Ppt on statistics and probability formulas

AP Statistics 41 days until the AP Exam

I can apply the properties and formulas of sampling distributions for proportions Quick Review The formula for the mean of a sampling distribution is: The formula for the standard deviation of the mean of a sampling distribution is: A parameter is: A statistic is: The symbol for population/Draw the sampling distribution of based on a random sample of 400. b) When n = 400, what is ? c) Is the probability in part (b.) larger or smaller than would be the case if n = 500? Think, don’t calculate. Example 4 A /

Università di Milano-Bicocca Laurea Magistrale in Informatica Corso di APPRENDIMENTO E APPROSSIMAZIONE Prof. Giancarlo Mauri Lezione 5 - Statistical Learning.

uniform prior (which is reasonable if all hypotheses are of the same complexity) ML is the standard (non-Bayesian) statistical learning method ML parameter learning Bag from a new manufacturer; fraction of cherry candies? Any is possible: continuum of/One more assumption FORMULA Learn_Naive_Bayes_Text (Examples, V) 1. Collect all words and other tokens that occur in Examples - Vocabulary all distinct words and other tokens in Examples 2. Calculate the required P(v j ) and P(w k |v j ) probability terms - For/

Lecture Slides Elementary Statistics Tenth Edition

. (The sampling distribution of the mean is typically represented as a probability distribution in the format of a table, probability histogram, or formula.) Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definition The value of a statistic, such as the sample mean x, depends on the particular values included in the sample, and generally varies from sample to sample. This variability of a/

CIVE2602 - Engineering Mathematics 2.2 (20 credits) Statistics and Probability Lecture 9 Hypothesis testing –Examples Undertaking experiments t-test for.

CIVE2602 - Engineering Mathematics 2.2 (20 credits) Statistics and Probability Lecture 9 Hypothesis testing –Examples Undertaking experiments t-test for two sample means P-values F-tests Dr D Borman ©Claudio Nunez / with an unknown σ (population standard deviation) Use the t-test n x =5 n y =5 X =24,Y =27Find sample means: Find sample standard deviation: Formula B: Formula A: Degrees of freedom, v = n – 2 = 5+5 -2 = 8 (assume underlying population is Normally distributed) F-test – test on the variance So/

GCSE Mathematics Linear Route Map – Foundation Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Common content: Estimation Optional content:

JULY Holiday Year 13 REVISION Year 12 Taxation: Income tax and National Insurance Taxation: Income tax and National Insurance Graphical representation Graphical representation STATISTICAL TECHNIQUES 2 STATISTICAL TECHNIQUES 2 Correlation and regression Correlation and regression STATISTICAL TECHNIQUES 3 STATISTICAL TECHNIQUES 3 Probabilities and estimation Probabilities and estimation CRITICAL PATH AND RISK ANALYSIS 3 CRITICAL PATH AND RISK ANALYSIS 3 Cost benefit analysis Cost benefit analysis CRITICAL/

Briggs UT-Dallas GISC 6382 Spring 2007

Statistics: Bivariate Calculation Formulae for Pearson Product Moment Correlation Coefficient (r) Correlation Coefficient example using “calculation formulae” As we explore spatial statistics, we will see many analogies to the mean, the variance, and the correlation coefficient, and their various formulae/ assumption made regarding the type of sampling involved: Free (or normality) sampling assumes that the probability of a polygon having a particular value is not affected by the number or arrangement of the/

GCSE Mathematics Linear Route Map – Higher Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Year 10 NumberAlgebra Statistics Ratio, proportion.

