Elementary Statistics and Inference. Elementary Statistics and Inference. 17 Expected Value and Standard Error. 22S:025 or 7P:025.

Size: px
Start display at page:

Download "Elementary Statistics and Inference. Elementary Statistics and Inference. 17 Expected Value and Standard Error. 22S:025 or 7P:025."

Transcription

1 Elementary Statistics and Inference S:05 or 7P:05 Lecture Elementary Statistics and Inference S:05 or 7P:05 Chapter 7 A. The Expected Value In a chance process (probability experiment) the outcomes of the chance process vary, but cluster around the expected value or the average. Example: Toss a coin 00 times. P( H ) = on each toss you would expect about 50% of the outcomes to be heads this is the expected value. Suppose in 00 tosses you obtained 57 heads, the difference between 57 and 50 is called chance error (+7). 3

2 Example: Suppose you selected 00 draws from the box, with replacement: 5 You would expect about ¾ of the 00 draws to be a, and about ¼ of the draws to be a 5. The expected sum would be (5 x 5) + (75 x ) = = The formula for the Expected Sum is: E( = (average of the number in the box) (number of draws) E ( sum ) = 00 = 00 4 E( = n (avg of box) = n X Note: see description on page 89 5 Example (page 89): Example : Suppose you are going to Las Vegas to play Keno. Your favorite bet is a dollar on a single number. When you win, they give you the dollar back and two dollars more. When you lose, they keep the dollar. There is a chance in 4 to win. About how much should you expect to win (or lose) in 00 plays, if you make this bet on each play? $.00 -$.00 -$.00 -$.00 P( W ) = 4 n=00 plays 6

3 average of the box = + ( 3) = $.5 4 E(= 00 avg of box = 00 (-$ $.5) = $ You would expect to lose $5 in 00 plays. 7 Exercise Set A (p. 90) #,, 3, 4, 5. Find the expected value for the sum of 00 draws at random with replacement from the box (a) 0 6 (b) (c) (d) Someone is going to play roulette 00 times, betting a dollar on the number 7 each time. Find the expected value for the net gain. (See pp ) 9 3

4 6. A game is fair if the expected value for the net gain equals 0: on the average, players neither win nor lose. A generous casino would offer a bit more than $ in winnings if a player staked $ on red-and-black in roulette and won. How much should they ypay to make it a fair game? (Hint: Let X stand for what they should pay. The box has 8 tickets X and 0 tickets -$. Write down the formula for the expected value in terms of X and set it equal to 0.) 0 8 X 0 Expected gain = = X 0 = 0 8X = 0 X = $. B. The Standard Error of the Sum Given the box: Avg of box = 5 / 5 = 3 4

5 In 5 draws with replacement, Expected Sum = E(=n avg of box E(=5 3=75 The actual sum will be Sum=expected value + chance error The chance error is a function of the standard deviation of the box. The chance error, called Standard Error (SE) is: SE = n (SD of box) See Note p. 9 3 In the box above, the SD of box =. (0 3) + ( 3) + (3 3) + (4 3) S = S = = = S = SE = 5 () = 0 + (6 3) 4 For the box example n = 5 draws with replacement The E( = n avg box = 5(3) = 75 SE( = n SD of box = 5() = 0 5 5

6 In 5 draws with replacement, we would expect the sum of the draws to be 75 give or take 0. Note: The sum of draws is likely to be around the expected value, give or take the standard error. Note: Observed values in a chance process are rarely more than or 3 standard errors away from the Expected Value. 6 Exercise Set B (p. 93) #,,

7 9 C. The Normal Curve For a large number of draws from a box, with replacement, the sum of the draws is approximately normally distributed. 0 Example: Suppose 5 draws with replacement are made from the box, with tickets as shown: X = avg of box = 3, S = SD of box = E( = n avg of box = 5 (3) = 75 SE ( = n SD of box = 5() = 0 Now the sums are approximately normally distributed with mean = 75, and S = 0. Find probability (chance) that the sum for any 5 draws will be between 50 and 00. 7

8 98.76% SE(=0 50 E(= sum sum mean Z = SE Using Normal Curve table we find 98.76% of the scores between ±.50 Standard Deviations from the mean. Example. In a month, there are 0,000 independent plays on a roulette wheel in a certain casino. To keep things simple, suppose the gamblers only stake $ on red at each play. Estimate the chance that the house will win more than $50 from these plays. (Red-or-black pays even money, and the house has 0 chances in 38 to win. Solution: What is probability that casino will gain $50.00 or more from 0,000 plays of roulette. 3 0 $ $ avg of box = expected gain on one play = = $ (.05) + 8(.05) S = 38 0(.95) + 8(.05) S = 38 S =

