Example. n = 4, p = ¼, q = 1 ¼ = ¾. Binomial Distribution Application


 Noel Bryant
 1 years ago
 Views:
Transcription
1 Example The probability of successful start of a certain engine is ¼ and four trials are to be made. Evaluate the individual and cumulative probabilities of success in this case. n = 4, p = ¼, q = 1 ¼ = ¾ (p+q) 4 = p 4 + 4p 3 q + 6p 2 q 2 + 4pq 3 + q 4 Number of Cumulative successes failures Individual probability probability 0 4 q 4 = (3/4) 4 = 81/256 81/ pq 3 = 4(1/4)(3/4) 3 = 108/ / p 2 q 2 = 6(1/4) 2 (3/4) 2 = 54/ / p 3 q = 4(1/4) 3 (3/4) = 12/ / p 4 = (1/4) 4 = 1/ /256 Σ = 1 Binomial Distribution Application Example: It is known that, in a certain manufacturing process, 1% of the products are defective. If the a customer purchases 200 of these products selected at random, what is the expected value and standard deviation of the number of defects? n = 50 q = 0.01 p = = 0.99 E(defects) = n.q = 200 x 0.01 = 2 σ(defects) = npq = 200 x 0.01 x 0.99 =
2 Example: The manufacturing company has a policy of replacing, freeofcharge, all defective products that are purchased. If the product manufacturing cost is $10 per unit and each product is sold for $15, how much profit is made from a sale of 1000 products? q = 0.01 For 1000 products, n = 1000 Expected # of defects, E(defects) = n.q = 10 Therefore, 1010 products must be manufactured to sell 1000 products. Manufacturing cost = $10 x 1010 = $10,100 Income = $15 x 1000 = $15,000 Profit = $15,000  $10,100 = $4900 Profit per unit = $4900/1000 = $4.90 Example: If the company decides to increase the manufacturing cost to $10.05 per unit in order to decrease the probability of defects to 0.1%, q = For 1000 products, n = 1000 Expected # of defects, E(defects) = n.q = 1 Therefore, 1001 products must be manufactured to sell 1000 products. Manufacturing cost = $10.05 x 1001 = $10, Income = $15 x 1000 = $15,000 Profit = $15,000  $10, = $ Profit per unit = $ /1000 = $4.94 2
3 Effect of Redundancy Consider a system consisting of 4 identical components, each having a failure probability of 0.1. q = 0.1 (p = 0.9) n = 4 (p+q) 4 = p 4 + 4p 3 q + 6p 2 q 2 + 4pq 3 + q 4 System state Individual probability all components working p 4 = (0.9) 4 = working, 1 failed 4p 3 q = 4(0.9) 3 (0.1) = working, 2 failed 6p 2 q 2 = 6(0.9) 2 (0.1) 2 = working, 3 failed 4pq 3 = 4(0.9)( 0.1) 3 = all components failed q 4 = (0.1) 4 = Σ = 1 Consider 4 criteria all components required for success (no redundancy) components required for success (partial redundancy) 2 components required for success (partial redundancy) 1 component required for success (full redundancy) System reliability, R = = = System with Derated States Consider a generation plant with two 10 MW units, each having a probability of failure (forced outage rate) of 10%. q = 0.1, p = 0.9, n = 2 Binomial Distribution: Capacity Outage Probability Table: (p + q) 2 = p 2 + 2pq + q 2 Units Out Cap Out (MW) Cap In (MW) Probability Cum. Prob If the generation plant operates to supply a 15 MW load, what is the probability of load loss (system failure)? Probability of load loss = Loss of Load Probability (LOLP) = 0.19 Expected # of days of load loss = 0.19 x 365 = days/yr Loss of Load Expectation (LOLE) 3
4 System with Derated States If the generation plant operates to supply a 15 MW load, what is the Expected Load Loss (ELL)? Capacity Outage Probability Table: Units Out Cap Out (MW) Cap In (MW) Probability Cum. Prob Units Out Cap Out (MW) Cap In (MW) Load Loss (MW) Probability Col.4 x Col Expected Load Loss (ELL) = 1.05 MW Example A generating plant is to be designed to satisfy a constant 10 MW load. Four alternatives are being considered: a) 1 x 10 MW unit b) 2 x 10 MW units c) 3 x 5 MW units d) 4 x 3.33 MW units The probability of unit failure is assumed to be For each unit, q = forced outage rate (FOR) = unavailability, U = 0.02 p = availability, A =
