Introduction to Probability and Statistics 131B Lecture 1
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Title 
Introduction to Probability and Statistics 131B Lecture 1

Title of Series  
Part Number 
1

Number of Parts 
15

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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 
University of California Irvine (UCI)

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Frequency
Sign (mathematics)
Lecture/Conference
Term (mathematics)
Mathematics
Multiplication sign
Open set
01:39
Lecture/Conference
3 (number)
Social class
05:23
Statistical hypothesis testing
Population density
Gamma function
Gammaverteilung
Multiplication sign
Moment (mathematics)
Functional (mathematics)
09:47
Logical constant
Density functional theory
Musical ensemble
Vapor barrier
Multiplication sign
Parameter (computer programming)
Mereology
Mathematics
Latent heat
Population density
Lecture/Conference
Term (mathematics)
Square number
Negative number
Analytic continuation
Subtraction
Alpha (investment)
Area
Theory of relativity
Gamma function
Moment (mathematics)
Set (mathematics)
Mortality rate
Factory (trading post)
Momenterzeugende Funktion
16:46
Logical constant
Trail
Randomization
State of matter
INTEGRAL
Decision theory
Multiplication sign
Distribution (mathematics)
1 (number)
Water vapor
Mereology
Generating function
Number
Sign (mathematics)
Population density
Spherical cap
Lecture/Conference
Natural number
Length
Condition number
Series (mathematics)
Product (category theory)
Cohen's kappa
Structural load
Moment (mathematics)
Exponentiation
Infinity
Limit (category theory)
Functional (mathematics)
Factory (trading post)
Order (biology)
Dependent and independent variables
Moving average
Uniform space
Table (information)
Marginal distribution
30:35
Point (geometry)
Multiplication sign
Equaliser (mathematics)
Water vapor
Parameter (computer programming)
Student's ttest
Number
Expected value
Centralizer and normalizer
Mathematics
Population density
Lecture/Conference
Wellformed formula
Square number
Area
Product (category theory)
Forcing (mathematics)
Moment (mathematics)
Independence (probability theory)
Division (mathematics)
Cartesian coordinate system
Functional (mathematics)
Approximation
Summation
Arithmetic mean
Table (information)
39:58
Area
Axiom of choice
Point (geometry)
Gamma function
Multiplication sign
Distribution (mathematics)
Set (mathematics)
Line (geometry)
Event horizon
Rule of inference
Proper map
Number
Mathematics
Population density
Numeral (linguistics)
Cuboid
Marginal distribution
Subtraction
48:26
Lecture/Conference
Block (periodic table)
Multiplication sign
Factory (trading post)
Sampling (statistics)
Variance
Staff (military)
Parameter (computer programming)
Prime number
Mereology
50:54
Trail
INTEGRAL
Multiplication sign
Insertion loss
Mereology
Weight
Event horizon
Frequency
Population density
Plane (geometry)
Manysorted logic
Lecture/Conference
Square number
Alpha (investment)
Statistical hypothesis testing
Infinity
Line (geometry)
Cartesian coordinate system
Limit (category theory)
Hand fan
Doubling the cube
Factory (trading post)
Thermal radiation
Module (mathematics)
Figurate number
Marginal distribution
56:46
12 (number)
Building
INTEGRAL
Differential (mechanical device)
Multiplication sign
Decision theory
Distribution (mathematics)
Water vapor
Parameter (computer programming)
Mereology
Event horizon
Expected value
Derivation (linguistics)
Population density
Lecture/Conference
Geometric series
Square number
Subtraction
Euklidischer Ring
Social class
Condition number
Area
Series (mathematics)
Gamma function
Exponentiation
Conditional expectation
Line (geometry)
Variable (mathematics)
Limit (category theory)
Affine space
Functional (mathematics)
Right angle
Moving average
Marginal distribution
1:13:38
Trail
Series (mathematics)
Divisor
State of matter
Multiplication sign
Interior (topology)
Infinity
Water vapor
Line (geometry)
Price index
Wave packet
Mathematics
Lecture/Conference
Term (mathematics)
Right angle
Subtraction
1:19:23
Axiom of choice
Building
Randomization
Multiplication sign
Decision theory
Equaliser (mathematics)
1 (number)
Water vapor
Mereology
Fraction (mathematics)
Expected value
Meeting/Interview
Square number
Ranking
Area
Product (category theory)
Moment (mathematics)
Sampling (statistics)
Sequence
Functional (mathematics)
Flow separation
Arithmetic mean
Binomial heap
Numeral (linguistics)
Normal (geometry)
Right angle
Chisquared distribution
Resultant
Directed graph
Point (geometry)
Computer programming
Trail
Statistics
Divisor
Civil engineering
Distribution (mathematics)
Rule of inference
Scattering
Theory
Number
Power (physics)
4 (number)
Population density
Degrees of freedom (physics and chemistry)
Root
Lecture/Conference
Term (mathematics)
Wellformed formula
Units of measurement
Statistical hypothesis testing
Addition
Multiplication
Forcing (mathematics)
Independence (probability theory)
Variance
Division (mathematics)
Mortality rate
Set (mathematics)
Cartesian coordinate system
Limit (category theory)
Local Group
Field extension
Summation
Number theory
Voting
Wahrscheinlichkeitsfunktion