9 SD of box = $.998 $.00 E( = n avg of box E( = 0,000(.05) = $ SE( = n SD of box = 0,000() = 00 5 Find Probability (Chance) that sum is greater than $50. SE(=00 50 E(=500 0 X Z Z = = = Area between ±.50 = 98.76% Area less than -.50 = =.6% So about 99.3% for casino to win more than $50 in 0,000 roulette plays. Exercise Set C (pp ) #,, 3, 4, 5 7 9

10

AMS 5 CHANCE VARIABILITY

AMS 5 CHANCE VARIABILITY AMS 5 CHANCE VARIABILITY The Law of Averages When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So if the coin is tossed a large number of times, the number of heads and

More information

Elementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.

Elementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025. Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 20 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 16 (cont.) 2 D. Making a Box Model Key Questions regarding box What numbers

More information

$2 4 40 + ( $1) = 40

$2 4 40 + ( $1) = 40 THE EXPECTED VALUE FOR THE SUM OF THE DRAWS In the game of Keno there are 80 balls, numbered 1 through 80. On each play, the casino chooses 20 balls at random without replacement. Suppose you bet on the

More information

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values. MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

More information

The overall size of these chance errors is measured by their RMS HALF THE NUMBER OF TOSSES NUMBER OF HEADS MINUS 0 400 800 1200 1600 NUMBER OF TOSSES

The overall size of these chance errors is measured by their RMS HALF THE NUMBER OF TOSSES NUMBER OF HEADS MINUS 0 400 800 1200 1600 NUMBER OF TOSSES INTRODUCTION TO CHANCE VARIABILITY WHAT DOES THE LAW OF AVERAGES SAY? 4 coins were tossed 1600 times each, and the chance error number of heads half the number of tosses was plotted against the number

More information

Week 5: Expected value and Betting systems

Week 5: Expected value and Betting systems Week 5: Expected value and Betting systems Random variable A random variable represents a measurement in a random experiment. We usually denote random variable with capital letter X, Y,. If S is the sample

More information

MONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010

MONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010 MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times

More information

Chapter 16: law of averages

Chapter 16: law of averages Chapter 16: law of averages Context................................................................... 2 Law of averages 3 Coin tossing experiment......................................................

More information

13.0 Central Limit Theorem

13.0 Central Limit Theorem 13.0 Central Limit Theorem Discuss Midterm/Answer Questions Box Models Expected Value and Standard Error Central Limit Theorem 1 13.1 Box Models A Box Model describes a process in terms of making repeated

More information

Chapter 16. Law of averages. Chance. Example 1: rolling two dice Sum of draws. Setting up a. Example 2: American roulette. Summary.

Chapter 16. Law of averages. Chance. Example 1: rolling two dice Sum of draws. Setting up a. Example 2: American roulette. Summary. Overview Box Part V Variability The Averages Box We will look at various chance : Tossing coins, rolling, playing Sampling voters We will use something called s to analyze these. Box s help to translate

More information

Expected Value. 24 February 2014. Expected Value 24 February 2014 1/19

Expected Value. 24 February 2014. Expected Value 24 February 2014 1/19 Expected Value 24 February 2014 Expected Value 24 February 2014 1/19 This week we discuss the notion of expected value and how it applies to probability situations, including the various New Mexico Lottery

More information

Section 7C: The Law of Large Numbers

Section 7C: The Law of Large Numbers Section 7C: The Law of Large Numbers Example. You flip a coin 00 times. Suppose the coin is fair. How many times would you expect to get heads? tails? One would expect a fair coin to come up heads half

More information

Betting systems: how not to lose your money gambling

Betting systems: how not to lose your money gambling Betting systems: how not to lose your money gambling G. Berkolaiko Department of Mathematics Texas A&M University 28 April 2007 / Mini Fair, Math Awareness Month 2007 Gambling and Games of Chance Simple

More information

We rst consider the game from the player's point of view: Suppose you have picked a number and placed your bet. The probability of winning is

We rst consider the game from the player's point of view: Suppose you have picked a number and placed your bet. The probability of winning is Roulette: On an American roulette wheel here are 38 compartments where the ball can land. They are numbered 1-36, and there are two compartments labeled 0 and 00. Half of the compartments numbered 1-36

