10.Deterministic Randomness 1.Random Sequences. 10.1.Random Sequences A sequence of numbers r 1, r 2,... is random if there are no discernible patterns.

Slides:

Advertisements

Similar presentations

Random Number Generation. Random Number Generators Without random numbers, we cannot do Stochastic Simulation Most computer languages have a subroutine,

Advertisements

Modeling and Simulation Monte carlo simulation 1 Arwa Ibrahim Ahmed Princess Nora University.

Random Number Generators. Why do we need random variables? random components in simulation → need for a method which generates numbers that are random.

06/05/2008 Jae Hyun Kim Chapter 2 Probability Theory (ii) : Many Random Variables Bioinformatics Tea Seminar: Statistical Methods in Bioinformatics.

Sampling Attila Gyulassy Image Synthesis. Overview Problem Statement Random Number Generators Quasi-Random Number Generation Uniform sampling of Disks,

Sep 16, 2005CS477: Analog and Digital Communications1 LTI Systems, Probability Analog and Digital Communications Autumn

Probability Distributions

CS 351/ IT 351 Modelling and Simulation Technologies Random Variates Dr. Jim Holten.

Pseudorandom Number Generators

Generating Continuous Random Variables some. Quasi-random numbers So far, we learned about pseudo-random sequences and a common method for generating.

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

Random Number Generation

1 Probability. 2 Probability has three related “meanings.” 1. Probability is a mathematical construct. Probability.

Continuous Random Variables and Probability Distributions

1 Simulation Modeling and Analysis Pseudo-Random Numbers.

Sep 20, 2005CS477: Analog and Digital Communications1 Random variables, Random processes Analog and Digital Communications Autumn

This is a discrete distribution. Poisson is French for fish… It was named due to one of its uses. For example, if a fish tank had 260L of water and 13.

Pseudorandom Number Generators. Randomness and Security Many cryptographic protocols require the parties to generate random numbers. All the hashing algorithms.

Lecture (16) Introduction to Stochastic Hydrology.

ETM 607 – Random Number and Random Variates

L7.1b Continuous Random Variables CONTINUOUS RANDOM VARIABLES NORMAL DISTRIBUTIONS AD PROBABILITY DISTRIBUTIONS.

Arithmetic Sequences. A sequence which has a constant difference between terms. The rule is linear. Example: 1, 4, 7, 10, 13,… (generator is +3) Arithmetic.

Random Numbers CSE 331 Section 2 James Daly. Randomness Most algorithms we’ve talked about have been deterministic The same inputs always give the same.

Dept of Bioenvironmental Systems Engineering National Taiwan University Lab for Remote Sensing Hydrology and Spatial Modeling STATISTICS Random Variables.

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.

Probability Distributions - Discrete Random Variables Outcomes and Events.

1 Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS Systems.

4.1 Probability Distributions. Do you remember? Relative Frequency Histogram.

22/10/2015 How many words can you make? Three or more letters Must all include A A P I Y M L F.

Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition.

Probabilistic and Statistical Techniques 1 Lecture 14 Dr. Nader Okasha.

© Buddy Freeman, Independence of error assumption. In many business applications using regression, the independent variable is TIME. When the data.

CHAPTER 10: Introducing Probability ESSENTIAL STATISTICS Second Edition David S. Moore, William I. Notz, and Michael A. Fligner Lecture Presentation.

Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition.

Random Number Generator. Random number Random number: Uniform distribution on [0,1] Random device: dice, coin -> cannot generate the equal sequence.

Essential Statistics Chapter 91 Introducing Probability.

CHAPTER 10 Introducing Probability BPS - 5TH ED.CHAPTER 10 1.

Chapter 10 Introducing Probability BPS - 5th Ed. Chapter 101.

Math 4030 – 6a Joint Distributions (Discrete)

CONTINUOUS RANDOM VARIABLES

8-3: Probability and Probability Distributions English Casbarro Unit 8.

4.3 More Discrete Probability Distributions NOTES Coach Bridges.

CHAPTER 5 Simulation Modeling. Introduction In many situations a modeler is unable to construct an analytic (symbolic) model adequately explaining the.

Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Engineering National Taiwan University 1/45 GEOSTATISTICS INTRODUCTION.

Continuous Random Variables and Probability Distributions

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

Chapter 20 Statistical Considerations Lecture Slides The McGraw-Hill Companies © 2012.

Master Method (4. 3) Recurrent formula T(n) = a  T(n/b) + f(n) 1) if for some  > 0 then 2) if then 3) if for some  > 0 and a  f(n/b)  c  f(n) for.

1 Chapter 10 Probability. Chapter 102 Idea of Probability u Probability is the science of chance behavior u Chance behavior is unpredictable in the short.

SS r SS r This model characterizes how S(t) is changing.

1 Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS Systems.

Module 9.4 Random Numbers from Various Distributions -MC requires the use of unbiased random numbers.

PH24010 MathCAD Statistics, Random Numbers & Histograms.

MONTE CARLO METHOD DISCRETE SIMULATION RANDOM NUMBER GENERATION Chapter 3 : Random Number Generation.

Fractiles Given a probability distribution F(x) and a number p, we define a p-fractile x p by the following formulas.

Random Variables By: 1.

Test for randomness : Chi square test

Continuous Probability Distribution

Review of Probability Theory

CONTINUOUS RANDOM VARIABLES

AP Statistics: Chapter 7

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

DRQ 8 Dr. Capps AGEC points

Distributions and expected value

Master Method (4. 3) Recurrent formula T(n) = aT(n/b) + f(n)

CS723 - Probability and Stochastic Processes

Statistics Lecture 12.

Random Variables A random variable is a rule that assigns exactly one value to each point in a sample space for an experiment. A random variable can be.

Uniform Probability Distribution

District Random Variables and Probability Distribution

Presentation transcript:

10.Deterministic Randomness 1.Random Sequences

10.1.Random Sequences A sequence of numbers r 1, r 2,... is random if there are no discernible patterns or regularities among them. A set of equally spaced numbers with equal probability of occurrence is called a discrete uniform distribution. A sequence with short range correlation can have an overall randomness : Tests for randomness (Kendall & Smith) : Frequency test : 1 digit. Serial test: 2 digits. Poker test: 5 digits. Gap test: gap between 0s.

A random (stochastic) variable is a variable that can take on a set or range of values, each with an associated probability. For a continuous random variable, the probability of finding it with value between r and r + dr is P(r) dr. P(r) = distribution function of the random variable. Uniform distribution P(r) = const. A random number generator generates sequences of uniformly distributed (pseudo-)random numbers.

Random Number Generator (Algorithm) Linear Congruence ( Power Residue ) Method To generate sequence { r 1, r 2,..., r k } over interval [ 0, M  1 ] : where a, c are some constants, & r 1 = seed. drand48: Ex Do § Ex Do §