Statistics for Economics Final Exam Cheat Sheet
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Cheat sheet for statistics for economics final exam at the University of Notre Dame. Exam covers sampling and sampling distribution, interval estimation, and hypothesis testing.
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![-
population ( parameters M ) -
( l -
a) is confidence level
+ =
⇒
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finite ( N )
-
PC tzta ,✓)=F Str
~tn -1
-
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uppertailtestltta :M > Mo ) :P( 2 > Zxkx
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desirable
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reject Ho
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-
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vai .=p(z<z* )
=
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nz
-
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upper tail test :p -val=p( 2>2*1
-
Std (f) =
0,5=5*3
' -
Var (d) ~~Sp2( F. +
th ) -
ztail : if 2*0 ,p-vai=zp(2<z* )
↳ standard error
-
Std (d) =
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-
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.
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.
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-
teststat :Z*= F -
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-
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-
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orpval .
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easel :O , Gozknown
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-
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-
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.
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,
+
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-
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-
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This document discusses algorithms analysis and recurrence relations. It begins by defining recurrences as equations that describe a function in terms of its value on smaller inputs. Solving recurrences is important for determining an algorithm's actual running time. Several methods for solving recurrences are presented, including iteration, substitution, recursion trees, and the master method. Examples are provided to demonstrate each technique. Overall, the document provides an overview of recurrences and their analysis to determine algorithmic efficiency.
線形回帰モデル
I introduced some key concepts in linear regression models:
1. Linear regression aims to fit a linear function to data to minimize error.
2. Maximum likelihood estimation is equivalent to least squares regression.
3. MAP estimation with a Gaussian prior is equivalent to ridge regression.
4. Linear classification models predict class probabilities using multiple linear functions.
5. The least squares method for classification has disadvantages like being sensitive to outliers.
2018 MUMS Fall Course - Statistical Representation of Model Input (EDITED) - ...
2018 MUMS Fall Course - Statistical Representation of Model Input (EDITED) - ...The Statistical and Applied Mathematical Sciences Institute
The document discusses statistical representation of random inputs in continuum models. It provides examples of representing random fields using the Karhunen-Loeve expansion, which expresses a random field as the sum of orthogonal deterministic basis functions and random variables. Common choices for the covariance function in the expansion include the radial basis function and limiting cases of fully correlated and uncorrelated fields. The covariance function can be approximated from samples of the random field to enable representation in applications.Dsp3
The document provides information about Expert Systems and Solutions, including their contact details and areas of expertise. They are calling for research projects from final year students in fields like electrical engineering, electronics and communications, power systems, and applied electronics. Students can assemble hardware projects in the company's research labs with guidance from experts.
Introducing Zap Q-Learning
Reinforcement learning: hidden theory, and new super-fast algorithms
Lecture presented at the Center for Systems and Control (CSC@USC) and Ming Hsieh Institute for Electrical Engineering,
February 21, 2018
Stochastic Approximation algorithms are used to approximate solutions to fixed point equations that involve expectations of functions with respect to possibly unknown distributions. The most famous examples today are TD- and Q-learning algorithms. The first half of this lecture will provide an overview of stochastic approximation, with a focus on optimizing the rate of convergence. A new approach to optimize the rate of convergence leads to the new Zap Q-learning algorithm. Analysis suggests that its transient behavior is a close match to a deterministic Newton-Raphson implementation, and numerical experiments confirm super fast convergence.
Based on
@article{devmey17a,
Title = {Fastest Convergence for {Q-learning}},
Author = {Devraj, Adithya M. and Meyn, Sean P.},
Journal = {NIPS 2017 and ArXiv e-prints},
Year = 2017}
Statistics for Economics Midterm 2 Cheat Sheet
Cheat sheet for second midterm in Statistics for Economics (ECON 30330) at University of Notre Dame. Covers topics such as discrete and continuous probability distribution, types of distributions, and linear combinations of random variables.
A/B Testing for Game Design
1. The document discusses A/B testing approaches for game design, noting key areas that can be tested like onboarding experiences, monetization strategies, and retention mechanics.