5 Capacity Outage Probability Tables units capacity (MW) Binom. Individual cum. out out in Distr. prob prob (a) 1 x 10 MW A U (b) 2 x 10 MW A AU U (c) 3 x 5 MW A A 2 U AU U (d) 4 x 3.33 MW A A 3 U A 2 U AU U LOLP = 0.01 LOLE = 365 x 0.02 = 7.3 d/yr LOLP = LOLE = 0.15 d/yr LOLP = LOLE = 0.43 d/yr LOLP = LOLE = 0.85 d/yr Expected Load Loss Capacity (MW) Load Loss Prob L i x p i Out In L i (MW) p i (MW) (a) 1 x 10 MW (b) 2 x 10 MW (c) 3 x 5 MW (d) 4 x 3.33 MW ELL = 0.2 MW = 200 kw ELL = MW = 4.00 kw ELL = MW = 5.96 kw ELL = MW = 7.89 kw 5
6 Comparative Analysis Effect of unit unavailability: System ELL (kw) at Different Unit FOR s 2% 4% 6%) (a) 1 x 10 MW (b) 2 x 10 MW (c) 3 x 5 MW (d) 4 x 3.33 MW System with Nonidentical Components All components must be identical to apply the Binomial Distribution. If components of a system have nonidentical capacities:  Units with identical capacities are grouped together  COPT is developed for each group  COPT for different groups are combined, one at a time  Final COPT for the system is used for reliability evaluation A pumping station has 2 x 20 t/hr units, each having an unavailability of 0.1, and 1 x 30 t/hr unit with an unavailability of Calculate the capacity outage probability table for this plant. COPT for 2 x 20 t/hr units: COPT for 1 x 30 t/hr unit: Units Out Cap Out (t/hr) Cap In (t/hr) Prob Units Out Cap Out (t/hr) Cap In (t/hr) Prob
7 System with Nonidentical Components Combining COPTs: 1 x 30 t/hr unit 2 x 20 t/hr units 40 / / / / / / / / / / / Each cell contains: Capacity In / probability Overall System COPT: Cap In (t/hr) Cap Out (t/hr) Prob
Normal Approximation. Contents. 1 Normal Approximation. 1.1 Introduction. Anthony Tanbakuchi Department of Mathematics Pima Community College
Introductory Statistics Lectures Normal Approimation To the binomial distribution Department of Mathematics Pima Community College Redistribution of this material is prohibited without written permission
More informationChapter 5: Normal Probability Distributions  Solutions
Chapter 5: Normal Probability Distributions  Solutions Note: All areas and zscores are approximate. Your answers may vary slightly. 5.2 Normal Distributions: Finding Probabilities If you are given that
More informationSOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions
SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions 1. The following table contains a probability distribution for a random variable X. a. Find the expected value (mean) of X. x 1 2
More informationNormal Distribution as an Approximation to the Binomial Distribution
Chapter 1 Student Lecture Notes 11 Normal Distribution as an Approximation to the Binomial Distribution : Goals ONE TWO THREE 2 Review Binomial Probability Distribution applies to a discrete random variable
More informationPlanning Reserve Margin (PRM)
Planning Reserve Margin (PRM) Nguyen Pham Planning Specialist, Power Supply & Planning Overview A more detailed version of the PRM presentation given in July 2015 Q & A on the PRM report based on 2012
More informationAccounting 402 Illustration of a change in inventory method
Page 1 of 6 (revised fall, 2006) The was incorporated in January, 20X5. At the beginning of, the company decided to change to the FIFO method. FrankLex had used the LIFO method for financial and tax reporting
More informationSampling Central Limit Theorem Proportions. Outline. 1 Sampling. 2 Central Limit Theorem. 3 Proportions
Outline 1 Sampling 2 Central Limit Theorem 3 Proportions Outline 1 Sampling 2 Central Limit Theorem 3 Proportions Populations and samples When we use statistics, we are trying to find out information about
More informationSample Questions for Mastery #5
Name: Class: Date: Sample Questions for Mastery #5 Multiple Choice Identify the choice that best completes the statement or answers the question.. For which of the following binomial experiments could
More informationUNIT I: RANDOM VARIABLES PART A TWO MARKS
UNIT I: RANDOM VARIABLES PART A TWO MARKS 1. Given the probability density function of a continuous random variable X as follows f(x) = 6x (1x) 0
More informationM 1313 Review Test 4 1
M 1313 Review Test 4 1 Review for test 4: 1. Let E and F be two events of an experiment, P (E) =. 3 and P (F) =. 2, and P (E F) =.35. Find the following probabilities: a. P(E F) b. P(E c F) c. P (E F)
