 1 Abizaid the sample spaces are what we got is except that The probability that parenteral is 0 will be 1 might be a probably it's 1 is of having a value of 1 further and rules A success and 1 might he 0 as being a failure be distribution function will look like this Opec Show It's For all of us Malaxis Aubrey yeah What's a probability Myron Avery blow this study what values can there and rule have 0 or 1 that exhaust every day because what 1 might keep us 1 the union of axes 0 and Acts is 1 has probably 1 destroying probability that cap Alexis who left of anything over here 0 cat The distribution function 0 until I get to 0 In jobs evaluate 0 is Westley so I jump up to 1 might be The circle Line is an empty and I jumped to 1 minus key probably Exs 0 North taxes in years but the Lexus here now What's probably cap Alexis Lester that what values does ran rebel take on positive probability 0 1 which ones are below here only 0 Republic apparatus last Pfizer Robert Kaplowitz is equal to 0 so that by this vision function will I change Intel 1 Soviet 1 and then will jump to 1 I'll have a jump of this size 4 Because think about the let's Oregon now What's a probably at the ran a rare will cap acts with this prescription smaller this thought well probably the cap boxes busses 1 because order to buy circuit that 0 0 4 1 in their both less than that The value of this function as 1 does the distribution function or CDF cumulative function for the Bernoulli and Or so that already Avery Bernoulli ran a rebel we mean that it satisfies us So We describe yearend rebel terms of its probabilistic property or in terms of its distribution and the next most basic 1 Busy binomial ran a rebel At in this example of book End independent But But Bernoulli trials are performed
32:31
Ii and experiment Louis Rios means new approved by Willie key for our success 1 might video failure and X is number of successes It and trials But what As the number assigned to sequences of S's apps Sequences of length and sold out WBO and Bernoulli trials where you Devi their success Failure How would recorded recorded Communist successor after every time you failure so you'd have a samples would be be sequences of light and whose components are either an hour and acts would just be a number of asses appearance So what possible values can access for counting successes and trials might have 0 1 2 up to an actual be some number between 0 and some integer between 0 and an inclusive What's the probability VAXes equal the case work is a number between laser between 0 and what Probably of OK successes if you perform experiments in independently and times and probably success each time is well are having ends spaces here and we have to to fill those spaces with asses and that's comedy asses case only apps and my escape Is a problem where the young probably Outcome with them I guess equal but what's the probability of getting us this particular sequence here maybe Shares decaying fat and from that point on Napster probably got out bullets Probably successive 1st time It was probably the last 2 times in a row squared The problem S times rugby PUK Followed by probably getting failures Russert 1 my speedily King In my right and not as a matter that they occurred consecutively whereby the same number wrestlers Sampson distributor manager Mike what would saying So far all the sequences With chaos is an end minus chaos have probably Katie 1 my speed and my problem that event tax equal case would just be that probably of 1 particular 1 times the number of sequences of land and asses and skating Acts so we know that we multiply this number of times the number of sequences of like and they have a asses and and landscape apps Parmentier are there like army sequences are chaos and unless ordered to leave depict places for the essence Escape Simba because if they positions for the gasses the rest get apps and this is for Katie Boulder 0 1 up to end a year honorable there is This Properties called the binomial Rand rebel end There are some parameters here Really a binomial energy and his number trials is covered success very useful and OK now in both these days is a we start out with This function Probably the sequel to arrives as opposed to the CDR this function is called me PMF probably mass function for in this case helping you get from probably functions to be distribution of wealth from twoyear was 0 they're jumped at jump size equal to be valued PMS Here and has another jump here because their job sightseers equal Valued given that 1 euro review sample over why lest Maybe I should take a lesson in theaters Where does all say some or wireless backs POY where It is probably tablets is equal industry gonna rebels a severe said Where this 0 similarly over here if we add up the the values of is probably mass function where The values a photo of the value of X policy tank in Soviet days is either 0 or some 9 0 value and it will only be nonzero where X can actually occur with probable cause it probably was relation generally between CDs and a and they know they came up big The CDF by the summit we Carter draw The source over John Fernand Bernoulli a rare will observe binomial being committed disused function we 0 until you get 2 0 they'll ever jump and dump size will be POV 1 probably that Of 0 probably 0 which began to 0 Which is 1 Peter 0 is why someone might to be ends a really small talk as big as 1 might and this flaps until you get to 1 And then I would jump size he won so this job sites here is near 0 and another jump here And a factory at 2 2 and the jump sites here is 1 Dollar jump that To be flat 3 and the dump site that too is key to and every time I come across in this case the venerable has only integer values every time you need an integer of a job and jump size will be the value of the and Dr. and it finally when you get to end after added by the function is what there no more jobs At