More information

Stat 20: Intro to Probability and Statistics

Stat 20: Intro to Probability and Statistics Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. Childers-Day UC Berkeley 22 July 2014 By the end of this lecture... You will be able to: Determine what we expect the sum

More information

John Kerrich s coin-tossing Experiment. Law of Averages - pg. 294 Moore s Text

John Kerrich s coin-tossing Experiment. Law of Averages - pg. 294 Moore s Text Law of Averages - pg. 294 Moore s Text When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So, if the coin is tossed a large number of times, the number of heads and the

More information

The Casino Lab STATION 1: CRAPS

The Casino Lab STATION 1: CRAPS The Casino Lab Casinos rely on the laws of probability and expected values of random variables to guarantee them profits on a daily basis. Some individuals will walk away very wealthy, while others will

More information

Chapter 17: expected value and standard error for the sum of the draws from a box

Chapter 17: expected value and standard error for the sum of the draws from a box Chapter 17: expected value and standard error for the sum of the draws from a box Context................................................................... 2 When we do this 10,000 times.....................................................

More information

Roulette Best Winning System!!!

Roulette Best Winning System!!! Roulette Best Winning System!!! 99.7% winning system - 100% risk free Guaranteed The roulette system detailed here is a well known winning system. Many people have made money out of this system, including

More information

Stat 20: Intro to Probability and Statistics

Stat 20: Intro to Probability and Statistics Stat 20: Intro to Probability and Statistics Lecture 18: Simple Random Sampling Tessa L. Childers-Day UC Berkeley 24 July 2014 By the end of this lecture... You will be able to: Draw box models for real-world

More information

Stat 134 Fall 2011: Gambler s ruin

Stat 134 Fall 2011: Gambler s ruin Stat 134 Fall 2011: Gambler s ruin Michael Lugo Setember 12, 2011 In class today I talked about the roblem of gambler s ruin but there wasn t enough time to do it roerly. I fear I may have confused some

More information

The Math. P (x) = 5! = 1 2 3 4 5 = 120.

The Math. P (x) = 5! = 1 2 3 4 5 = 120. The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct

More information

Probability: The Study of Randomness Randomness and Probability Models. IPS Chapters 4 Sections 4.1 4.2

Probability: The Study of Randomness Randomness and Probability Models. IPS Chapters 4 Sections 4.1 4.2 Probability: The Study of Randomness Randomness and Probability Models IPS Chapters 4 Sections 4.1 4.2 Chapter 4 Overview Key Concepts Random Experiment/Process Sample Space Events Probability Models Probability

More information

MrMajik s Money Management Strategy Copyright MrMajik.com 2003 All rights reserved.

MrMajik s Money Management Strategy Copyright MrMajik.com 2003 All rights reserved. You are about to learn the very best method there is to beat an even-money bet ever devised. This works on almost any game that pays you an equal amount of your wager every time you win. Casino games are

More information

The Normal Approximation to Probability Histograms. Dice: Throw a single die twice. The Probability Histogram: Area = Probability. Where are we going?

The Normal Approximation to Probability Histograms. Dice: Throw a single die twice. The Probability Histogram: Area = Probability. Where are we going? The Normal Approximation to Probability Histograms Where are we going? Probability histograms The normal approximation to binomial histograms The normal approximation to probability histograms of sums

More information

Statistics and Random Variables. Math 425 Introduction to Probability Lecture 14. Finite valued Random Variables. Expectation defined

Statistics and Random Variables. Math 425 Introduction to Probability Lecture 14. Finite valued Random Variables. Expectation defined Expectation Statistics and Random Variables Math 425 Introduction to Probability Lecture 4 Kenneth Harris kaharri@umich.edu Department of Mathematics University of Michigan February 9, 2009 When a large

More information

STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables

STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Discrete vs. continuous random variables Examples of continuous distributions o Uniform o Exponential o Normal Recall: A random

More information

MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC

MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC DR. LESZEK GAWARECKI 1. The Cartesian Coordinate System In the Cartesian system points are defined by giving their coordinates. Plot the following points:

More information

In the situations that we will encounter, we may generally calculate the probability of an event

In the situations that we will encounter, we may generally calculate the probability of an event What does it mean for something to be random? An event is called random if the process which produces the outcome is sufficiently complicated that we are unable to predict the precise result and are instead

More information

Roulette. Math 5 Crew. Department of Mathematics Dartmouth College. Roulette p.1/14