00:06
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00:30
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00:52
say last term late on Tuesday office our was at can and will be the same and while on Thursday at a that's there show as those that's OK we think of my complicated scheduled for a minute around but for all
01:55
the fuss 2 Wednesday what take me Torre where my office is located photo of
02:46
course OK so so for all the leaders but to the crux of the case to old to the for sure if that was the case 0 covers an ironwork horrible start Monday a week from today's quizzes resist Friday and 3 by personal amid termed the midterm will be they of the 3rd week and then the finals last day of classes and we'll be book here is E I don't know if call and I recommend ape the 3rd edition work came
05:23
from any questions we can't that fire alarm it's Over the test center
06:02
but offset CEO of great 7 the lead entering the race for the 2 days after the greats you test backed by Wednesday I hope you couldn't later today what a solved problem 1 0 X has a gamma distribution Bedias density for the and relax it is less cash court as new had and 50 Street thanks the mean the rare et seq moment later actually was very sorry and Nemo Jerry function and a idea here is that says Epps Alexis is a density it's in eros 1 solid thing you really have to use in this problem which means this is equal to the Gamma function Elf Overland Trail that's only thing you need this problem and I was aware that they have put for continues an array was expected value is always in of X times density acts in its case against the ayatollahs not on the it'll from mines the new user also will have to hear it from 0 next times a density and investigators is constant lambda over again over which at he cake and I combine these extra last year getting
09:51
guests and now this looks like Pa
09:55
the main part of the damn advances density but with parameter alpha plus 1 itself general Elf overland but now not alphabet itself plus 1 sure you're Rodolfo plus 1 year here so this be landed today over gamma Velva times gamma Belfour plus 1 over land that the they offer 1 which is well under off over Banda the offer plus 1 is 1 of what scam of plus 1 itself but this is a factorial barrier Miguel so they answer for the expected buyers L whether the ballots Tuesday s if completed expected Ivax areas so would put better here's where things which computes expect direct scored the 2nd goal is in that previous cases of putting it the LECs squared their wish I'd say elects there which would let squared and insult don't write to the secular life best combining the extras and again this looks like the a part of the gamma density but with Trevor Alpha passed 2 and this time so health and Lander so of elfin Landry down Welfel Orlando they offer but we don't have awful way of alpha plus To be damn about us to over band that they offer plus 2 of poor well and not every squared where but the ratio gamma novelist to over down use that relation of there now plus 2 be offer plus London Times and as Alpha plus 1 times ever felt so we insert this year and see gala velvet terms cancel Alpha times Alpha plus 1 sets a 2nd moment their workers attacked 1st square to get the various variants of acts with this bias the 2nd squared but and that is helpful overland square but King and then finally for the moment generate function this would always be there'll be ability for continuous and rebels with density capital at the Capitol acts as muted years just definition of the died of a random variable and now we put in the specific density function could now it which means we only rate from 0 to intervene presidency vanishes for negative values and if there's a solid set of provided X terms this pilots rental terms like that are not this looks like the important part of the gamma density without Constance a different from the evidence the gamma density with herself member has part None constant stuff were we're over there where but we don't have member we have solid this change over here would ever gamma office still but on here we have around the minus Tito they and canceling Robert back sewers problem immigration officer using the fact that you know that's a density and that means at this show and that news different values and often elaborated himself prop but it is a question
16:49