42:32
But except for free But the geometric Darryl Which can over 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 or it was it was as if was It was And there will XBU venerable which is the number of the trial on which the 1st so it be something like this to to toss a coin Intel to get ahead that occurred on trial number 3 tours of the sequence still Taylor said X of that sequence 3 4yearold I can tell you treaty That occurred on trial number 7 next would be 7 so in other words of 2 4 5 4 6 1 3 acts of that sequences being or you have children until you get a girl Bankers 1st time than the 1st success occurs on trial want I think I misspelled here I think is are they engineers here risen idea For ability for free Baker backward Auto crept in a so far Professor missiles awarded on a neck brace for a while OK so what kind of values can have
45:23
Well when Its success might have been the 1st time you try me or the 2nd or 3rd for the Soviet acts of violence Sure Or But keeps Goya right Freddy value in their what's probably that X is equal OK he was probably the 1st success occurs on the case file Hawkeye welcomed where terror for this to be true rerecording outcomes what I get here Earlier failure failure earlier success What's the probability of sequence bodies are independent trials multiply the probabilities of individual comes probably years 1 1 might be 1 might be what Sami will my skis we have a nice 1 and then the 1 might be the case buyers 1 He wears as for Cable 1 2 3 etc Right Um But at or what that Want to this summer beat probably Texas finite 1 so this summer better be 1 is at 1 I don't know how but all but 4 what went on but was so I did too is a set hairy here A factor of the because he doesn't depend on McCain on something on Sunday The carrot doesn't depend on December returned from front and I change variables And I came eyes when retain instead of this suit came ice while Everton J and after just 3 months of the range and I start over cable 1 when 1 J will be 0 and what's a sequel to remember this series bars lesson 1 this is finite And what the series called Geometric series that's why we use the word geometric values or geometric somewhere out over Sosebee This is 1 over 1 minus We all know what in book but which is what And before the break but do 1 more I think this is the settlers called negative finals all negative binomial related to match But also for all the tree This I will perform in a trials and tell Va Successes occur Oh it's something like the gym and issued free throws entirely made temperature and I see people smiling because they think I would take me a long time and that Are you might think of some air fare Professional baseball players and real could take on the infinitely They not so acts will be the number the trial would see our success occur this is asking how late trials may have to do before I got my our success only free throws and frontal I've made 10 And probably successor will be key More and arrogant 1 might let's try write Dundee TMF for for our our new ran Rebel XT take I value and what's that now what's the least number Charles You could performing and get our success near Somerset 5 or a could take forever 18 cadre large numbers of God in Kerala now was a public that it took trials to get our successes but chartered are picture of 1 thing I know overture We are success occurred on trial case asked those here
52:41
At Nowhere else We have to have a comedy other successes are that came I'm eyes went out of their minds want success is doing here so what would be the probability of a particular sequence that have well our successes in the rest failures A real problem successes he and his event Charles repeatedly are and enormous Reed And so now we deceptive All these sequences with arsenic passes and came eyes are doubts have this probably we number sequences that any passes but this access to go here Why is that it is right that's the 1 warrior Alas success Sony Laser put our minds 1 successes in here and being used our minds will be deceptive choose are minus 1 positions assert that would be successes from the king might be the key and were being negative binomial And then they CMF would be at and so this Would look something like this year's are arbalest 1 are forced to etc. This CDs would be 0 target art and has a jump of size well Where is easier with cable are cases are becomes 1 minus 0 feet to the This is our 1 so you size PVR as flats in the unit emphasized EUR might plus 1 and new job of size You are close to etc. every every integer has a small jump and the keeps something like that Never reaches 1 but it crosses 1 as you go Fervent Part of Greater brick combined more But gave perhaps 1 of Most important friend Robles a skull was signed so yeah way of our land our positive and not follow user To indicate that the venerable has