Simultaneous equations Simultaneous equations Probability Review and revision 9 Statistics recap and review Algebra: introduction to quadratics and rearranging formulae Algebra: introduction to quadratics and rearranging formulae Volume Algebra recap and review Algebra recap and review Linear and quadratic equations and their graphs Linear and quadratic equations and their graphs Sketching graphs Sketching graphs Geometry and measures recap and review Geometry and measures recap and review GCSE Mathematics/

4 - 1 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Statistics for Managers Using Microsoft Excel Basic Probability & Discrete.

l Addition rule l Conditional probability formula l Multiplication rule 4 - 23 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Event Probability Using Contingency Table Joint Probability Marginal (Simple) Probability 4 - 24 © 1998 Prentice-Hall, Inc. Statistics for Managers Using Microsoft Excel, 1/e Contingency Table Example Experiment: Draw 1 card. Note kind, color & suit. P(Ace) P(Ace AND Red)P(Red) 4/

Statistical Probabilistic Model Checking Håkan L. S. Younes Carnegie Mellon University.

Holds in state s iff probability is at least  that  holds over paths starting in s P <  (  )   P ≥1–  (  ) 7 Path Formulas Until:  1 U ≤T  2 Holds over path  iff  2 becomes true in some state along  before time T, and  1 is true in/sampling can be used to verify probabilistic properties of systems Sequential acceptance sampling adapts to the difficulty of the problem Statistical methods are easy to parallelize 28 Other Research Failure trace analysis “failure scenario” [Younes & Simmons 2004a] /

G. Cowan Statistics for HEP / LAL Orsay, 3-5 January 2012 / Lecture 2 1 Statistical Methods for Particle Physics Lecture 2: Tests based on likelihood ratios.

://www.pp.rhul.ac.uk/~cowan/stat_orsay.html G. Cowan Statistics for HEP / LAL Orsay, 3-5 January 2012 / Lecture 2 2 Outline Lecture 1: Introduction and basic formalism Probability, statistical tests, confidence intervals. Lecture 2: Tests based on likelihood ratios/ for fairly small samples. Median[q 0 |1] from Asimov data set; good agreement with MC. 37 Monte Carlo test of asymptotic formulae G. Cowan Statistics for HEP / LAL Orsay, 3-5 January 2012 / Lecture 2 Consider again n ~ Poisson (  s + b), m ~/

Outliers Split-sample Validation

3 To include the cases for the teaching sample, we enter the selection criteria: "split = 1". After completing the formula, click on the Continue button to close the dialog box. Selecting the teaching sample - 4 To activate the selection, / to full model - 1 In the cross-validation analysis, the relationship between the independent variables and the dependent variable was statistically significant. The probability for the model chi-square (17.487) testing overall relationship was = 0.008. The significance/

1 Sociology 601, Class 4: September 10, 2009 Chapter 4: Distributions Probability distributions (4.1) The normal probability distribution (4.2) Sampling.

statistics and p-values using DISPLAY NORMPROB and DISPLAY INVNORM note differences between these results and Page 668! display invnorm(.025) -1.959964 display invnorm(.975) 1.959964 * to verify that +/-1.96 are the z-scores you want display normprob(-1.96).0249979 display normprob(1.96).9750021 18 Notes about working with the normal curve The table for deriving probabilities/ error of a sample shrinks as n increases Recall the formula for a variance of a probability distribution: σ 2 = Σ((y – μ) 2 * /

Outliers Split-sample Validation

3 To include the cases for the teaching sample, we enter the selection criteria: "split = 1". After completing the formula, click on the Continue button to close the dialog box. Selecting the teaching sample - 4 To activate the selection, / to full model - 1 In the cross-validation analysis, the relationship between the independent variables and the dependent variable was statistically significant. The probability for the model chi-square (17.487) testing overall relationship was = 0.008. The significance/

Chapter 6 The Normal Distribution and Other Continuous Distributions

X to the standardized normal (the “Z” distribution) by subtracting the mean of X and dividing by its standard deviation: The Z distribution always has mean = 0 and standard deviation = 1 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.. The Standardized Normal Probability Density Function The formula for the standardized normal probability density function is Where e = the mathematical constant approximated by 2.71828 π = the mathematical/

Multiple Regression – Assumptions and Outliers

, select the Compute… command from the Transform menu. Formula for probability for Mahalanobis D² First, in the target variable text box, type the name "p_mah_1" as an acronym for the probability of the mah_1, the Mahalanobis D² score. Second,/variables at least 5 to 1? No Inappropriate application of a statistic Yes Run regression again using transformed variables and eliminating outliers Impact of assumptions and outliers - 4 Yes Probability of ANOVA test of regression less than/equal to level of /

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-1 Chapter 6 The Normal Distribution and Other Continuous Distributions.

Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-72 Chapter Summary  Presented key continuous distributions  normal, uniform, exponential  Found probabilities using formulas and tables  Recognized when to apply different distributions  Applied distributions to decision problems Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-73 Chapter Summary  Introduced sampling distributions  Described the sampling distribution of the mean/

G. Cowan Statistical Data Analysis / Stat 4 1 Statistical Data Analysis Stat 4: confidence intervals, limits, discovery London Postgraduate Lectures on.

cover the true value of  with probability ≥ 1 . Equivalent to confidence belt construction; confidence belt is acceptance region of a test. Statistical Data Analysis / Stat 4 6 Relation between confidence interval and p-value Equivalently we can consider a significance/use where cf. Cowan, Cranmer, Gross, Vitells, arXiv:1007.1727, EPJC 71 (2011) 1554. 63 Monte Carlo test of asymptotic formulae G. Cowan Statistical Data Analysis / Stat 4 Consider again n ~ Poisson (  s + b), m ~ Poisson(  b) Use q  /

Chapter 6 Normal Probability Distributions

. (The sampling distribution of the mean is typically represented as a probability distribution in the format of a table, probability histogram, or formula.) Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definition The value of a statistic, such as the sample mean x, depends on the particular values included in the sample, and generally varies from sample to sample. This variability of a/

G. Cowan Shandong seminar / 1 September 2014 1 Some Developments in Statistical Methods for Particle Physics Particle Physics Seminar Shandong University.

probability, assuming μ, to find data at least as “extreme” as the data observed. The critical region of a test of size α can be defined from the set of data outcomes with p μ < α. Often use, e.g., α = 0.05. If observe x ∈ w μ, reject μ. G. Cowan Shandong seminar / 1 September 2014 4 Test statistics and/ 71 (2011) 1554 G. Cowan Shandong seminar / 1 September 2014 14 Monte Carlo test of asymptotic formula Here take  = 1. Asymptotic formula is good approximation to 5  level (q 0 = 25) already for b ~ 20. G./

Year 10.

with Fractions Decimals and Percentages Statistical Measures Summer Examinations and Revision Summer Examinations and Revision Year 11 AQA GCSE Mathematics (4365) Route Map – Foundation Tier Year 11 Probability 1 Representing Data Volume Fractions and Decimals Holiday Inequalities Enlargements Trial and Improvement Mock Examinations and Revision Mock Examinations and Revision Holiday Holiday Percentages Ratios Scatter Graphs Maps and Scale Drawings Algebra Recap Holiday Formulae Constructions Loci Quadratic/

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 6-1 Chapter 6 The Normal Distribution and Other Continuous Distributions Basic Business.

Prentice-Hall, Inc. Chap 6-56 Chapter Summary  Presented key continuous distributions  normal, uniform, exponential  Found probabilities using formulas and tables  Recognized when to apply different distributions  Applied distributions to decision problems Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 6-57 Mean and Standard Deviation of the Uniform Distribution Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 6-58 指數分數 ─ 林惠玲、陳正倉「應用統計學」 p.226 Basic Business/

Lesson 6: Queues and Markov Chains

(ii) the queuing system is described by an ergodic process (time averages are equal to the corresponding statistical averages). The Little formula relates T and N quantities for a queue ( denotes the ‘mean rate of requests accepted into the system’): J. C./ the same derivations made in the M/M/S case, we can obtain the following state probability distribution: © 2013 Queuing Theory and Telecommunications: Networks and Applications – All rights reserved The M/M/S/S Queue (cont’d) Since the mean/

Statistical Inference I: Hypothesis testing; sample size

not reject H0 Type II Error (β) Review Question 1 If we have a p-value of 0.03 and so decide that our effect is statistically significant, what is the probability that we’re wrong (i.e., that the hypothesis test gave us a false positive)? .03 .06/power to detect a reduction of 10 points or more in the treatment group relative to placebo. What is 10 in your sample size formula? a. Standard deviation b. mean change c. Effect size d. Standard error e. Significance level Homework Problem Set 3 Reading: continue/

INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2007 Pearson Education Asia Chapter 8 Introduction to Probability.