More informationChapter 4. iclicker Question 4.4 Prelecture. Part 2. Binomial Distribution. J.C. Wang. iclicker Question 4.4 Prelecture
Chapter 4 Part 2. Binomial Distribution J.C. Wang iclicker Question 4.4 Prelecture iclicker Question 4.4 Prelecture Outline Computing Binomial Probabilities Properties of a Binomial Distribution Computing
More informationBinomial Distribution Problems. Binomial Distribution SOLUTIONS. Poisson Distribution Problems
1 Binomial Distribution Problems (1) A company owns 400 laptops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your salespeople. (a) What is the likelihood that 5
More information6.2 Normal distribution. Standard Normal Distribution:
6.2 Normal distribution Slide Heights of Adult Men and Women Slide 2 Area= Mean = µ Standard Deviation = σ Donation: X ~ N(µ,σ 2 ) Standard Normal Distribution: Slide 3 Slide 4 a normal probability distribution
More information16. THE NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION
6. THE NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION It is sometimes difficult to directly compute probabilities for a binomial (n, p) random variable, X. We need a different table for each value of
More informationThe Value of Reliability in Power Systems  Pricing Operating Reserves 
Energy Laboratory MIT EL 99005 WP Massachusetts Institute of Technology The Value of Reliability in Power Systems  Pricing Operating Reserves  June 1999 THE VALUE OF RELIABILITY IN POWER SYSTEMS  PRICING
More informationSection 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 informationChapter 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 informationChapter 6 Discrete Probability Distributions
Chapter 6 Discrete Probability Distributions 40. From recent experience, 5 percent of the computer keyboards produced by an automatic, highspeed machine are defective. What is the probability that out
More information2 Binomial, Poisson, Normal Distribution
2 Binomial, Poisson, Normal Distribution Binomial Distribution ): We are interested in the number of times an event A occurs in n independent trials. In each trial the event A has the same probability
More informationBinomial Random Variables
Binomial Random Variables Dr Tom Ilvento Department of Food and Resource Economics Overview A special case of a Discrete Random Variable is the Binomial This happens when the result of the eperiment is
More informationCh. 6.1 #749 odd. The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.77340.5= 0.2734
Ch. 6.1 #749 odd The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.77340.5= 0.2734 The area is found by looking up z= 2.07 in Table E and subtracting from 0.5. Area = 0.50.0192
More informationQUANTITATIVE METHODS IN BUSINESS PROBLEM #2: INTRODUCTION TO SIMULATION
QUANTITATIVE METHODS IN BUSINESS PROBLEM #2: INTRODUCTION TO SIMULATION Dr. Arnold Kleinstein and Dr. Sharon Petrushka Introduction Simulation means imitation of reality. In this problem, we will simulate
More informationBINOMIAL OPTIONS PRICING MODEL. Mark Ioffe. Abstract
BINOMIAL OPTIONS PRICING MODEL Mark Ioffe Abstract Binomial option pricing model is a widespread numerical method of calculating price of American options. In terms of applied mathematics this is simple
More informationAP STATISTICS 2010 SCORING GUIDELINES
2010 SCORING GUIDELINES Question 4 Intent of Question The primary goals of this question were to (1) assess students ability to calculate an expected value and a standard deviation; (2) recognize the applicability
More informationOverview of the U.S. Market for Green Certificates. Presentation for the ERRA Licensing/Competition Committee June 11, 2013
Overview of the U.S. Market for Green Certificates Presentation for the ERRA Licensing/Competition Committee June 11, 2013 1 Topics Compliance Renewable Energy Certificate Markets: Renewable Energy Portfolio
More informationProbability Distributions
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
More informationICAP/UCAP Overview. Aaron Westcott Awestcott@nyiso.com 518 356 7657. If possible, Please mute your phones Please do not use the hold button.