on distribution with land their anaerobic they gun 18 natural number value of X is equally case surrender the case or factorial you might find the that this somewhat came out Sr Noise BY is it true in this case that this summer's 1 As he died some missing but maybe to slander doesn't depend on case or pull out and that term kickback froze after sigh grabbed by some that Katie going from 0 to recognize that Some Kaitlers era infinity landed K factory Floor At SeaLand summer's eve and meet you miners Lander times Yolanda or 1 this venerable is used and counting Where there are large numbers Those are independent of events each with very small probability you might consider a block of a radioactive substance Like material and factory your apartment ask a question harmony particles Willard In the next 10 minutes be modeled by a sonorous wise that actually is actually on an example of binomial random variable account of a number of alphaparticles Actually something more like a binomial where each Adam Mr. now sparkle with some small probably and the items are acting independently So you have something like a large number of files only Charles would that be hungry arms would be in a little box of radioactive substances on the order of what 100 thousand tenderly without borders and its and tenderness 23 10 23 items or On that ordered and they're all our tossing it going with very small probability of success at the point of that had A mail are being there probably is bigger smallest Lydia thing in your While you better small otherwise we want Radiation so let's look back for more food br binomial ran rural and see its relation to the precise beds a sequence Aragan rebels
1:00:22
At the end of probably success will depend on and I'm going to assume that The limit is goes end times he and his mother says Public success On a given drama and years number trials trying so I'm probably just come out with some number lender which also and It will be positive I want He that's computer The probably Exon 0 Well Where recall about Binomial this case piece of indicating 1 might eventually Mbytes K that's what we bovine Omar or honorable tremors and peace event before we decide he didn't depend on an order cancer or So the public access 0 B. forward only tables and 2 0 as 1 the European 0 Hearts 1 every year 1 minus yen To me end L I haven't sat as an most of eternity Anything well there is a delicate balance On this number is less than 1 right Raising it foreign Do raise a number of us in 1 foreigner gets us 0 alright On the other hand this summer's going 2 0 He going 0 like his intensity and going through a violent and here we get 1 I want to be and will be 1 So By 1 might be 0 or might be Something between we got well what information away Rocky and only 1 piece of information is given and kind pianist converting to ban for simplicity while we just assume and time again is equal same are Sicily and times actually movers Skinner's Llandovery and hear what we do 5 0 amid say that But But And then this would be approximately equal to 1 minor slammed over at the end of your is that to his Angus There is 1 of 80 most honor limits and calculus emerges to move member this fund member there were with the name of on this summer will but also the vertices demise land self and skin converters lender and X and his binomial with tremors and probably access 0 covers ease the minds Exs on what's probably Exs equal 0 0 0 is 1 of your doctoral was 1 you my son These have the same probably being 0 when enters large probably accident 0 is approximately the same as the problem son With Prem Let's consider now the probability that accent is Katie was 1 divided by the probability an accident See it 11 so we could our visitors That figure out what Probably accent is equal pay plus 1 is converting to because we know what this is converting to so wouldn't get cable 0 were disclosed you my family for your racialism we get the public voluminous and probably Texans want an image of 1 year probably too For 2 years 3 And the reason I did this It is Similar to the 1 last time and coyote capture from Member we look at ratio won a referendum gobbled up things canceling Dr. factorial summer will happen here What is to come up with Suzette definition they're here we have and to escape us 1 and then he had to make a fast 1 1 minus V and B And my escape minus 1 in the finale areas and to escape he and decaying 1 minus D & minus They did was user definition of binomial right now sums of the occasions to occur due factories hobbies factorial steer and look at this or nice cancelation with Fiennes and this stuff will handle that more but to to adapt
1:07:28