Roulette. Math 5 Crew. Department of Mathematics Dartmouth College. Roulette p.1/14 Roulette p.1/14 Roulette Math 5 Crew Department of Mathematics Dartmouth College Roulette p.2/14 Roulette: A Game of Chance To analyze Roulette, we make two hypotheses about Roulette s behavior. When we

More information

HONORS STATISTICS. Mrs. Garrett Block 2 & 3

HONORS STATISTICS. Mrs. Garrett Block 2 & 3 HONORS STATISTICS Mrs. Garrett Block 2 & 3 Tuesday December 4, 2012 1 Daily Agenda 1. Welcome to class 2. Please find folder and take your seat. 3. Review OTL C7#1 4. Notes and practice 7.2 day 1 5. Folders

More information

Slide 1 Math 1520, Lecture 23. This lecture covers mean, median, mode, odds, and expected value.

Slide 1 Math 1520, Lecture 23. This lecture covers mean, median, mode, odds, and expected value. Slide 1 Math 1520, Lecture 23 This lecture covers mean, median, mode, odds, and expected value. Slide 2 Mean, Median and Mode Mean, Median and mode are 3 concepts used to get a sense of the central tendencies

More information

Expected values, standard errors, Central Limit Theorem. Statistical inference

Expected values, standard errors, Central Limit Theorem. Statistical inference Expected values, standard errors, Central Limit Theorem FPP 16-18 Statistical inference Up to this point we have focused primarily on exploratory statistical analysis We know dive into the realm of statistical

More information

Probability and Expected Value

Probability and Expected Value Probability and Expected Value This handout provides an introduction to probability and expected value. Some of you may already be familiar with some of these topics. Probability and expected value are

More information

Chapter 5. Discrete Probability Distributions

Chapter 5. Discrete Probability Distributions Chapter 5. Discrete Probability Distributions Chapter Problem: Did Mendel s result from plant hybridization experiments contradicts his theory? 1. Mendel s theory says that when there are two inheritable

More information

Week 4: Gambler s ruin and bold play

Week 4: Gambler s ruin and bold play Week 4: Gambler s ruin and bold play Random walk and Gambler s ruin. Imagine a walker moving along a line. At every unit of time, he makes a step left or right of exactly one of unit. So we can think that

More information

Midterm Exam #1 Instructions:

Midterm Exam #1 Instructions: Public Affairs 818 Professor: Geoffrey L. Wallace October 9 th, 008 Midterm Exam #1 Instructions: You have 10 minutes to complete the examination and there are 6 questions worth a total of 10 points. The

More information

(SEE IF YOU KNOW THE TRUTH ABOUT GAMBLING)

(SEE IF YOU KNOW THE TRUTH ABOUT GAMBLING) (SEE IF YOU KNOW THE TRUTH ABOUT GAMBLING) Casinos loosen the slot machines at the entrance to attract players. FACT: This is an urban myth. All modern slot machines are state-of-the-art and controlled

More information

Expected Value and the Game of Craps

Expected Value and the Game of Craps Expected Value and the Game of Craps Blake Thornton Craps is a gambling game found in most casinos based on rolling two six sided dice. Most players who walk into a casino and try to play craps for the

More information

THE CHAOS THEORY ROULETTE SYSTEM

THE CHAOS THEORY ROULETTE SYSTEM THE CHAOS THEORY ROULETTE SYSTEM Please note that all information is provided as is and no guarantees are given whatsoever as to the amount of profit you will make if you use this system. Neither the seller

More information

V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPECTED VALUE

V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPECTED VALUE V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPETED VALUE A game of chance featured at an amusement park is played as follows: You pay $ to play. A penny and a nickel are flipped. You win $ if either

More information

Betting on Excel to enliven the teaching of probability

Betting on Excel to enliven the teaching of probability Betting on Excel to enliven the teaching of probability Stephen R. Clarke School of Mathematical Sciences Swinburne University of Technology Abstract The study of probability has its roots in gambling

More information

Chapter 26: Tests of Significance

Chapter 26: Tests of Significance Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the P-value: The area under

More information

Example. A casino offers the following bets (the fairest bets in the casino!) 1 You get $0 (i.e., you can walk away)

Example. A casino offers the following bets (the fairest bets in the casino!) 1 You get $0 (i.e., you can walk away) : Three bets Math 45 Introduction to Probability Lecture 5 Kenneth Harris aharri@umich.edu Department of Mathematics University of Michigan February, 009. A casino offers the following bets (the fairest