ICAP/UCAP Overview Aaron Westcott Awestcott@nyiso.com 518 356 7657 If possible, Please mute your phones Please do not use the hold button. Agenda What is ICAP/UCAP? How are ICAP and UCAP calculated? How
More informationImportant Probability Distributions OPRE 6301
Important Probability Distributions OPRE 6301 Important Distributions... Certain probability distributions occur with such regularity in reallife applications that they have been given their own names.
More informationMath 141. Lecture 7: Variance, Covariance, and Sums. Albyn Jones 1. 1 Library 304. jones/courses/141
Math 141 Lecture 7: Variance, Covariance, and Sums Albyn Jones 1 1 Library 304 jones@reed.edu www.people.reed.edu/ jones/courses/141 Last Time Variance: expected squared deviation from the mean: Standard
More informationPr(X = x) = f(x) = λe λx
Old Business  variance/std. dev. of binomial distribution  midterm (day, policies)  class strategies (problems, etc.)  exponential distributions New Business  Central Limit Theorem, standard error
More informationUtilising SCADA data to enhance performance monitoring of operating assets: The move to realtime performance management
Utilising SCADA data to enhance performance monitoring of operating assets: The move to realtime performance management Keir Harman EWEA Workshop Malmo, December 2014 1 SAFER, SMARTER, GREENER Asset Operations
More informationChapter 5. Random variables
Random variables random variable numerical variable whose value is the outcome of some probabilistic experiment; we use uppercase letters, like X, to denote such a variable and lowercase letters, like
More informationBINOMIAL DISTRIBUTION
MODULE IV BINOMIAL DISTRIBUTION A random variable X is said to follow binomial distribution with parameters n & p if P ( X ) = nc x p x q n x where x = 0, 1,2,3..n, p is the probability of success & q
More informationYou flip a fair coin four times, what is the probability that you obtain three heads.
Handout 4: Binomial Distribution Reading Assignment: Chapter 5 In the previous handout, we looked at continuous random variables and calculating probabilities and percentiles for those type of variables.
More informationChapter 9 Monté Carlo Simulation
MGS 3100 Business Analysis Chapter 9 Monté Carlo What Is? A model/process used to duplicate or mimic the real system Types of Models Physical simulation Computer simulation When to Use (Computer) Models?
More informationGLOSSARY. Glossary of Terms for Capacity Based Demand Response PUBLIC. Issue 3.0 GOT1
PUBLIC GOT1 GLOSSARY Glossary of Terms for Capacity Based Demand Response Issue 3.0 This document provides a glossary of terms with definitions used in the Capacity Based Demand Response program. Public
More informationChapter 15 Binomial Distribution Properties
Chapter 15 Binomial Distribution Properties Two possible outcomes (success and failure) A fixed number of experiments (trials) The probability of success, denoted by p, is the same on every trial The trials
More informationStatistical Impact of Slip Simulator Training at Los Alamos National Laboratory
LAUR1224572 Approved for public release; distribution is unlimited Statistical Impact of Slip Simulator Training at Los Alamos National Laboratory Alicia GarciaLopez Steven R. Booth September 2012
More informationBinomial Distribution n = 20, p = 0.3
This document will describe how to use R to calculate probabilities associated with common distributions as well as to graph probability distributions. R has a number of built in functions for calculations
More informationChapter 5 Discrete Probability Distribution. Learning objectives
Chapter 5 Discrete Probability Distribution Slide 1 Learning objectives 1. Understand random variables and probability distributions. 1.1. Distinguish discrete and continuous random variables. 2. Able
More informationCHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.
Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,
More informationReserves in Capacity Planning A Northwest Approach
Reserves in Capacity Planning A Northwest Approach System Planning Committee June 2010 Electronic copies of this report are available on the PNUCC Website www.pnucc.org 101 SW Main Street, Suite 1605 Portland,
More informationEMPIRICAL FREQUENCY DISTRIBUTION
INTRODUCTION TO MEDICAL STATISTICS: Mirjana Kujundžić Tiljak EMPIRICAL FREQUENCY DISTRIBUTION observed data DISTRIBUTION  described by mathematical models 2 1 when some empirical distribution approximates
More informationChapter 2, part 2. Petter Mostad
Chapter 2, part 2 Petter Mostad mostad@chalmers.se Parametrical families of probability distributions How can we solve the problem of learning about the population distribution from the sample? Usual procedure:
More information3.4. The Binomial Probability Distribution. Copyright Cengage Learning. All rights reserved.
3.4 The Binomial Probability Distribution Copyright Cengage Learning. All rights reserved. The Binomial Probability Distribution There are many experiments that conform either exactly or approximately
More informationSolar Panels and the Smart Grid
Solar Panels and the Smart Grid In the Pepco Region Steve Sunderhauf Jeff Roman Joshua Cadoret David Pirtle Outline Pepco Region Background Renewable Portfolio Standards (RPS) Pepco s Blueprint for the
More informationChapter 4. Probability Distributions
Chapter 4 Probability Distributions Lesson 41/42 Random Variable Probability Distributions This chapter will deal the construction of probability distribution. By combining the methods of descriptive
More informationCh5: Discrete Probability Distributions Section 51: Probability Distribution
Recall: Ch5: Discrete Probability Distributions Section 51: Probability Distribution A variable is a characteristic or attribute that can assume different values. o Various letters of the alphabet (e.g.
More information5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.
The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution
More informationWorld s Greenest High Performance Data Center
World s Greenest High Performance Data Center EcoDataCenter Sustainability for future generations Our Services Colocation Data Center for Mission Critical Requirements Lockable racks, cages, private rooms
More informationSecurity of Supply Concept and Definition: On the Way to a Common Understanding?
Security of Supply Concept and Definition: On the Way to a Common Understanding? Presentation for FrenchGerman Conference on SoS Dr. Christoph Maurer Paris 21 May 2015 0 21.05.2015 Security of Supply
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Objectives After this lesson we will be able to: determine whether a probability
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups
More information*This view is a sample image of electricity consumption.
Supplydemand balance of electricity is indicated based on the comparison between actual demand updated every five minutes and the maximum supply capacity. Demand forecast* is provided at around 8am, indicating
More information0 x = 0.30 x = 1.10 x = 3.05 x = 4.15 x = 6 0.4 x = 12. f(x) =
. A mailorder computer business has si telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. 0 2 3 4 5 6 p(.0.5.20.25.20.06.04
More informationChapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
More informationPart I Learning about SPSS
STATS 1000 / STATS 1004 / STATS 1504 Statistical Practice 1 Practical Week 5 2015 Practical Outline In this practical, we will look at how to do binomial calculations in Excel. look at how to do normal
More informationSolar Power Frequently Asked Questions
General information about solar power 1. How do I get solar power? Solar Power Frequently Asked Questions Many companies install solar power systems including some electricity retailers. It is worth comparing
More informationtable to see that the probability is 0.8413. (b) What is the probability that x is between 16 and 60? The zscores for 16 and 60 are: 60 38 = 1.