. To develop the notion of independent events. To develop Bayes’s formula. Chapter 8: Introduction to Probability and Statistics Chapter Objectives  2007 Pearson Education Asia Basic Counting Principle and Permutations Combinations and Other Counting Principles Sample Spaces and Events Probability Conditional Probability and Stochastic Processes Independent Events Bayes’ Formula 8.1) 8.2) 8.3) 8.4) Chapter 8: Introduction to Probability and Statistics Chapter Outline 8.5) 8.6) 8.7)  2007 Pearson/

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 6 Random Variables 6.3 Binomial and Geometric.

1, 2, 3,.... Like binomial random variables, it is important to be able to distinguish situations in which the geometric distribution does and doesn’t apply! The Practice of Statistics, 5 th Edition30 The Practice of Statistics, 5 th Edition31 Geometric Probability Formula The Lucky Day Game. The random variable of interest in this game is Y = the number of guesses it takes to correctly/

What is statistic. Statistics is a tool for creating an understanding from a set of numbers.

it is used to draw conclusions or inferences about characteristics of populations based on data from a sample. We use statistics to make inferences about parameters. Therefore, we can make an estimate, prediction, or decision about a population based on/two chess players played 12 games, what is the probability that Player A would win 7 games, Player B would win 2 games, and the remaining 3 games would be drawn?" The following formula gives the probability of obtaining a specific set of outcomes when there /

Statistical Modelling Chapter VI 1 VI. Determining the analysis of variance table VI.AThe procedure VI.B The Latin square example VI.C Rules for determining.

. Order (high to low) of precedence of operators in a structure formula is ‘  ’, ‘/’, ‘*’ and ‘+’. For example, the structure formula A * B / C is the same as A * ( B / C ). Statistical Modelling Chapter VI 23 Example VI.1 Calf diets (continued) The factors/levels for the factor can be described using a probability distribution function. Definition VI.11: A factor will be designated as fixed if it is anticipated that a probability distribution function will not provide a satisfactory description the/

MGT-491 QUANTITATIVE ANALYSIS AND RESEARCH FOR MANAGEMENT OSMAN BIN SAIF Session 27.

Wallis test A paired sample t test Wilcoxin rank sum test Friedman test Correlation Regression F- test 2 Statistics in Business research Statistics is an area that most management and marketing students find difficult. The formulae are often complicated, the calculations tedious, degrees of freedom mysterious, and probability tables confusing. But in fact students need no longer grapple with any of these. In real life, business/

HCI 510 : HCI Methods I Statistics. HCI 510: HCI Methods I Descriptive Statistics Inferential Statistics Significance T-Test.

, the mean or average quiz score is determined by summing all the scores and dividing by the number of students taking the exam. Descriptive Statistics The Mean or average is probably the most commonly used method of describing central tendency. For example, consider the/ The bottom part is a measure of the variability or dispersion of the scores. T-Test Statistical Analysis of the t-test This formula is essentially another example of the signal-to- noise metaphor in research: the difference between the/

GCSE Mathematics Linear Route Map – Foundation Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Common content: Estimation Optional content:

and National Insurance Taxation: Income tax and National Insurance Graphical representation Graphical representation STATISTICAL TECHNIQUES 2 STATISTICAL TECHNIQUES 2 Correlation and regression Correlation and regression STATISTICAL TECHNIQUES 3 STATISTICAL TECHNIQUES 3 Probabilities and estimation Probabilities and estimation CRITICAL PATH AND RISK ANALYSIS 3 CRITICAL PATH AND/ Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation  Student /