2. It introduces Bayesian approaches to A/B testing, noting that observing results allows updating beliefs about hypotheses rather than relying on passing a threshold for significance.
3. Key challenges with frequentist approaches are discussed like multiple comparisons inflating false positive rates, and "peeking" at intermediate results invalidating conclusions. Bayesian methods account for uncertainty and can incorporate prior information and new evidence iteratively.
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ch3.ppt
The simplest and most common form of mathematical induction infers that a statement involving a natural number n (that is, an integer n ≥ 0 or 1) holds for all values of n. The proof consists of two steps:
The base case (or initial case): prove that the statement holds for 0, or 1.
The induction step (or inductive step, or step case): prove that for every n, if the statement holds for n, then it holds for n + 1. In other words, assume that the statement holds for some arbitrary natural number n, and prove that the statement holds for n + 1
Introduction to Monads in Scala (2)
The document discusses functional programming concepts like monads, functors, and for comprehensions in Scala. It provides definitions and laws for functors, monads, and monadic operations like map, flatMap, filter. It shows the equivalence between for comprehensions and flatMap/map implementations. It also discusses monadic zeros and filtering laws. Key concepts covered include the functor laws, monad laws, equivalence between map/flatMap and for comprehensions, and laws for operations like filter.
Formulas statistics
This document provides formulas and notation for key concepts in statistics. It includes formulas for descriptive statistics like mean, standard deviation, and quartiles. It also includes formulas for probability, random variables, sampling distributions, confidence intervals, hypothesis tests, ANOVA, regression, and correlation. The document defines notation, formulas, and assumptions for inference on one and two population means and proportions, chi-square tests, ANOVA, and regression analysis.
Implementation of parallel randomized algorithm for skew-symmetric matrix game
The document describes a parallel randomized algorithm for solving skew-symmetric matrix games. The algorithm finds an ε-optimal strategy x for the matrix A in time O(f(n)) with probability ≥ 1/2, where f(n) is a polynomial. The algorithm initializes vectors X and U, and then iteratively updates X and U based on a randomly selected index k until the stopping criterion of U/t ≤ ε is reached, guaranteeing ε-optimality of the output vector x. The algorithm is proven to halt within t = 4(-2ln(n)) iterations with probability ≥ 1/2.
Linear differential equation with constant coefficient
The document discusses linear differential equations with constant coefficients. It defines the order, auxiliary equation, complementary function, particular integral and general solution. It provides examples of determining the complementary function and particular integral for different types of linear differential equations. It also discusses Legendre's linear equations, Cauchy-Euler equations, and solving simultaneous linear differential equations.
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2018 MUMS Fall Course - Statistical Representation of Model Input (EDITED) - ...
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Intermediate Macroeconomics
This document summarizes key concepts in macroeconomics including:
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- Real vs nominal GDP and how constant dollar GDP is used
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Calculus III
1) The plane containing points p1(1,2,3), p2(3,4,3), and p3(1,3,4) has the equation 2x - 2y + 2z - 4 = 0.
2) The line perpendicular to the plane x + 2y + 3z + 4 = 0 and passing through the point (5,6,7) is r(t) = (5 + t, 6, 7 + 3t).
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Introduction to Philosophy: God and the Good Life
Notes for Introduction to Philosophy: God and the Good Life (PHIL 10111) at the University of Notre Dame
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Notes for Calculus B (MATH 10360) at the University of Notre Dame. Topics include integration, volume of rotation of a curve, integration by parts, Euler's method, initial value, etc.
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Notes for Principles of Macroeconomics (ECON 10020 or ECON 20020) at the University of Notre Dame. Topics include the role of financial institutions and financial markets in capitalist economies, government management of the business cycle, and current monetary policy in the United States. Etc.
Principles of Microeconomics Notes
1. International trade allows countries to benefit from specializing in goods where they have a comparative advantage and trading for other goods.