Review Problems for Exam 3 Math 1040 1 1. Find the probability that a standard normal random variable is less than 2.37. Looking up 2.37 on the normal table, we see that the probability is 0.9911. 2. Find
More informationData Realty Colocation Data Center Ignition Park, South Bend, IN. Owner: Data Realty Engineer: ESD Architect: BSA LifeStructures
Data Realty Colocation Data Center Ignition Park, South Bend, IN Owner: Data Realty Engineer: ESD Architect: BSA LifeStructures Project Overview Data Realty is a data center service provider for middle
More informationSTAT 3502. x 0 < x < 1
Solution  Assignment # STAT 350 Total mark=100 1. A large industrial firm purchases several new word processors at the end of each year, the exact number depending on the frequency of repairs in the previous
More informationChapter 5  Practice Problems 1
Chapter 5  Practice Problems 1 Identify the given random variable as being discrete or continuous. 1) The number of oil spills occurring off the Alaskan coast 1) A) Continuous B) Discrete 2) The ph level
More informationChapter 3: DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
Chapter 3: DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Part 4: Geometric Distribution Negative Binomial Distribution Hypergeometric Distribution Sections 37, 38 The remaining discrete random
More informationMinimizing Impact of Electric Utility Outages with Backup Generation
Minimizing Impact of Electric Utility Outages with Backup Generation Introduction of the Speaker Michael Dempsey, PE Senior Electrical Engineer Carter & Burgess, Inc. Energy & Power Solutions Facility
More informationExercises  The Normal Curve
Exercises  The Normal Curve 1. Find e following proportions under e Normal curve: a) P(z>2.05) b) P(z>2.5) c) P(1.25
More informationCDP, Inc.'s Infrastructure Services Availability Commitment is to have the CDP, Inc. Data Center Infrastructure Components available 100% of the time.
Service Level Agreement (SLA) Infrastructure Services Availability Commitment Scope: Service Availability Commitment: CDP, Inc.'s Infrastructure Services Availability Commitment is to have the CDP, Inc.
More informationSolar and Wind Energy for Greenhouses. A.J. Both 1 and Tom Manning 2
Solar and Wind Energy for Greenhouses A.J. Both 1 and Tom Manning 2 1 Associate Extension Specialist 2 Project Engineer NJ Agricultural Experiment Station Rutgers University 20 Ag Extension Way New Brunswick,
More informationStat 515 Midterm Examination II April 6, 2010 (9:30 a.m.  10:45 a.m.)
Name: Stat 515 Midterm Examination II April 6, 2010 (9:30 a.m.  10:45 a.m.) The total score is 100 points. Instructions: There are six questions. Each one is worth 20 points. TA will grade the best five
More informationBoiler efficiency for community heating in SAP
Technical Papers supporting SAP 2009 Boiler efficiency for community heating in SAP Reference no. STP09/B06 Date last amended 26 March 2009 Date originated 28 May 2008 Author(s) John Hayton and Alan Shiret,
More informationMath 201: Statistics November 30, 2006
Math 201: Statistics November 30, 2006 Fall 2006 MidTerm #2 Closed book & notes; only an A4size formula sheet and a calculator allowed; 90 mins. No questions accepted! Instructions: There are eleven pages
More informationStudy Design Sample Size Calculation & Power Analysis. RCMAR/CHIME April 21, 2014 Honghu Liu, PhD Professor University of California Los Angeles
Study Design Sample Size Calculation & Power Analysis RCMAR/CHIME April 21, 2014 Honghu Liu, PhD Professor University of California Los Angeles Contents 1. Background 2. Common Designs 3. Examples 4. Computer
More informationAP Statistics 7!3! 6!
Lesson 64 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!