Zgoda number 2 photo number 1 X is uniformly distributed on Mir will from 0 1 given by X Y is used only to rely on it or from 0 to that so we number at random between 0 1 acts that wire some number between 0 next Granneman added said at following their 1st gasses the 1st part a fine time there's a native Texan wife OK do we know will lead initial density of why given tablets is Alexis do because if way duo we did expressly joint density is a conditional 1 currency marginal acts do we know this right that's where teams for Catholics to be uniformly distributed under what has a stance they now quinoa the value of Kappa waxes Eagle Alexi Watson this distribution wife uniformity in often 0 2 X auto what's alike over 0 X X Oh the densities constant and value is 1 over the length of 1 over X Men Water what next year work should be restrictions are white ex rel X is less 1 or less table on where life that's less acts ever it's bigger than 0 otherwise what's stance of equal to 0 occurring OK so the joint density its war erupts times 1 if 0 fossilized next is somewhat and 0 otherwise they started I guess that's part B R I find the marginal decision of Argasidae for why value fine Maazel's by integrating out the other Grabel when your drug just so a severe over there X variable of the joint density now want to be the limits of immigration why states and that's where his ex have to be rolls of Hawaii between Bly and once a center should be from white to and what is this function hits Water Rex DX and there will be a lot of moderates is locked uh log wrote 1 minus Lorna otherwise bachelor 1 is 0 so we met minus slaughter white this might look little strange here where negative it my and work my probably density airbase was positive now lies between 0 1 so blogger is negative that's what mine either rewrite this as 1 white without my act if you're scrimmage auto so that's a density again what loads on my here why is between 0 and 1 person at a time and then find a conditional 1st decision of XTO white he let's just joint Over the bottle of life and this is 1 over
23:41
acts and this is why white my why did this no the limits are restrictions on XOY 0 less than white less than that that good as part C R D I would need computer expected value of cap elects given capitalized I was just be relaxed Times e conditional density of acts given 1 definition of it so what are the limits of integration here this that conditional Betsy 0 unless happens of bravery in which verbal why so why should go from 0 to act earlier next time 1 over X or with my assigned D argue White DX answer is yes the EXE and this looks like minus X overwrought whining and solid are so that was a bit of a civilian why states bravery X X could yet some wider 1 Expos from white 1 might really extra canceled so the despite its X over log life is heard from wider 1 so we get 1 we get minus 1 of and track value wives white over or 3 like this that's why my over sir they I think E 3 x 1 show X sub R R & & posts songwriter rare world around Rolando Ed that relaxes the somewhat but they were swastikas Buick b momentarily function for 1 is discrete ran verbal some and some of the sun and the rebels takes on the values 0 2 infinity nonnegative integers brigade the TK tons of probability that's 1 escape that's what you get from moralist definitions but you're the only bodies were this is different from 0 in Kazan on a major and water what it is a sign of its Lambert the or cave factorial Biedermeier slander every early this summer has a factory of Icelanders for out and now of both CUT and lend our race the archaic we provide them off by land at times unity raises the bar tebibyte case for a time start now this series is investors for mental function busy some cake was easy to care backdrop that would be busy so into and will not fight on exponential xli at exponents both landing gear is planned needed minus 1 Ito and best Auger function Posada next part was gave moment Joey function for X this becomes a product of experts also these are all in the pen the venerable sound regime he expected Ira product of an apparent rebels becomes a product of expected values all those expected orders would be the same equal to this we have that by itself are times we just get this race R B to the land our leaders minus 1 so what's sadistic and also asked What's the distribution of acts as well its post on private land are excess probably landlocked Texas bosonic land that is smaller generate function this is defined miserable containing origin any time you have a moment what looks like this has to come from with distribution real momentary like that would not the but land the times are excess Santos tremor land and finally resolved
30:37
approximations find numbers Easter products as fast Posey what point 8 5
30:45
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31:08
for Kaif Iran X is a sum over independent random variables so you apply these settlements to its are as big enough for are these fungus and land equal 1 so
31:37
if we subtract the young expected IUX from Max and divide by this warily variants we got something it's a properly normal so what's expected Ivax proposed honorable of the value of land and its variants is also a member of Saudi it that offer you expect divided by you could start here OK there and do that another way is here where the moment I functions for different and evaluate the revived 0 we could be expected value we French twice the virus 0 get 2nd moment dropped the 2nd such squares 1st on the variants of those ways that they waited on the short of it is that they expect live lambda its its parameter and its primary would be land at times which is a 100 And if we divide by the square of its various strains that also meets Premier which is again this is approximately normal is approximately normally distributed means of Swat at central at E so starry with the Polish Apple Exs or that policy 4 we shed subtract a hundred from both sides and abide by 10 for but and this is about equal to the probability that Kaposi's is less Woolsey minus Sunday over 10 Zia's industries which is normal means Iran's what we want that to be equal to appoint 8 5 0 you go to the table which lost faith and find that the trial of 4 . 