2. While Luxembourg has an absolute advantage in both TVs and t-shirts, it has a comparative advantage in TVs due to lower opportunity costs of production. Burundi has a comparative advantage in t-shirts.
3. When Luxembourg and Burundi specialize and trade according to their comparative advantages, both countries increase their overall production possibilities through gains from trade.
Principles of Microeconomics Midterm 2 "Cheat Sheet"
Own price elasticity of demand measures how responsive consumers are to changes in the price of a good. Income elasticity of demand measures responsiveness to changes in consumer income. Supply elasticity measures producer responsiveness to price changes. More inelastic sides of demand and supply curves are more affected by taxes and subsidies. Externalities occur when an action imposes positive or negative effects on a third party not involved in the primary transaction.
IB Theory of Knowledge EA: Disagreement Between Experts in a Discipline
Given access to the same facts, experts can still disagree due to various intrinsic and extrinsic factors. In ethics, disagreements arise from differences in personal backgrounds and political views, allowing issues to be understood from multiple perspectives. However, in natural science disagreements often create uncertainty, especially when not resolved. Motivations like gaining prestige or attention can influence experts' conclusions. While disagreements advance knowledge by disproving theories, they can confuse non-experts if leading to unresolved debates. Overall, disagreements among experts affect both the depth of knowledge in their discipline and how the public understands issues.
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IB Math SL IA: Probability in Guess Who
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2) Through creating tree diagrams and calculating probabilities, the analysis found that asking about common traits leads to a 76% chance of winning when going first and a 5% chance when going second.
3) Testing this with 20 games against siblings found an 85% win rate for the common trait strategy, somewhat higher than predicted due to the small sample size.
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IB Extended Essay: Comparison of the Effects of Vegan and Meat Inclusive Diet...
This document is a 3,552 word extended essay that investigates the differing effects of vegan and omnivorous diets on pollution. The essay begins with an abstract and introduction describing the motivation and research question. It then outlines the methods used, which involved analyzing secondary sources from books, websites, and journals. The main body of the essay discusses the key findings. It concludes that while both diets impact the environment, an omnivorous diet that includes meat production has significantly greater negative effects through higher greenhouse gas emissions, water pollution from animal waste, and soil erosion from cattle farming. Overall, the essay determines that a vegan diet creates less pollution than an omnivorous diet.
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Lecture slide titled Tax System, Behaviour, Justice, and Voluntary Compliance Culture in Nigeria - Prof Oyedokun.pptxAbhay Bhutada Leads Poonawalla Fincorp To Record Low NPA And Unprecedented Gr...
Under the leadership of Abhay Bhutada, Poonawalla Fincorp has achieved record-low Non-Performing Assets (NPA) and witnessed unprecedented growth. Bhutada's strategic vision and effective management have significantly enhanced the company's financial health, showcasing a robust performance in the financial sector. This achievement underscores the company's resilience and ability to thrive in a competitive market, setting a new benchmark for operational excellence in the industry.
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Vicinity Jobs’ data includes more than three million 2023 OJPs and thousands of skills. Most skills appear in less than 0.02% of job postings, so most postings rely on a small subset of commonly used terms, like teamwork.
Laura Adkins-Hackett, Economist, LMIC, and Sukriti Trehan, Data Scientist, LMIC, presented their research exploring trends in the skills listed in OJPs to develop a deeper understanding of in-demand skills. This research project uses pointwise mutual information and other methods to extract more information about common skills from the relationships between skills, occupations and regions.1. Elemental Economics - Introduction to mining.pdf
After this first you should: Understand the nature of mining; have an awareness of the industry’s boundaries, corporate structure and size; appreciation the complex motivations and objectives of the industries’ various participants; know how mineral reserves are defined and estimated, and how they evolve over time.