More information

Chapter 20: chance error in sampling

Chapter 20: chance error in sampling Chapter 20: chance error in sampling Context 2 Overview................................................................ 3 Population and parameter..................................................... 4

More information

Midterm Exam #1 Instructions:

Midterm Exam #1 Instructions: Public Affairs 818 Professor: Geoffrey L. Wallace October 9 th, 008 Midterm Exam #1 Instructions: You have 10 minutes to complete the examination and there are 6 questions worth a total of 10 points. The

More information

6.042/18.062J Mathematics for Computer Science. Expected Value I

6.042/18.062J Mathematics for Computer Science. Expected Value I 6.42/8.62J Mathematics for Computer Science Srini Devadas and Eric Lehman May 3, 25 Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that tells you

More information

3.2 Roulette and Markov Chains

3.2 Roulette and Markov Chains 238 CHAPTER 3. DISCRETE DYNAMICAL SYSTEMS WITH MANY VARIABLES 3.2 Roulette and Markov Chains In this section we will be discussing an application of systems of recursion equations called Markov Chains.

More information

Automatic Bet Tracker!

Automatic Bet Tracker! Russell Hunter Street Smart Roulette Automatic Bet Tracker! Russell Hunter Publishing, Inc. Street Smart Roulette Automatic Bet Tracker 2015 Russell Hunter and Russell Hunter Publishing, Inc. All Rights

More information

Expectations. Expectations. (See also Hays, Appendix B; Harnett, ch. 3).

Expectations. Expectations. (See also Hays, Appendix B; Harnett, ch. 3). Expectations Expectations. (See also Hays, Appendix B; Harnett, ch. 3). A. The expected value of a random variable is the arithmetic mean of that variable, i.e. E() = µ. As Hays notes, the idea of the

More information

You can place bets on the Roulette table until the dealer announces, No more bets.

You can place bets on the Roulette table until the dealer announces, No more bets. Roulette Roulette is one of the oldest and most famous casino games. Every Roulette table has its own set of distinctive chips that can only be used at that particular table. These chips are purchased

More information

Lecture 13. Understanding Probability and Long-Term Expectations

Lecture 13. Understanding Probability and Long-Term Expectations Lecture 13 Understanding Probability and Long-Term Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).

More information

This Method will show you exactly how you can profit from this specific online casino and beat them at their own game.

This Method will show you exactly how you can profit from this specific online casino and beat them at their own game. This Method will show you exactly how you can profit from this specific online casino and beat them at their own game. It s NOT complicated, and you DON T need a degree in mathematics or statistics to

More information

PROBABILITY C A S I N O L A B

PROBABILITY C A S I N O L A B A P S T A T S A Fabulous PROBABILITY C A S I N O L A B AP Statistics Casino Lab 1 AP STATISTICS CASINO LAB: INSTRUCTIONS The purpose of this lab is to allow you to explore the rules of probability in the

More information

Lecture 25: Money Management Steven Skiena. http://www.cs.sunysb.edu/ skiena

Lecture 25: Money Management Steven Skiena. http://www.cs.sunysb.edu/ skiena Lecture 25: Money Management Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Money Management Techniques The trading

More information

Random Variables. Chapter 2. Random Variables 1

Random Variables. Chapter 2. Random Variables 1 Random Variables Chapter 2 Random Variables 1 Roulette and Random Variables A Roulette wheel has 38 pockets. 18 of them are red and 18 are black; these are numbered from 1 to 36. The two remaining pockets

More information

Statistics 100A Homework 3 Solutions

Statistics 100A Homework 3 Solutions Chapter Statistics 00A Homework Solutions Ryan Rosario. Two balls are chosen randomly from an urn containing 8 white, black, and orange balls. Suppose that we win $ for each black ball selected and we

More information

THE ROULETTE BIAS SYSTEM

THE ROULETTE BIAS SYSTEM 1 THE ROULETTE BIAS SYSTEM Please note that all information is provided as is and no guarantees are given whatsoever as to the amount of profit you will make if you use this system. Neither the seller

More information

Unit 19: Probability Models

Unit 19: Probability Models Unit 19: Probability Models Summary of Video Probability is the language of uncertainty. Using statistics, we can better predict the outcomes of random phenomena over the long term from the very complex,

More information

36 Odds, Expected Value, and Conditional Probability

36 Odds, Expected Value, and Conditional Probability 36 Odds, Expected Value, and Conditional Probability What s the difference between probabilities and odds? To answer this question, let s consider a game that involves rolling a die. If one gets the face

More information

Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 13. Random Variables: Distribution and Expectation

Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 13. Random Variables: Distribution and Expectation CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 3 Random Variables: Distribution and Expectation Random Variables Question: The homeworks of 20 students are collected

More information

Solution Let us regress percentage of games versus total payroll.