8 5 in here it's about on 1 . 0 4 Z my asunder Over 10 should be called 1 . 0 4 assault resist choir by 10 that honored mother what I status because 10 . 4 added and 10 . 4 questions from member force may be a way to do number 4 after a review Chapter with review of Chapter 6 South forwards from 7 a are doing now because some of the students are newcomers and haven't seen made it may not have seen the fact that they are likely to have get so it's got a number 5 2 X and are independent Xpress drama 1 at 70 is that their Ma told and Caesar even by the and the joint density would be what or in the Panorama rebels a joint density is a product of the barge also and thank have fears was a finely joint density of expos wireline of such a list of products was lighter X or Y Y Syria we have you as a function GE 1 of exwife equal to X or Y those is function of X and Y and it's actually just like to invert these acts as equal function of you and be 1 course auto idiot exit window you and me you times his acts but and why it is another function of X and off by you and me get why when you Andy was just knowing a vivid Jacoby G have but cause she hoped for well being won the Axis 1 white dg Lundy why is minus acts of wives Square 2 DX 0 and DG 2 Y is 1 of the several years won over water and the change of area former Merrill formula for the density says that the density of U and V O U and movies it is the joint density for X and Y evaluated each 1 of you V H 2 of you mean Annan
40:04
while rap survivor Jacoby and evaluate 1 H 2 and that's a change of rural farmers OK well here's a joint density will act miserly evaluate their wares a each 1 of its 2 . 6 1 2 times to its being the miners to me must and then won over a J at a 22 2 so this is being what is a wide at the ex still would be won over age to overwrite wherever survivor aides who was won over f solidly while or forward this as a B 1 over aged 2 and is not becomes 2 in the numerator aviculare comrades to hear was aides to its me time and this is what they us a new lessons and reading and their lessons these sets a joint density simple distilled little bit Kish but I think we find the Maazel starts fired a R B find marginal density of you'll see they which is carried out there I knew that of oil was racial reduced from 0 to infinitely Brooks and what is this look like cyber gamma density With premier Alfred to and land equal to 1 plus you is Reaganera gamma density wears a gamut as they look like member that was extremely has landed the awful download Belfour Baxter the ophthalmitis want Eli Islam that could also expresses views Barbie's haggis news media make me in the box here but like this by proper choice of Elf and land that I really veto the 1st from all their probably made a ophthalmitis warning of what would it yourself to the office too and awkward Hollywood glamor to get this month plus you deserve would become gamma 1 plus 2 over Elf is so absurd Gamma Gamma Belfour that's too and other offers to over lenders want us to Tooley Alpha which is to and what scam of to its 1 camera to lose 1 and so this 1 or want us square the top and then fine Media artsy what's probably acts is less a line for wise lesson 1 these are continuous honorary boats and have the same distribution so I'd be the difference between this and the probably wires lesson abuse saying what public wise equally their independent 0 so at this point this probably be happy because this plus probably wise last night's adds up to 100 people half on the eve the the density of the but if you this from 0 2 1 a to 1 more for the break number 6 NATO a questions a vast area a lot of rain rare also did bone was out of God rose number of off rules but sustains that stuff probably it is 1 of 3 which is 1 minds probably 0 and empty here it is to over tender the 23 when they spot but peak times the number around I will say is about to to act so How would you use a lot rare events E. says that we add up all those killed but of rocks bubbly for Sondra drummer too but it it was all over and Romania recession session we talked about the atoms of
48:27
living alphaparticles particles but 2 the 23 out of the blocks of any substance Rick whether individual items in itself
48:39
