Probability & Statistics Probability Theory Mathematical Probability Models Event Relationships Distributions of Random Variables Continuous Random.

Slides:

Advertisements

Similar presentations

Modeling of Data. Basic Bayes theorem Bayes theorem relates the conditional probabilities of two events A, and B: A might be a hypothesis and B might.

Advertisements

Special random variables Chapter 5 Some discrete or continuous probability distributions.

Let X 1, X 2,..., X n be a set of independent random variables having a common distribution, and let E[ X i ] = . then, with probability 1 Strong law.

Exponential Distribution. = mean interval between consequent events = rate = mean number of counts in the unit interval > 0 X = distance between events.

Probability Distribution

Review of Basic Probability and Statistics

Programme in Statistics (Courses and Contents). Elementary Probability and Statistics (I) 3(2+1)Stat. 101 College of Science, Computer Science, Education.

Estimation of parameters. Maximum likelihood What has happened was most likely.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference (Sec. )

Samples vs. Distributions Distributions: Discrete Random Variable Distributions: Continuous Random Variable Another Situation: Sample of Data.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Continuous random variables Uniform and Normal distribution (Sec. 3.1, )

Overview of STAT 270 Ch 1-9 of Devore + Various Applications.

Probability theory 2011 Outline of lecture 7 The Poisson process  Definitions  Restarted Poisson processes  Conditioning in Poisson processes  Thinning.

A random variable that has the following pmf is said to be a binomial random variable with parameters n, p The Binomial random variable.

The moment generating function of random variable X is given by Moment generating function.

Syllabus for Engineering Statistics Probability: rules, cond. probability, independence Summarising and presenting data Discrete and continuous random.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Special discrete distributions Sec

One Sample  M ean μ, Variance σ 2, Proportion π Two Samples  M eans, Variances, Proportions μ1 vs. μ2 σ12 vs. σ22 π1 vs. π Multiple.

PROBABILITY REVIEW PART 2 PROBABILITY FOR TEXT ANALYTICS Thomas Tiahrt, MA, PhD CSC492 – Advanced Text Analytics.

Statistics for Engineer Week II and Week III: Random Variables and Probability Distribution.

Random Variables and Stochastic Processes –

Poisson Random Variable Provides model for data that represent the number of occurrences of a specified event in a given unit of time X represents the.

Advanced Higher Statistics Data Analysis and Modelling Hypothesis Testing Statistical Inference AH.

Probability Definitions Dr. Dan Gilbert Associate Professor Tennessee Wesleyan College.

The Triangle of Statistical Inference: Likelihoood Data Scientific Model Probability Model Inference.

Math b (Discrete) Random Variables, Binomial Distribution.

Lecture V Probability theory. Lecture questions Classical definition of probability Frequency probability Discrete variable and probability distribution.

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

Methodology Solving problems with known distributions 1.

Probability Refresher COMP5416 Advanced Network Technologies.

IE 300, Fall 2012 Richard Sowers IESE. 8/30/2012 Goals: Rules of Probability Counting Equally likely Some examples.

4.3 More Discrete Probability Distributions NOTES Coach Bridges.

Probability and Statistics Dr. Saeid Moloudzadeh Uniform Random Variable/ Normal Random Variable 1 Contents Descriptive Statistics Axioms.

Chapter 3 Statistical Models or Quality Control Improvement.

A Joint Distribution of Discrete Random Variables X Marginal Y Distribution Of Y Marginal Distribution.

Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:

Statistical NLP: Lecture 4 Mathematical Foundations I: Probability Theory (Ch2)

Introduction A probability distribution is obtained when probability values are assigned to all possible numerical values of a random variable. It may.

Lec. 19 – Hypothesis Testing: The Null and Types of Error.

Discrete Probability Distributions Chapter 4. § 4.3 More Discrete Probability Distributions.

Probability and Statistics Dr. Saeid Moloudzadeh Poisson Random Variable 1 Contents Descriptive Statistics Axioms of Probability Combinatorial.

Statistics -Continuous probability distribution 2013/11/18.

The Pure Birth Process Derivation of the Poisson Probability Distribution Assumptions events occur completely at random the probability of an event occurring.

Chapter 6 – Continuous Probability Distribution Introduction A probability distribution is obtained when probability values are assigned to all possible.

Statistical Modelling

Advanced Higher Statistics

IEE 380 Review.

Discrete Probability Distributions

STAT 312 Chapter 7 - Statistical Intervals Based on a Single Sample

PROBABILITY DISTRIBUTION Dr.Fatima Alkhalidi

Introduction to logistic regression a.k.a. Varbrul

AP Statistics: Chapter 7

TM 605: Probability for Telecom Managers

Maximum Likelihood Find the parameters of a model that best fit the data… Forms the foundation of Bayesian inference Slide 1.

The Normal Probability Distribution Summary

Sampling Distribution

Sampling Distribution

Working with Continuous Random Variables and the Normal Distribution

Lecture Slides Elementary Statistics Twelfth Edition

Statistical NLP: Lecture 4

Categorical Data Analysis

CHAPTER 6 Statistical Inference & Hypothesis Testing

CHAPTER 15 SUMMARY Chapter Specifics

Vital Statistics Probability and Statistics for Economics and Business

Introduction to Probability Distributions

Chapter 3 : Random Variables

Introduction to Probability Distributions

Statistical Models or Quality Control Improvement

1/2555 สมศักดิ์ ศิวดำรงพงศ์

Presentation transcript:

Probability & Statistics Probability Theory Mathematical Probability Models Event Relationships Distributions of Random Variables Continuous Random Variables Normal Log Normal Extreme Value Discrete Random Variables Bernoulli Poisson Stochastic Processes

Probability & Statistics Probability Theory Statistical Analysis Mathematical Probability Models Analysis of Data Event Relationships Estimation of Parameters Distributions of Random Variables Fitting of Distributions Continuous Random Variables Hypothesis Testing Normal Design of Experiments Log Normal Extreme Value Discrete Random Variables Bernoulli Poisson Stochastic Processes