Solution Let us regress percentage of games versus total payroll. Assignment 3, MATH 2560, Due November 16th Question 1: all graphs and calculations have to be done using the computer The following table gives the 1999 payroll (rounded to the nearest million dolars)

More information

THE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/

THE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/ THE WINNING ROULETTE SYSTEM by http://www.webgoldminer.com/ Is it possible to earn money from online gambling? Are there any 100% sure winning roulette systems? Are there actually people who make a living

More information

The Easy Roulette System

The Easy Roulette System The Easy Roulette System Please note that all information is provided as is and no guarantees are given whatsoever as to the amount of profit you will make if you use this system. Neither the seller of

More information

A WHISTLE BLOWER S GUIDE FROM HARINGEY RESIDENT AND GAMBLING INDUSTRY EXPERT DEREK WEBB OF PRIME TABLE GAMES

A WHISTLE BLOWER S GUIDE FROM HARINGEY RESIDENT AND GAMBLING INDUSTRY EXPERT DEREK WEBB OF PRIME TABLE GAMES HARINGEY COUNCIL OVERVIEW AND SCRUTINY COMMITTEE INVESTIGATION OF BETTING SHOP CLUSTERING A WHISTLE BLOWER S GUIDE FROM HARINGEY RESIDENT AND GAMBLING INDUSTRY EXPERT DEREK WEBB OF PRIME TABLE GAMES Introduction

More information

REWARD System For Even Money Bet in Roulette By Izak Matatya

REWARD System For Even Money Bet in Roulette By Izak Matatya REWARD System For Even Money Bet in Roulette By Izak Matatya By even money betting we mean betting on Red or Black, High or Low, Even or Odd, because they pay 1 to 1. With the exception of the green zeros,

More information

Orange High School. Year 7, 2015. Mathematics Assignment 2

Orange High School. Year 7, 2015. Mathematics Assignment 2 Full name: Class teacher: Due date: Orange High School Year 7, 05 Mathematics Assignment Instructions All work must be your own. You are encouraged to use the internet but you need to rewrite your findings

More information

Basic Probability. Probability: The part of Mathematics devoted to quantify uncertainty

Basic Probability. Probability: The part of Mathematics devoted to quantify uncertainty AMS 5 PROBABILITY Basic Probability Probability: The part of Mathematics devoted to quantify uncertainty Frequency Theory Bayesian Theory Game: Playing Backgammon. The chance of getting (6,6) is 1/36.

More information

Solution. Solution. (a) Sum of probabilities = 1 (Verify) (b) (see graph) Chapter 4 (Sections 4.3-4.4) Homework Solutions. Section 4.

Solution. Solution. (a) Sum of probabilities = 1 (Verify) (b) (see graph) Chapter 4 (Sections 4.3-4.4) Homework Solutions. Section 4. Math 115 N. Psomas Chapter 4 (Sections 4.3-4.4) Homework s Section 4.3 4.53 Discrete or continuous. In each of the following situations decide if the random variable is discrete or continuous and give

More information

Basic Probability Theory II

Basic Probability Theory II RECAP Basic Probability heory II Dr. om Ilvento FREC 408 We said the approach to establishing probabilities for events is to Define the experiment List the sample points Assign probabilities to the sample

More information

Introduction to Discrete Probability. Terminology. Probability definition. 22c:19, section 6.x Hantao Zhang

Introduction to Discrete Probability. Terminology. Probability definition. 22c:19, section 6.x Hantao Zhang Introduction to Discrete Probability 22c:19, section 6.x Hantao Zhang 1 Terminology Experiment A repeatable procedure that yields one of a given set of outcomes Rolling a die, for example Sample space

More information

HOW THE GAME IS PLAYED

HOW THE GAME IS PLAYED Roubingo is a revolutionary new bingo game that has the feel and excitement of las vegas stye roulette but meets the requirements of class 2 gaming. HOW THE GAME IS PLAYED Roubingo is a variation of the

More information

Russell Hunter Publishing Inc

Russell Hunter Publishing Inc Russell Hunter Street Smart Roulette Video Course Russell Hunter Publishing Inc Street Smart Roulette Video Guide 2015 Russell Hunter and Russell Hunter Publishing. All Rights Reserved All rights reserved.