part or not for newly random rebel and if it does it within our playing with some primary he is very small something like this Adams acting independently some means all these things would be independent this would be 1 of the 1st item is now part of their otherwise we wanted so was sample found on a for soul and this is kept blacks so then the problem acts last it to would be well probably X is 1 0 was probably acts as 1 us probably access to probably Texas 0 4 0 what's probably Texas cave Kate Exs was on most of to the case over case factory the mites to advocate 0 here would minus 2 . 4 K equal 1 2 or 1 of these mines to duplicate what to get to over 2 factorial times you might be 1 us 2 plus 2 or 5 times my charm what expected Ivax while census is brought song to the city but to me it was like being evasive acts again or post on the variance in the both the parameters of the possible at stake attended break which is what will always do do they can avert what the staff region in the world and up and start through review they were let's approximately a 10 minutes prime number 7 here's
50:59
the density of Jew and rebels it is done by his demise when axis between 0 1 4 figure the next thing and it's of course 0 otherwise so it's difficult ways of exwife which is expected by next time times wife bias expected Ivax fans expected so but these 3 things Budapest they need to marginal density for acts to complete that we need a marginal for white and is making do with which I don't speak for life says we have battery let's do this 1st visit me double winner role of Alexei times a life Times a joint density not what are the limits of integration what region in the plane is described by 0 works a but there's no Lexa light satisfied this is in the 1st quarter and obviously and we where X is equal limelight like now where were the Of all charter for the 2nd quarter to be bigger than the 1st both sides this region up here and we won a over that read sort of described that well what does why do it starts at their own ghost To infinity period 0 turned now offer expire why what is acts to worry that Expos 0 2 expired why like this 1 x values go where we process line here right 1 of the 1st quarter net on the hours are lying do go from 0 to hero as were wise people Alexei otherwise excellent have that ability litigation ballots substitute value for advancing it seems my his wife did they have winner ATX 1st Ballwin yet x squared over to make illegal acts d acts is that where over to be evaluated between lively didn't have thought frontier in and they get a Y square times why would be wise to why do want and know what setting too period redeem be part of a dam that events again I with healthy for the 4 and led people to 1 so what what city that's movies Jamil Over lenders of 4 4 or 1 of the 4 ship right this is member the evidence in an from 0 to infinitely y the Alpha minds 1 minds lambda y is equal to gamble Delta over led to the Elf in that Ottorino Myers 1 3 Elf should be formed and I we had planned a wider White members what so what's 1 the 4th its Aswan Dam of 4 is like the 3 factorial 3 5 over 2 3 but it actually I think in this whole tests you never had to do with a by snow was there I do want or loss part lasagna radiative is 1 of Rex you Tom I had dinner in excess of 50 in attacks 1 I take it back up case so are
56:30
over what elsewhere which it expected Ivax expected by wives modified track From here so they get a sector buybacks we need be marginal agreed to agree so let's get the module for acts
56:48
get vase joint and whether the limits of life going to be axis why then as what rose from 0 Melbourne Knights 0 but accident Friday Selena great next affinity Myers Why do I see you might why that way of life for accident earlier this year 0 truck the value at X subtracting lines to my sex life marginal before acts sexes were next is positive so that's an exponential venerable right so what's expected by vexed by an exponential From around this year 1 here sir if you have dinner ready light of integrating acts times you the mindset right X times the density and what's is hurdle what you use gamut because there would look to level equal 1 says began to or what ballots could be marginal density for why that means will integrate the joint density in the Xray want and what should be the limits of integration here for acts biased sex acts goes from 0 to 1 great from 0 to Y minus why DX this doesn't depend on a roll of 1 from 0 YDX why is my presidency that so it's expected either white he again this is it like the the Bok of born part gamma density with Prada L equals free and equal 1 as a demo 3 and these villagers never ever vendors and my aunt process meat to doctoral work To expected Ivax is 1 of my wives too but directs Times wires 3 so of 4 days of light years 3 miners who put but or case boast River expect directs given capitalize of Of visibly integral part of the times density initial Nancy Baxter why so now we need to compute this initial density and that's the joint over the marginal the joint is Eada mice a marginal is Hawaii minimize fire which is 1 over why and what are the limits here where is this from 0 1 0 is and that so the conditional distribution of acts given capitalize the light is white what you call that uniform money away from 0 to coming back appeared what are the limits of immigration that X Expos on 0 2 Y axis times 1 why the acts relaxed dances x squared over to evaluated at why would give Weisgerber to them we have like 1 or Weiss these fire to about life 0 let you might just written down from here have around rebels uniform on from 0 why what's is suspected by its midpoint while