Random Number Generation

Documents about Random Number Generation

	lesson1 Colorado, AMATH 7400 Excerpt: ... Stochastic Simulation APPM 7400 Lesson 1: Random Number Generators August 25, 2008 Lesson 1: Random Number Generators () Stochastic Simulation August 25, 2008 1 / 29 Random Numbers What is a random number? Lesson 1: Random Number Generators ( ...
	RNGSoftware George Mason, CSI 709 Excerpt: ... B Software for Random Number Generation random number generation !software-( generation of random number!software-( C (programming language) Fortran! random number generation seed of a random number generator seed of a random number generator Random number generators are widely available in a variety of software packages. Although the situation may not be as dire as when Park and Miller (1988) stated, "good ones are hard to find", the user must be careful in selecting a random number generator. Basic Uniform Generators Some programming languages, such as C, Fortran, and Ada 95, provide builtin random number generators. In C, the generator is the function rand() in stdlib.h. This function returns an integer in the range 0 through RAND MAX, so the result must be normalized to the range (0, 1). (The scaling should be done with care. It is desirable to have uniform numbers in (0, 1) rather than [0, 1].) The seed for the C random number generator is set in srand(). In Fortran, the generator is the subroutine ran ...
	chap13 Cal Poly, CS 3734 Excerpt: ... Lecture Notes to Accompany Scientific Computing An Introductory Survey Second Edition by Michael T. Heath Chapter 13 Random Numbers and Stochastic Simulation Copyright c book. 2001. Reproduction permitted only for noncommercial, educational use ...
	hw7 NYU, G22 2112 Excerpt: ... Scientic Computing Homework 7 Due: Dec. 22 1. Exercise 3 at the end of the Lecture Notes chapter on Monte Carlo methods. Note that in Matlab, the uniform random number generator if RAND. 2. Exercise 4, same chapter. The ow chart of the code would be ...
	Assignment Five Western Michigan, ECE 580 Excerpt: ... ECE 5800 Severance Assignment Seven The purpose of this assignment is to investigate the statistical properties of the Linear Congruential Generation (LCG) algorithm discussed in lecture. This algorithm is implemented for you already in the form of ...
	randseed UCLA, CS 190 Excerpt: ... Routine Name: Description: Usage: Example: randseed Initializes random-number generator with new random seed. randseed [seed] genesis > echo {randseed} 803971369 genesis > randseed 54321 Re-seeding the random-number generator insures that a simulat ...
	Statistics6401Midterm CSU Mont. Bay, STATISTICS 6401 Excerpt: ... Statistics 6401 Midterm The Midterm will cover Chapters 4, 5, 6, 10 Sections 1,2,3 You may use one page of notes to write down the probability models and important formulas. Study the Homework problems, lecture notes, examples in the book. Topics: Discrete random variables: Expectation and Variance, pmf and cdf. Discrete probability models: prototype experiment, Bernoulli, Binomial, Poisson, Poisson Process, Geometric, Negative Binomial, Hypergeometric, know the means and variances for each model, convergence relationships. Continuous random variables: Expectation and Variance, pdf and cdf. Continuous probability models: Uniform, Normal, DeMoivre-Laplace limit theorem, Exponential, Gamma, Weibull, Beta, know the means and variances for each model. Functions of random variables: CDF Method, PDF Method, random number generation . Jointly distributed random variables: Discrete and Continuous, joint pmf and joint pdf. Independence and Dependence: Marginal and contional pmf and pdf. Sums of rand ...
	Readme CSU Long Beach, CECS 340 Excerpt: ... Excel Examples for Chapter 2, Discrete-Event System Simulation, 4th edition: Version 1, Dec 21, 2004 The examples have been tested in Excel 2000 (SP-3) and Excel 2003 (SP1), and get the same results in both versions. In these versions of Excel, y ...
	hw5 CSU Long Beach, HW 340 Excerpt: ... CECS 340 Homework Assignment 5, Spring 2006, Professor Ebert Show all work to receive credit. Total Points= 70 1. Use the Inverse Transform Technique to develop a random number generator for a random variable X whose range space is RX = [0, ] and w ...
	section2.2 Wisconsin Milwaukee, CS 526 Excerpt: ... Lehmer Random Number Generators: Implementation Discrete-Event Simulation: A First Course Section 2.2: Lehmer Random Number Generators: Implementation Section 2.2: Lehmer Random Number Generators: Implementation Discrete-Event Simulation c 2006 P ...