She s so baby or a factorial staff separately All of the right objects are diverted or stack the group's work or or The fire out after this castles on this case factor Laura on doctoral is 1 over a fast want and what I want this yeah I didn't end my escape from this ratio Text Direct and now we multiply that by but survivor Spartacus Who will deal with rich on such yes Putting bitter together a small fire idea was 1 or Cape us 1 I didn't end might escape times in Igor oneliners Fiennes Simitis what now let's consider what happens as an ghost renewing this Doesn't move What is a case specs friends Boynton Let's examine here what is a ratio a lace K over and it was a ghost poster wonder what is and fee and boasts a 11 deaths converters to slander the 2nd part converters Aulander underwriters Landover take us 1 more what 1 might as he and that to Davos PM ghosts 0 so 1 rise PM goes to wonder why are 1 goes to 1 so we get this ratio So in this far limit is an goes to infinity He added of case must 1 over And case is Landover us 1 and limit an goes to infinity Piano 0 is sled NFJ assists but I more About Where 1 oneliners where Where it is on the last trial can well he egg was a 0 so 1 my scans were 1 of snowy here he is very far from that so what's a limit as goes to infinity piano want does exist what's as a ratio If you have 1 or 2 0 2 that's where you with potatoes earlier echoes through land over what Orlando ranked at or near 0 in 1 year you get land gives a rose to my slander so this goes to ease my What about the limits and then goes to infinity piano after 2 of our time I use the fact that I know how these ratios behave What is this ratio to that's when kids want where we get Landover fears run land over to and what have you slammed rely on over to
1:14:46
Times lie under my slander or Where'd over to and through the mist Backdrop our Moslem goes to infinity Deanna 3 or 4 For all of us This would be lowered if report the to over there was I give Landis squared no Landover 3 or 4 cable to in the top either at Landover free and Ms. Reno emerges that Landis squared over to factor slam What as landed 2 over 3 factorial minus going like that works They give birth general case and the case a factorial demise It is so Bernoulli trials large numbers of Bernoulli Charleswood very small probably of success in fact this happens than ever only ran a variable is almost like a son And that's why I was on rules not so much on their use for example among number of people go to a 7 11 years Taipei of 11 Member you will go to a cell between midnight and 1 AM is modeled using the son ran parole Izaak well under a lot of people in Taipei at our butts probability that 1 of them picked at random decides to go to some 11 between midnight and 1 is figures small small and back Population of Taipei Times probability of individual goes there is some number between so much well not because they never some light And so the number of people and all the people that are deciding whether or not to go through some ago this independently somebody's An apartment or 7 street persons in the park progress romp or on the street and others in a restaurant and bar don't communicate with each other the decisions are more or less independent much of independent route files a lot of them small probably success success is what person decides to go its own way so we got number of people the Goto alone in a certain time spent in big cities would be modeled using some venerable also used in reproduction Some plants for example never there were Elm trees When I was young they all died and said but they would make Allison's and thousands and thousands of seats looked like me on what was worrying probably success of these individuals Well there weren't old trees are mailed trees everywhere there just a few elm trees covers excessively given with small so number offspring of a given oak trees would be modeled using a son and heir to use in modeling the number of alphaparticles admitted Some reason many many many our applications for Sunday rule has is and on comes from generally speaking this kind of a number of a large number of independent trials probably successes A small book it about bats A bunch of examples of all state and rebels of consider Some examples of continuous trend revels a question on this By way of what we just did years called lot rare events where most final results and probably along with the essential limit which would later members means It was as if to say yes but but also 4 As a all Area may say that if cap Alaska has a derivative The end As over He was falsely Truong error some examples where this does more Kapil ever be a role Of its fervor And call the density of capped left or of X
1:21:26
Sometimes it's got the more fancy name probably probability density function and will usually identify red Errol's X by specifying the density so most basic example would be For the or the He At all or is it a court to keep the keep open They then they rang a rural satisfies this property that probably get the verbal smaller value acts 0 eyes and Verney VX whoever YTY that's remains generally if I say that cap elects density ever go out means racial fell For this particular example what is this function look like should density function looks like that is a gravel efforts 1 0 where else Suarez is interval of like what would look like if I take a less over here is 0 because a integrating 0 my here if I move elects rear 0 until I get to hear of capital left Kapovic cyclists and then what happened I'm hearing 1 from 0 reacts with 1 from their acts 1 0 well binary from zeroed X this function where my getting I'm getting very under the graph but what is That look like well as concentrate 1 and some of mirror a rectangle with base acts in height 1 man is area acts so what is a graph alphabetical acts like line with 1 goes up from 0 0 Mexico 0 2 1 lexical 1 and then happens after that Do I get a March immolation after that will ever 0 from there aren't so no more is what Kapor left looks like a deserter Bourbeau thing that might be asks What's a problem if it