In the other part will see other conditional expectation I think show but but but but but but there we integrate why times a conditional density of white next life so we need this conditional that's that's the joint density divided by the marginal White House acts this is Elias wife where it's different from 0 areas and what was this you minor sex sorry right this is EU the miners why minus purposes and this is 4 0 annexed less son wife quick and so the conditional expectation what are the limits integration here will act suspects was why do goes From next to and say are king key well we could maybe change variables equal why checks this becomes a rope from 0 to mandatory Z class acts in my Aziz pleasing river that Jake so it to a girl's times it easy What's that that's 1 because it's a gamma ray right and then at times in a row you might easily been X the final part here identified Malaysian
1:05:21
hi surrender will expect rise text life well here that's Dulles little GOY what is a will do this is why overtook so what would be expected capital Eds given capitalized words is Geof and wouldn't be best capital over to them what's a distribution of this we need to know that his list why exposed and what where's the marginal 1 right here tho but so let's computer name decision function a stake Edgardo fabulous density and what we're doing all what they frivolous says motivated density of 2 times there were 2 wives why which is what seed densities for capital I it's cool I realize what times to to the minors who behind this is 4 0 lesson line less than entity which would be for while I need my eyes to what what's that decisions that have a name that we know get road parameter what Iraq agreed to Ardelle minus 1 of best bid to lenders was damn tremors got for auto Brooke JXY next wired event director Ron arose from repeat but for from we missed means it that therefore he amassed by that are computer expected Ivax various let's I would be expected directs this is Kate cousin Ali case it in fact are a key anabolic building series that way ever I guess we studied reduced to series in the past 2 series with at 1 another 1 was us for us they won exponential on genetics writing is going to reverse this almost looks like they geometric series provide differentiate this suspect to far ordered by a different take termite termite OK minus 1 and achieving In my mind this year now sure this is a bullets but it could but were tour might be derivatives of this is because they are now 1 4 1 minus 1 might minors times specter of water my me and this a B minus 1 or be square so that's 1 or but e Reyes it is expected by next where miners the square of expert value so we need we know there's still a need to has allowed Sec ear why did I do that
1:13:39
hardly it the 1st one by different training for a different state again we differentiate this place 2nd ever lists of like right and horror
1:14:15
writer did the sector of this like the executor of that and so I get this in the look like they sector of but I don't have Kate times came Eyes Wide case but that's never stopped past I often just change it to order 1 right Brazil or is that series for those 2nd start through this on starts at once so let's check out the 1 that people want what is it was like a is 1 it's 1 and 1 Peter minus 1 and then will start to novel on case various Cape Times case players OK minus 1 plus 1 that don't think the scare that this 1st turn is he past T1 line as some K equal to 0 2 infinity case they minus 1 1 might lead to the minus 2 and then he won might be sunk a call To times want times on my the photo or right others looks pretty good bets the effort however but just 1st this term is exactly why different take the 1st time I get a my from attainable where diversity economic is another 1 of those away and I have this is almost month I get put this over here and there but the 1 my ski back inside but I ran off by 1 might Kansas I get this thing this summer's wanna repeat what happens this year the cake a oneterm there for what would be the people want what is it wears a swipe players want that's 1 Brazos times Pereira that's it that's the case or want 2nd changes to see some cable want playing online indicator lights on words like if the person here that's the cake or want her as as she won last being DEC where deeply squared repeating past times of might as well we just did that spending the but that where we find that was Water repeat with different take this twice 1st on of my my party squared 2nd time to Over P. Cuba scissors to keen on might be over GQ us working at factor IX squared the track 1 he squared with now but she dealt 1st trick there another
1:19:25
way to do this is computer moments function for geometric which is pretty easy I get the variants more take the log different shapes twice since that a 0 there's no way to compute the PMF of X plus Y but they were here to do 2 things
1:20:08
what's interpretation of a geometric venerable its number right member trial dates to success you're doing independent Bernoulli trials province successes Peter so these are both the number of trials to get a success right so Expos nor a chance to get what to successes