Psychology 215: Statistics for Social Science Kate Bezrukova Introduction.

than that of the Ho , Type I error and p-value??  is the probability of a Type I error (e.g.,  =.05) a Type I error refers to when we mistakenly reject Ho. p-value is the probability of obtaining the sample statistic actually obtained, if Ho is true Testing the statistical significance of correlation coefficients definition formula: r -  t = s r ; s r = √ (1-r/

Lectures of Stat -145 (Biostatistics) Text book Biostatistics Basic Concepts and Methodology for the Health Sciences By Wayne W. Daniel Prepared By: Sana.

and Methodology for the Health Sciences86 Chapter 3 Probability The Basis of the Statistical inference Text Book : Basic Concepts and Methodology for the Health Sciences 88 Key words: Key words: Probability, objective Probability, Probability, objective Probability, subjective Probability, equally likely Mutually exclusive, multiplicative rule Conditional Probability, independent events, Bayes theorem Text Book : Basic Concepts and/ by the following formula Text Book : Basic Concepts and Methodology for the /

Program on « NONEQUILIBRIUM STEADY STATES » Institut Henri Poincaré 10 September - 12 October 2007 Pierre GASPARD Center for Nonlinear Phenomena and Complex.

and mass at unit temperature and density 0.001) STATISTICAL AVERAGE: PROBABILITY MEASURE Ergodicity (Boltzmann 1871, 1884): time average = phase-space average stationary probability density representing the invariant probability measure  Spectrum of unitary time evolution: Ergodicity: The stationary probability/ & THEIR HELFAND MOMENT Transport coefficients: Green-Kubo formula: microscopic current: Einstein formula: Helfand moment: Transport property: moment: self-diffusion: shear viscosity: bulk /

Statistics for clinicians Biostatistics course by Kevin E. Kip, Ph.D., FAHA Professor and Executive Director, Research Center University of South Florida,

. Prior: Posterior: Prior: Posterior: SECTION 2.5 Binomial Distribution Model Probability Model: Mathematical equation or formula used to generate probabilities based on certain assumptions about the process. Very important for statistical inference. Binomial Model: Two possible outcomes – often labeled as “success”/holds for samples that: Minimum[np, n(1-p)] > 5, where n is the sample size and p is probability of the outcome in the population. Central Limit Theorem (Practice) CharacteristicNµσµXµX σXσX Age /

G. Cowan Aachen 2014 / Statistics for Particle Physics, Lecture 41 Statistical Methods for Particle Physics Lecture 4: discovery, exclusion limits Graduierten-Kolleg.

G. Cowan Aachen 2014 / Statistics for Particle Physics, Lecture 42 Outline 1 Probability Definition, Bayes’ theorem, probability densities and their properties, catalogue of pdfs, Monte Carlo 2 Statistical tests general concepts, test statistics, multivariate methods, goodness-of/Cowan, Cranmer, Gross, Vitells, arXiv:1007.1727, EPJC 71 (2011) 1554. 51 Monte Carlo test of asymptotic formulae G. Cowan Aachen 2014 / Statistics for Particle Physics, Lecture 4 Consider again n ~ Poisson (  s + b), m ~ Poisson( /

G. Cowan Interdisciplinary Cluster Statistics Workshop, Munich, 17,18 Feb 2014 1 Overview of Statistical Methods in Particle Physics Glen Cowan Physics.

(2014) G. Cowan Interdisciplinary Cluster Statistics Workshop, Munich, 17,18 Feb 2014 32 Bayesian vs. Frequentist Approaches Frequentist: Probability only assigned to (repeatable) data outcomes. Results depend on probability for data found and not found, e.g., p-value/1007.1727, EPJC 71 (2011) 1554 40 Monte Carlo test of asymptotic formula G. Cowan Interdisciplinary Cluster Statistics Workshop, Munich, 17,18 Feb 2014 Here take  = 1. Asymptotic formula is good approximation to 5  level (q 0 = 25) already/

Discrete Probability Distributions Chapter66 Discrete Distributions Uniform Distribution Bernoulli Distribution Binomial Distribution Poisson Distribution.