More information

Section 6.1 Discrete Random variables Probability Distribution

Section 6.1 Discrete Random variables Probability Distribution Section 6.1 Discrete Random variables Probability Distribution Definitions a) Random variable is a variable whose values are determined by chance. b) Discrete Probability distribution consists of the values

More information

MONEY MANAGEMENT. Guy Bower delves into a topic every trader should endeavour to master - money management.

MONEY MANAGEMENT. Guy Bower delves into a topic every trader should endeavour to master - money management. MONEY MANAGEMENT Guy Bower delves into a topic every trader should endeavour to master - money management. Many of us have read Jack Schwager s Market Wizards books at least once. As you may recall it

More information

Vamos a Las Vegas Par Sheet

Vamos a Las Vegas Par Sheet Vamos a Las Vegas Par Sheet by Michael Shackleford May 3, 2014 Introduction Vamos a Las Vegas (VLV) is a conventional 5 reel video slot machine. They player may bet 1 to 20 pay lines and 1 to 20 credits

More information

Prediction Markets, Fair Games and Martingales

Prediction Markets, Fair Games and Martingales Chapter 3 Prediction Markets, Fair Games and Martingales Prediction markets...... are speculative markets created for the purpose of making predictions. The current market prices can then be interpreted

More information

Statistics Class 10 2/29/2012

Statistics Class 10 2/29/2012 Statistics Class 10 2/29/2012 Quiz 8 When playing roulette at the Bellagio casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 13 or to bet $5 that the outcome is any one

More information

ECE 316 Probability Theory and Random Processes

ECE 316 Probability Theory and Random Processes ECE 316 Probability Theory and Random Processes Chapter 4 Solutions (Part 2) Xinxin Fan Problems 20. A gambling book recommends the following winning strategy for the game of roulette. It recommends that

More information

X X AP Statistics Solutions to Packet 7 X Random Variables Discrete and Continuous Random Variables Means and Variances of Random Variables

X X AP Statistics Solutions to Packet 7 X Random Variables Discrete and Continuous Random Variables Means and Variances of Random Variables AP Statistics Solutions to Packet 7 Random Variables Discrete and Continuous Random Variables Means and Variances of Random Variables HW #44, 3, 6 8, 3 7 7. THREE CHILDREN A couple plans to have three

More information

STRIKE FORCE ROULETTE

STRIKE FORCE ROULETTE STRIKE FORCE ROULETTE Cycles, cycles, cycles... You cannot get away from them in the game of Roulette. Red, black, red, black... Red, red, red, red. Black, black, black... Red, red, black, black... 1st

More information

Can I hold a race night, casino night or poker night? Click here for printer-friendly version

Can I hold a race night, casino night or poker night? Click here for printer-friendly version Can I hold a race night, casino night or poker night? Click here for printer-friendly version Can I hold a race night or casino night to raise funds for charity? You should read all of the information

More information

How to Beat Online Roulette!

How to Beat Online Roulette! Martin J. Silverthorne How to Beat Online Roulette! Silverthorne Publications, Inc. How to Beat Online Roulette! COPYRIGHT 2015 Silverthorne Publications Inc. All rights reserved. Except for brief passages

More information

TABLE OF CONTENTS. ROULETTE FREE System #1 ------------------------- 2 ROULETTE FREE System #2 ------------------------- 4 ------------------------- 5

TABLE OF CONTENTS. ROULETTE FREE System #1 ------------------------- 2 ROULETTE FREE System #2 ------------------------- 4 ------------------------- 5 IMPORTANT: This document contains 100% FREE gambling systems designed specifically for ROULETTE, and any casino game that involves even money bets such as BLACKJACK, CRAPS & POKER. Please note although

More information

GLOSSARY ADR. cage. a secured area within a casino where records of transactions are kept, money is counted and chips can be exchanged for cash CAGR

GLOSSARY ADR. cage. a secured area within a casino where records of transactions are kept, money is counted and chips can be exchanged for cash CAGR The following glossary contains explanations and definitions of certain terms used in this prospectus as applicable to our Company and business. These terms and their meanings used in this prospectus may

More information

FACT A computer CANNOT pick numbers completely at random!