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Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.1：1制作加拿大麦吉尔大学毕业证硕士学历证书原版一模一样
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- 1. - population ( parameters M ) - ( l - a) is confidence level + = ⇒ - finite ( N ) - PC tzta ,✓)=F Str ~tn -1 - simple random sample [ I - ten 'Fn ,I+tE,v . In ] 4. Determine crit . value ( same prob . of being selected ) - When n > 1000 , Use Standard - lowertailtestcha :m< Mo ) :P( ztzxta - infinite normal Table - uppertailtestltta :M > Mo ) :P( 2 > Zxkx - random sample ( each elm . 2. population proportion twotailtestltta :m¥mo ) Comes from same pop . E. is - ( 1 - X ) is Confidence level - lfteststatoo :P( 2<-2 ; )=E selected independently ) [ F- 2 ; F "n⇒ ' , 15+2; F "n→ ' ] - ifteststat > o :p( z > zq)=E - pop . mean : M . desirable margin of error 5. Compare Critval . { test . Stat - pop . Std :O - pop . mean WIO known towertailtest : lfteststattzxirejecttto - pop . proportion :p - Zxz Fntmarginoferrr - upper tail test :# teststat > zx : reject Ho . Sample ↳ solve n - twotailtest : - point estimator - pop . prop . - Ifteststatcoteststattzairejecttto - sample Mean :I - 2g #nt= margin of error - ifteststat > oteststat > zq : reject Ho - sample Std :S 3. difference in means type terror : reject Ho when - sample proportion :p - A=I , - Iz Hoistrul - Underlying pop has expected - E 1 d) =M , - Mz type # error : accept Ho value ME variance 02 - Varcd )=¥+ ⇒ when Ho is false - ELI )=M - a~N( M , - Mz , # + ¥ ) . level ofsig ( × ) : maxprob . 02 - Vara )=T a) O , ,Oz known that can be tolerated for - Stdlx )= TF =0E [ ixixz , .ee#Font.uixz)+qfEn.+nEztftypeIerr0r ↳ standard error of mean . p - value approach ( Gknown ) - I~N( M , # ) if pop . b) 0 , ,0z Unknown 1. Develop Ho , Ha is normally distributed or → assume 0 ,=oz=op 2. Specify × if n >_ 30 ( central limit theorem )Var(4) =Op2(÷ntn÷ ) 3. Cakteststat Z* - EC f) =÷E( xktnlnp )=p . Pooled sample variance 4. Computers - value - Var( F) = ( ht )2Var( × ) - sp2= 5 ? ( ni - 1) +5221^2-1 ) - lowertailtest :p . vai .=p(z<z* ) = ntznp ( 1 - D) = #fe= 0,52 Ni + nz - 2 - upper tail test :p -val=p( 2>2*1 - Std (f) = 0,5=5*3 ' - Var (d) ~~Sp2( F. + th ) - ztail : if 2*0 ,p-vai=zp(2<z* ) ↳ standard error - Std (d) = Sptnfhz ifz*>o ,p-vai=zp( 2>2*1 - F~N( p , #n# ) When - Uset - distribution 5. Compare p-valGx npzg { n( 1 - p )z5 [hiixzttezirspfnttnz .LI#zlttE.vsPFnntz ] - If pval > x. cannot reject Ho . Interval Estimation - V=n,+nz - 2 - lfp . vak x. reject Ho 1. pop . mean M . hypothesis testing pop . prop . - teststat :Z*= F - P a) oknown - Critical value approach repos - ( l - X ) is Confidence ( Usedfcroknownoq - Canusecritval . orpval . difference in means level UNKNOWN ) - easel :O , Gozknown - PL - BEZE b) =1 - X 1. Develop Ho , Ha Teststat :z*=I . - Ez - do IOI - b) =F 2. Specify levelofsigx It # PCZ > ZE )= E 3. cake . test Stat - Case 2 :O , EQ unknown - Assume 01=02 [ I -2g . In ,I+Zq . # ] Z for 0 known tes+s+a+:t*= I # 2- do b) 0 Unknown I - Mo SP in , + 's Ztoyn ~N( Oil ) * useomycritval . approach- t distribution degrelsoffreedomfort : n , + nz - 2 - degrees of freedom =V=n - Itfor 0 unknown