Hypergeometric Formula Since the hypergeometric formula and tables are tedious and impractical, use Excel’s hypergeometric function to find probabilities. Hypergeometric Distribution Using Software: Excel Figure 6.27 6-97 6-98 Module 4, the probabilities are given below the graph. Copy and paste graph as a bitmap; copy and paste probabilities into Excel. “Spin” N and n; overlay a normal or binomial curve. Hypergeometric Distribution Using Software: Visual Statistics Figure/

PROBABILITY & STATISTICAL INFERENCE LECTURE 3 MSc in Computing (Data Analytics)

€35,000 - €40,000  Some Mathematical Jargon:  The formula for the normal distribution is formally called the normal probability density function (pdf) The Shaded portion of the Histogram is the Proportion of interest Can visualise this using the histogram of salaries. Since the histogram of salaries is symmetric and bell shaped, we model this in statistics with a Normal distribution curve. Proportion = the proportion/

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 Normal Distribution as an Approximation to the Binomial Distribution Section 5-6.

© 1998, Triola, Elementary Statistics Addison Wesley Longman 7 Figure 5-24 Solving Binomial Probability Problems Using a Normal Approximation Can the problem be easily solved with the binomial probability formula ? Use binomial probability formula Yes P( x ) =/ p x q (n – x ) !x! n!n! 7 6 5 4 Are np  5 and nq  5 both true ? No Yes Compute µ = np and  =  npq Draw the normal curve, and identify the region representing the probability/

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-1 Chapter 6 The Normal Distribution and Other Continuous Distributions.

Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-81 Chapter Summary  Presented key continuous distributions  normal, uniform, exponential  Found probabilities using formulas and tables  Recognized when to apply different distributions  Applied distributions to decision problems Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-82 Chapter Summary  Introduced sampling distributions  Described the sampling distribution of the mean/

Chapter 6 Normal Probability Distributions 6-1 Overview 6-2 The Standard Normal Distribution 6-3 Applications of Normal Distributions 6-4 Sampling Distributions.

of the mean is typically represented as a probability distribution in the format of a table, probability histogram, or formula.) Definition  The value of a statistic, such as the sample mean x, depends on the particular values included in the sample, and generally varies from sample to sample. This variability of a statistic is called sampling variability. Estimators Some statistics work much better than others as estimators/

SW388R7 Data Analysis & Computers II Slide 1 Multinomial Logistic Regression: Complete Problems Outliers and Influential Cases Split-sample Validation.

To include the cases for the teaching sample, we enter the selection criteria: "split = 1". After completing the formula, click on the Continue button to close the dialog box. SW388R7 Data Analysis & Computers II Slide 74 Selecting the/model to full model - 1 In the cross-validation analysis, the relationship between the independent variables and the dependent variable was statistically significant. The probability for the model chi- square (25.513) testing overall relationship was = 0.003. The significance/

Lecture 6. Basic statistical modeling The Chinese University of Hong Kong CSCI3220 Algorithms for Bioinformatics.

is equal to 0.7? Last update: 5-Oct-2015CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 201511 Statistical estimation Questions we can ask (cont’d): – Maximum likelihood estimation: Given a model with unknown parameter values, what / ln a > ln b) – This value can be found by differentiating the log likelihood and equating it to zero: – The formula for estimating the prior probabilities Pr(Y) can be similarly derived Last update: 5-Oct-2015CSCI3220 Algorithms for Bioinformatics | Kevin /

A Geographic Study Using Spatial Statistics. Problem Statement.

substantially more complex. See Wong and Lee p. 151 compared to p. 155 Gore/Bush 2000 by State Is there evidence of clustering? Join Count Statistic for Gore/Bush 2000 by State See spatstat.xls (JC-%vote tab) for data (assumes free or normality sampling) – The JC-%state tab uses % of states won, calculated using the same formulaeProbably not legitimate: need to use/