1:20:36
soul what what's a probably that the number of trials to get to his successors is OK was well if from In terms of success and failure imitates Kate to success is the last trial have resulted the kids from result in success Frank well says that in years there have to be a minus 2 failures and 1 so there will be altogether minus 2 failures and successes of iPads wanted dictators sequence like that they asked all absent and ask What's the you'd probably that well for the we get key squared for the failures we hadn't won my speed to these same to did matter actually where this is worth about her you probably have any sequence with 2 asses and minus 2 us would have that building now we have to count how sequences are there where there is an here and only 1 AS there is a choice about the summer choices we have 1 choice tanks Sami forces were here they rest sets you could also use a formula for the he met give up some of our theories of Exxon's plant reveal that their independent we will all of and this is our water repeat squared appease verses water repeal 4th and ovaries of acts and is the same as razor wire expected I've Exs as expected by wire on I'm this the MEDIA variants of acts as expected value of X squared quantities squared to being the same minus 1 repeal 4th and then substitute the value on their parades left at that point and finally numbered I'm mad Texas binomial what primary what's expected by exorcist boats remember our party represented by normal program the sum of an independent movies with that divided newly published years these songs he and times of being but the Razorbacks both races in the the ground rules of some of the various the eyes of the summit and the around rules as what's the rates Bernoulli P compromise so varied so some being this some of the races for now and and we want announced problem is a central limit their what probability that is less than 59 . 8 probably Texas minors Our aim is 50 a hundred years a half so acts Midas and P 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racial on 1 of the exercises in the book is terrify me this vision for a water white or that being take wonder why this pose a greater this in so there would be F mn they have OK so that however a review Chapter 6 Carter recommend doing some of exercises distributions that we use in analyzing data From samples of alone suppose that don't and X 1 through are I IDE isn't it abbreviation will use commonly independent identically distributed the normal be numerics Sigma squared Bari equal water and some might go want end of exile as what decision well we know the sounds of normalcy is normal again and you establish that what what tools we have for identifying distributions of random rebels only functions would take a momentary function over some of its but about of independent rebels of the product of a which functions what's a momentary function of XI so what's expected West Samoa Jerry function for X buyer I did 2 3 Sept Sarah what steps erode ex parte as 1 and summer and I put the wanna ran with the team that I needed you over and times as some of its allies where I'd be the products units urine X 1 time unity your next to times EU foreign accent that expected by their products but these are independents be the product of their expected values and they're all the same so I could put 1 areas NATO and number theory and things like this what by the of the sink to the end so what is assigned crime that is yielded knew she overran plus stigma squared over to be over and squared thing inside the parenthesis power and now we multiplied excellent by and when you do that the becomes the new team boss saying most square Over To our baby can I just changes so that rewrite the same thing idea but the 2 under the T spread because only caucus in the cheeseburger to Izzy various things under the the same me here there among this by again it's isn't squared actually and or else I get a cheeseburger too and must Sukova shifty square or to over and so that means that X bars oral with mean new and variants they was burned over and thanks I think a still Chapter 6 part of the sample variances his best In this case several variants by multiply by and minus 1 and abide by Sigma squared this is chi squared with and my 1 reason car OK and important additional factor but X partner squared with novels X far AS bird areas offenders auto auto a so 0 or almost in that situation there where you was now being an well rare forcing whispered and Z or we can use that bar Aziz normal means Iran's wants we have turned expire to a normal and we don't want you never nor a me new abrasive whispered party converted to normal means of track right we would abide by they should take are biased means which found was new divide by experienced wherever there is a means bus being signal over rude and this is normal with means no want his squared our so X minus new overstatement abide by rude and divided by the square root that's our you that and now it to divide by number degrees of freedom 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