	Assignment Seven Western Michigan, ECE 580 Excerpt: ... ECE 5800 Fall 2008 Severance Assignment Seven Due 17 October 2008 The purpose of this assignment is to investigate the statistical properties of the Linear Congruential Generation (LCG) algorithm discussed in lecture. This algorithm is implemented ...
	section2.1 Wisconsin Milwaukee, CS 526 Excerpt: ... urn with replacement For practical reasons, we will draw without replacement If m is large and the number of draws is small relative to m, then the distinction is largely irrelevant Section 2.1: Lehmer Random Number Generators: Introduction Discrete-Event Simulation c 2006 Pearson Ed., Inc. 0-13-142917-5 Lehmer Random Number Generators: Introduction Lehmers Algorithm Lehmers algorithm for random number generation is dened in terms of two xed parameters: modulus m, a xed large prime integer multiplier a, a xed integer in Xm The integer sequence x0 , x1 , . . . is dened by the iterative equation xi+1 = g (xi ) with g (x) = ax mod m x0 Xm is called the initial seed Section 2.1: Lehmer Random Number Generators: Introduction Discrete-Event Simulation c 2006 Pearson Ed., Inc. 0-13-142917-5 Lehmer Random Number Generators: Introduction Lehmer Generators Because of the mod operator, 0 g (x) < m However, 0 must not occur since g (0) = 0 Since m is prime, g (x) = 0 if x ...
	assign5 CSU Long Beach, ASSIGN 340 Excerpt: ... CECS 340 Assignment 5, Fall 2005, Professor Ebert Due Date: Thursday, October 20th, 11:00AM 1. Use a random-number generator to generate (using a short C+ program or Excel) 1,000 data points for random variable X, where X has the uniform distributio ...
	lecture7 W. Alabama, CS 240 Excerpt: ... Randomized Quicksort Lower Bounds for Sorting Non-Comparison Sorting CS 240 Lecture 7 Instructor: Matthew Nichols1 D. R. Cheriton School of Computer Science, University of Waterloo October 2, 2007 1 Based on lecture notes by Therese Biedl Instruc ...
	CSIS110Lecture22 Fort Lewis, CSIS 110 Excerpt: ... CSIS 110 - Lecture 22 Announcements: Quiz Wednesday. Read Chapter 5, sections 5.1 to 5.4. Programming Assignment on course web page Midterm Grades: 30% Quizzes, 35% HW/Labs, 35% Programs Random Numbers In the real world, some things occur randomly, s ...
	CSIS110Lecture22 Fort Lewis, CSIS 110 Excerpt: ... CSIS 110 - Lecture 22 Announcements: Quiz Wednesday. Read Chapter 5, sections 5.1 to 5.4. Programming Assignment on course web page Midterm Grades: 25% Quizzes, 35% HW/Labs, 40% Programs Random Numbers In the real world, some things occur randomly, s ...
	CSIS110Lecture21 Fort Lewis, CSIS 110 Excerpt: ... CSIS 110 - Lecture 21 Announcements: Read Chapter 5, sections 5.1 to 5.4. Let's discuss the programming assignment any questions? I have your midterm grades if you want them, or you can wait until next week to look them up on WebOpus. No class next ...
	1903lab08 UWI Mona, IO 1903 Excerpt: ... ACS-1903 Lab 8 Nov 14, 2008 Arrays Hand this page in to your lab demonstrator Student number Name _ _ Summary: The purpose of this lab is to get experience working with arrays in Java. The files mentioned below are in this folder. 1. The file St ...
	Handout07 CSU Mont. Bay, WEEK 39004950 Excerpt: ... Handout07 Stat3900/4950 These two programs use random number generation to run simple simulations. See Cody&Smith Ch. 17 Sec. C ppp. 355-356 - /* This program simulates rolling a fair die 1000 times. / / To generate more random values, increase the number in the do loop. / data uni; n+1; do i = 1 to 1000; X = int(1 + 6ranuni(0); output; end; /* Note: The int( ) function in SAS truncates a value at the integer. / proc print data=uni; var X; run; / Plot a picture of the random numbers generated. / proc chart data=uni; vbar X / midpoints = 1 2 3 4 5 6; run; / Simulate heights of men from a Normal distribution with / / mean 65 and standard deviation 3. / data nor; n+1; do i = 1 to 100; Y = 65 + 3rannor(0); output; end; proc print data=nor; var Y; run; /* Plot a picture of the random numbers generated. */ proc chart data=nor ...