6.1 - 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 6 Normal Probability Distributions 6-1 Review and Preview 6-2 The Standard Normal.

are unaffected by previous outcomes, and independent events are easier to analyze and result in simpler calculations and formulas. 6.1 - 73 Copyright © 2010, 2007, 2004 Pearson Education, Inc. Caution Many methods of statistics require a simple random sample. /. Each trial must have all outcomes classified into two categories (commonly, success and failure). 4.The probability of success remains the same in all trials. Solve by binomial probability formula, Table A-1, or technology. 6.1 - 95 Copyright © 2010,/

STATISTICS PNPCOMPTROLLERSHIPCOURSE. Statistics The term has two meanings.The term has two meanings. Statistics (singular) is the science of collecting,

Statistics comprises those methods used to organize and describe information that has been collected.Descriptive Statistics comprises those methods used to organize and describe information that has been collected. Inferential Statistics involves the theory of probability and comprises those methods and techniques/= SS/ Σf The variance for a grouped data of a sample, denoted by s 2, is defined by the following formula: s 2 = SS/ (Σf -1) s 2 = SS/ (Σf -1) Standard Deviation The standard deviation is /

Chapter 3 Statistical thermodynamics Content 3.1 IntroductionIntroduction 3.2 Boltzmann statisticsBoltzmann statistics 3.3 Partition functionPartition.

energy, that is: 3.1.7 Kinds of statistical system MaxwellMaxwell-Boltzmann statistics usually called Boltzmann statisticsBoltzmann Bose-Einstein statisticsEinstein FermiFermi-Dirac statisticsDirac 3.2 Boltzmann Statistics Microcosmic state number of localized system Most probable distribution of localized system Degeneration Degeneration and Microcosmic state number Most probable distribution of non-localized system The other form of Boltzmann formula Entropy in Helmholz free energy expression 3.2.1/

1 STAT 500 – Statistics for Managers STAT 500 Statistics for Managers.

that the flight time is uniformly distributed between 4 hours and 5 hours. a)What is the probability that the flight will be no more than 10 minutes late? b)What is the probability that the flight will be no more than 30 /100) = 1 – e - x = 0.8647 Or you can use Excel formula, =EXPONDIST(100,1/50,1) P (X > 100) = 1 – 0.8647 = 0.1353 Exponential Probability Distribution - Example 25 STAT 500 – Statistics for Managers Agenda for this Session# 3 Part 3 Continuous Random Variables Uniform Distribution /

Briggs UT-Dallas GISC 6382 Spring 2007 1 Spatial Statistics Concepts (O&U Ch. 3) Centrographic Statistics (O&U Ch. 4 p. 77-81) – single, summary measures.

“calculation formulae” Classic Descriptive Statistics: Bivariate Calculation Formulae for Pearson Product Moment Correlation Coefficient (r) As we explore spatial statistics, we will see many analogies to the mean, the variance, and the correlation coefficient, and their various formulae There is/the assumption made regarding the type of sampling involved: –Free (or normality) sampling assumes that the probability of a polygon having a particular value is not affected by the number or arrangement of the /

GCSE Mathematics Linear Route Map – Foundation Tier Topic NumberAlgebra Geometry & Measures Topic Statistics Common content: Estimation Optional content:

STATISTICAL TECHNIQUES 2 STATISTICAL TECHNIQUES 2 Correlation and regression Correlation and regression STATISTICAL TECHNIQUES 3 STATISTICAL TECHNIQUES 3 Probabilities and estimation Probabilities and estimation AND OR AND Repayments and credit Repayments and/ Foundation  Savings Growth - Nuffield Foundation Savings Growth - Nuffield Foundation  Savings Facts and Formulae - Nuffield Foundation Savings Facts and Formulae - Nuffield Foundation  Student Loans 1 – MEI (Username: mei-imps Password: imps/