zeros is is less than 1 but is probability that has lessened cap Alexis less be well but is a stroke area so why Remember this in name beer disjoint probably union of the 2 events a summer probably sell em Think it as being a head was being demanded be with this event This would be an antiunion Exs Lester will be seen their inherent warrior dear between these 2 numbers for that number If And villas are destroyed events like you can't have acts between here and glossary back so that's the same readers track And the first one is what its inner ophthalmitis and later be What's a secular eyes internally to 8 whereby fire truck the 2nd hero from the first one But I get hero from Avie this relational assaults if you know that writer rebel X has Density function f the probably lies between 2 numbers is in a density between us so using what a particular density function were looking at this as just I just uses religion here which is general aged between capital accents less so What defined probably around was between innings and rules between 2 numbers Yeah greater the density between those 2 numbers ballots use this particular example of our numbers are like here and here would be in a of 1 B from A new area of a rectangle Of light 1 and based be might say so that their goal is to be my physical and the uniform ran verbal its course corresponds to pick a number random between 0 1 the phrase figure number random between 0 1 means figure ran a relax with stance that cover the most important at our regular variables a normal so we here This relation is a general 1 for Renner relax best effort probably axes between these 2 0 AP of OK so here's a writer I will that adds Socalled moral decisions would mean new embracing was where will see what those terms means later but they're just 2 parameters that describe as federal its density is given by it
1:31:35
With The With all or Each Might look a little Complicated now But By the end of their 3 weeks we'll be dreaming office the back says normal Maine 0 grades 1 in a distribution of then Ever acts is equal 1 over there to buy You that's where to work to fight for no lesson The sewer for this Render rare white and dark gray granite continues federal with density of the left the public Capel exited with my family would be this is taking a license infinitely be Boston here and watch this friend but this number being what's probably around revelers number 1 Merrill that's the assessed be 1 0 and particularly their old this density should be 1 of the factors that 1 Thanks for more autograph this looks like what is EU my sex squared like this isn't even function goes to Costa 0 plus arises areas value of sex is seen as a sign of my sex because you square an expert in mind the same so looks I got so there over the interval from minus 3 0 would be equal to the interval from 0 to and So this would be equal to square root to over 5 in a row 0 2 very by sex where it over to India in other words I take ahead A double half the whole nite worry soak Brewer so this is 1 of my way so I members want is showed when you square you want That number can be minus 1 positive it's square we swear that number 2 or 5 in a row 0 2 infinitely Niedermeyer sex squared over to the ads they show that that's what For that Where pirate who look at that arrow square problem we have is a cat reliever in January that Look There's no way Nobody's ever found 1 in 300 years Maybe 300 home on bit renewing calculus every 200 years but there is a trick by English Nolan father square But it is it is it Each she as is for Estrada's mineral times in a row in the 1 I use a different variable It doesn't change value by userdefined variable another subsided get double and a 0 0 2 infinitely 0 2 MIS X spread fast why squared over to the acts you want you took to eat I suppose You're take to eat What are you do doing to me when you're doing multiple Errol sometimes you change variables What variable looks appropriate what's the function and the export X workers wives where Diaz are work from a reporter Plus changes too For Hornets sold Wyche part Of twodimensional space We over here X zeros A life lessons on the that's 1st quarter Right And his biographer squandered 4 data goes from 0 Pirates goes from 0 offending an 82 are squared or 2 and then what do we put here for insurgents Mail rate from 0 Piirto Decatur if I minerals are you demise are spread or 2 Dr and help with federal aid to a substitution you equal to our square were to do you would be hard times are becomes pirate who mineral were limits by our 0 User and we are isn't really wasn't really becomes do you injuries The mice you Anderson be pirates who Minus EU minus you between 0 and would survive the spot 0 what survivor sing at 0 Minus 1 but we subtract becomes plus 1 becomes I never took end Oh answer here's this is pirate to modify by your you want so yes it does great 1 and 1 9 So you will in effect says by Miller will render variables with Trevor and and a half so society tossing a point and time firing army had no doors are as large a but Moreno verbal were those routers to Beirut and is essentially a normal ran verbal that's Culver central and that sort of saw will support probably terms probability secular River and be Barbara rats This 1 reason nor intervals or so Prevalent because of this result here and it's true for more than just this example will do that