FACT A computer CANNOT pick numbers completely at random! 1 THE ROULETTE BIAS SYSTEM Please note that all information is provided as is and no guarantees are given whatsoever as to the amount of profit you will make if you use this system. Neither the seller

More information

Making $200 a Day is Easy!

Making $200 a Day is Easy! Making $200 a Day is Easy! Firstly, I'd just like to say thank you for purchasing this information. I do not charge a huge amount for it so I hope that you will find it useful. Please note that if you

More information

Fourth Problem Assignment

Fourth Problem Assignment EECS 401 Due on Feb 2, 2007 PROBLEM 1 (25 points) Joe and Helen each know that the a priori probability that her mother will be home on any given night is 0.6. However, Helen can determine her mother s

More information

Lesson 13: Games of Chance and Expected Value

Lesson 13: Games of Chance and Expected Value Student Outcomes Students analyze simple games of chance. Students calculate expected payoff for simple games of chance. Students interpret expected payoff in context. esson Notes When students are presented

More information

The Contrarian Let It Ride System For Trading Binary Options Profitably

The Contrarian Let It Ride System For Trading Binary Options Profitably The Contrarian Let It Ride System For Trading Binary Options Profitably by: William Hughes of Mass Money Machine This publication is subject to all relevant copyright laws. Reproduction or translation

More information

Week 2: Conditional Probability and Bayes formula

Week 2: Conditional Probability and Bayes formula Week 2: Conditional Probability and Bayes formula We ask the following question: suppose we know that a certain event B has occurred. How does this impact the probability of some other A. This question

More information

Live Dealer Electronic Table Games

Live Dealer Electronic Table Games Sands Bethlehem Live Dealer Electronic Table Games March 31, 2015 The Venetian The Palazzo Sands Expo Sands Bethlehem Paiza Sands Macao The Venetian Macao Four Seasons Hotel Macao The Plaza Macao Sands

More information

INFO ABOUT THE ODDS BETTING ON LOTTO, LOTTERIES OR KENO?

INFO ABOUT THE ODDS BETTING ON LOTTO, LOTTERIES OR KENO? INFO ABOUT THE ODDS BETTING ON LOTTO, LOTTERIES OR KENO? YOU MAY HEAR OF PEOPLE HAVING A WIN WITH LOTTO AND POWERBALL, GETTING LUCKY IN THE LOTTERY, OR HAVING WINNING NUMBERS COME UP IN THE POOLS OR KENO.

More information

ROULETTE STRATEGY OUTSIDE PDF

ROULETTE STRATEGY OUTSIDE PDF ROULETTE STRATEGY OUTSIDE PDF ==> Download: ROULETTE STRATEGY OUTSIDE PDF ROULETTE STRATEGY OUTSIDE PDF - Are you searching for Roulette Strategy Outside Books? Now, you will be happy that at this time

More information

Term Project: Roulette

Term Project: Roulette Term Project: Roulette DCY Student January 13, 2006 1. Introduction The roulette is a popular gambling game found in all major casinos. In contrast to many other gambling games such as black jack, poker,

More information

Chapter 4 Lecture Notes

Chapter 4 Lecture Notes Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a real-valued function defined on the sample space of some experiment. For instance,

More information

Example: Find the expected value of the random variable X. X 2 4 6 7 P(X) 0.3 0.2 0.1 0.4

Example: Find the expected value of the random variable X. X 2 4 6 7 P(X) 0.3 0.2 0.1 0.4 MATH 110 Test Three Outline of Test Material EXPECTED VALUE (8.5) Super easy ones (when the PDF is already given to you as a table and all you need to do is multiply down the columns and add across) Example:

More information

CASINO GAMING AMENDMENT RULE (No. 1) 2002

CASINO GAMING AMENDMENT RULE (No. 1) 2002 Queensland Subordinate Legislation 2002 No. 100 Casino Control Act 1982 CASINO GAMING AMENDMENT RULE (No. 1) 2002 TABLE OF PROVISIONS Section Page 1 Short title....................................................

More information

Beating Roulette? An analysis with probability and statistics.

Beating Roulette? An analysis with probability and statistics. The Mathematician s Wastebasket Volume 1, Issue 4 Stephen Devereaux April 28, 2013 Beating Roulette? An analysis with probability and statistics. Every time I watch the film 21, I feel like I ve made the

More information

Probability Models.S1 Introduction to Probability

Probability Models.S1 Introduction to Probability Probability Models.S1 Introduction to Probability Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard The stochastic chapters of this book involve random variability. Decisions are

More information