	BSM_Amp_Lecture UMBC, ENEE 785 Excerpt: ... e ratio Usat /Tamp , expressed in dBm. Finally, the small-signal gain, $UnsaturatedGaindB, of the amplier should be specied in dB. The small-signal gain in an amplier of length L is related to the parameter g0 by the equation G0 = exp(g0 L). 2 The amplier type that uses the xed output power is used to pin the ampliers output power to a particular level. I will not go into how this option works in this lecture. See the code for further details on this model. As yet, we do not have an amplier model that solves the rate equations in the ocsOptAmplier class, but Jonathan Hu has implemented this using measured data for the absorption and emission spectra of the erbium-doped bers we use in experiments. 3 Random number generation Random number generators are commonly used in computer science and applied math in many applications. In fact, many compilers have built-in random number generators (in C/C+, its the rand() function), but these tend to be very simple implementations. ...
	TP3 Rutgers, TP 3 Excerpt: ... PHYSICS 509, Assignment 4 Montecarlo Simulation of the 2-d Ising Model Announcement: There will be no lecture on Tuesday April 11th Friday April 14th and Tuesday April 18th. Classes will resume on Friday April 21st This problem set will explore the s ...
	08_c22 Old Dominion, CS 475 Excerpt: ... 231 1) then the quotient is q = m/a = 44488 and the remainder is r = m mod a = 3399. Similarly, if a = 16807 then q = 127773 and r = 2836. In both cases r < q. For all x Xm = {1, 2, . . . , m 1} dene the two functions (x) = a(x mod q) r x/q Then, for any x Xm g(x) = ax mod m = ax m ax/m = ax m x/q + m x/q m ax/m = ax (aq + r) x/q + m(x) = a x q x/q r x/q + m(x) = a(x mod q) r x/q + m(x) = (x) + m(x). An ecient, portable implementation of a Lehmer random number generator is based upon this alternate representation of g(x) and the following theorem. and (x) = x/q ax/m . 50 2. Random Number Generation Theorem 2.2.1 If m = aq + r is prime, r < q, and x Xm , then (x) = x/q ax/m is either 0 or 1. Moreover, with (x) = a(x mod q) r x/q (x) = 0 if and only if (x) Xm ; (x) = 1 if and only if (x) Xm . Proof First observe that if u and v are real numbers with 0 < u v < 1 then the integer dierence ...
	class26 Penn State, STAT 414 Excerpt: ... Uniform distribution, Random numbers, and Q-Q Plots Class 26 De.nition A continuous r.v. X has a uniform distribution, denoted U (a; b) ; if its p.d.f. is: f (x) = for a x b: 1 ba The distribution function of a uniform r.v. X is: F (x) = 0 for x < a xa F (x) = for a x < b ba F (x) = 1 for x b Theorems 1. The mean of a uniform r.v. X is = E (X) = a+b : 2 (ba)2 12 : 2. The variance of a uniform r.v. X is 2 = V ar (X) = 3. The m.g.f. of a uniform r.v. X is: M (t) = for t 6= 0: e tb eta t (b a) Applications 1. Random assignment to treatment. Randomly assign half of the class to "Lecture" and randomly assign half of the class to "Self-study." 2. Random selection for participation in a survey. Randomly select half of the class for participation in a survey on the quality of this class. 3. (Pseudo) random number generation . (a) Good random numbers should have no correlation, follow a certain probability distribution, be reproducible and cheap. (b) Software packages produce random numbers b ...
	CS483_HPC_Notes003A_EstimatingPI Wisc Platteville, CS 483 Excerpt: ... CS 483 High Performance Computing (HPC) Notes 003A Monte Carlo Estimation of PI 1 References 2 Monte Carlo Method Monte Carlo is world famous for gambling city. Gambling is based on random or pseudorandom occurrences of events that people try t ...
	lec16 UCSD, CSE 8 Excerpt: ... CSE 8A: Lecture 16 Random number generation Randomizing a sequence Automatic documentation generation and the Javadoc utility Package naming, and CLASSPATH (Reading: Savitch Ch 5 on Javadoc and Packages) CSE 8A, UCSD LEC 16 Page 1 of 21 Random number generation Random numbers are useful in many applications: cryptography, software testing, games, probabilistic data structures, etc. A truly random number would be truly unpredictable However, algorithms are predictable! So, you don't write a program to generate truly random numbers on a computer; you generate pseudorandom numbers (you could connect your computer to a nonalgorithmic device and collect truly random bits from it; see /dev/random on Unix systems, or various web services) A good pseudorandom number generator will generate a sequence of numbers that will pass most statistical tests of randomness. the numbers will look very random How to do that? CSE 8A, UCSD LEC 16 Page 2 of 21 Line ...