Introduction to Probability and Statistics 131B Lecture 1

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Introduction to Probability and Statistics 131B Lecture 1
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Frequency Sign (mathematics) Lecture/Conference Term (mathematics) Mathematics Multiplication sign Open set
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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
Point (geometry) Multiplication sign Equaliser (mathematics) Water vapor Parameter (computer programming) Student's t-test Number Expected value Centralizer and normalizer Mathematics Population density Lecture/Conference Well-formed 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)
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Lecture/Conference Block (periodic table) Multiplication sign Factory (trading post) Sampling (statistics) Variance Staff (military) Parameter (computer programming) Prime number Mereology
Trail INTEGRAL Multiplication sign Insertion loss Mereology Weight Event horizon Frequency Population density Plane (geometry) Many-sorted 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
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
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
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 Chi-squared 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) Well-formed 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
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Group updates so let's review of bets we are finding All-Star would Chapter 6 Oh I highly recommend it didn't take 131 a last read out by what the sent does abusing them frequently but they can't Chapter 6 starts out with user will use each of a normal run rural and word Donota but only to see 1 of the Sabine normal mean 0 that's 1 in there we define you to be a squared this is a follow-up high squared venerable . 1 degrees but the square of a normal and these arrays 1 expert and a precise that Zia on all means their own ranks 1 means that ain't deaths of at all but market which means said it's probably easier said any sets me is payroll being of the best have OK if I were but all but would not say key she said could can't that's the definition any memorable same density is this the St. over Terry voters will recall widespread agrees show he now so this symbol here means say distribution of you a sky expert and reason that means as St. Pierre as the of Vermont as saying density if you have the same density is this news called Keisker there's reason U.S. ties were In other words like some Of the squares of an independent normal means referenda rebels and Zia's normal with means 0 rates want a new NCR independent auto her there's Z divided by the square of where does was called 18 GE end dissertation at sea statistic banned agrees or so will be where scatter around the rebel look in Chapter 5 for the best means for chi squared and answer I was on Sept 6 2 6 4 the densities don't to memorize that could be that you work with a lot of stuff that you do without intending rise of another our common distribution is following ties fertile and degrees of freedom skies where with and degrees of freedom and you and appended call for better you over and divide by B over am doesn't have and it's I must ordered and enters the number now you don't 0 0 OK maybe I should the folly his wife and you can look up and see for that are we did have a problem the final but the density for 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 this is going to be a teacher statistic with an minus 1 degree of freedom but civil fighters this and my is 1 might on canceled also there is a segment of an hour later in the numerator there's a stigma and the denominator means they canceled and so we get X bar my new over Road and asked it is a team for ago they died Perry agreed so be typical will this in the future a lot of times we should assume were sampling from normal that the samples are independent and metabolites are sampling is using this ratio


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