More informationElectricity Pricing and Marginal Cost Analysis
Electricity Pricing and Marginal Cost Analysis Learn practical tools to analyse a host of issues in electricity analysis including efficient tools to work with supply and demand data; creating flexible
More informationChapter 2: Data quantifiers: sample mean, sample variance, sample standard deviation Quartiles, percentiles, median, interquartile range Dot diagrams
Review for Final Chapter 2: Data quantifiers: sample mean, sample variance, sample standard deviation Quartiles, percentiles, median, interquartile range Dot diagrams Histogram Boxplots Chapter 3: Set
More informationStats on the TI 83 and TI 84 Calculator
Stats on the TI 83 and TI 84 Calculator Entering the sample values STAT button Left bracket { Right bracket } Store (STO) List L1 Comma Enter Example: Sample data are {5, 10, 15, 20} 1. Press 2 ND and
More informationChapter 22 Real Options
Chapter 22 Real Options Multiple Choice Questions 1. The following are the main types of real options: (I) The option to expand if the immediate investment project succeeds (II) The option to wait (and
More informationRELIABILITY OF ELECTRIC POWER GENERATION IN POWER SYSTEMS WITH THERMAL AND WIND POWER PLANTS
Oil Shale, 27, Vol. 24, No. 2 Special ISSN 28189X pp. 197 28 27 Estonian Academy Publishers RELIABILITY OF ELECTRIC POWER GENERATION IN POWER SYSTEMS WITH THERMAL AND WIND POWER PLANTS M. VALDMA, M. KEEL,
More informationInternational Examinations. Advanced Level Mathematics Statistics 2 Steve Dobbs and Jane Miller
International Examinations Advanced Level Mathematics Statistics 2 Steve Dobbs and Jane Miller The publishers would like to acknowledge the contributions of the following people to this series of books:
More informationCHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS
CHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS TRUE/FALSE 235. The Poisson probability distribution is a continuous probability distribution. F 236. In a Poisson distribution,
More informationRevisions of FIT Scheme to promote usage of. Renewable Electric Energy
February 2015 Revisions of FIT Scheme to promote usage of Renewable Electric Energy On January 22, 2015, the Agency for Natural Resources and Energy ( ANRE ) has promulgated a ministerial ordinance and
More informationCapacity Performance Proposal
Capacity Performance Proposal October 15, 2014 Section II Capacity Products Capacity Performance Product Base Capacity Product Specific Resource Types and Coupling Storage Resources Intermittent Resources
More informationDistribution Analysis
Finding the best distribution that explains your data ENMAX Energy Corporation 8 October, 2015 Introduction Introduction Statistical tests Goodness of fit We often fit observations to a model (e.g., lognormal
More informationReview. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 7 Estimates and Sample Sizes 7 1 Review and Preview 7 2 Estimating a Population Proportion 7 3 Estimating a Population
More informationExpansion Planning for Electrical Generating Systems
VIC Library TECHNICAL REPORTS SERIES No. 241 Expansion Planning for Electrical Generating Systems A Guidebook jwti INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1984 TECHNICAL REPORTS SERIES No. 241 EXPANSION
More informationBinomial Probability Distribution
Binomial Probability Distribution In a binomial setting, we can compute probabilities of certain outcomes. This used to be done with tables, but with graphing calculator technology, these problems are
More informationProbability Distributions
CHAPTER 6 Probability Distributions Calculator Note 6A: Computing Expected Value, Variance, and Standard Deviation from a Probability Distribution Table Using Lists to Compute Expected Value, Variance,
More information1 Math 1313 Final Review Final Review for Finite. 1. Find the equation of the line containing the points 1, 2)
Math 33 Final Review Final Review for Finite. Find the equation of the line containing the points, 2) ( and (,3) 2. 2. The Ace Company installed a new machine in one of its factories at a cost of $2,.
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 2 Solutions
Math 70/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 2 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
More informationChapter 7: OneSample Inference
Chapter 7: OneSample Inference Now that you have all this information about descriptive statistics and probabilities, it is time to start inferential statistics. There are two branches of inferential
More informationCLOUD Computing: CostEffective Risk Management with Additional Product Deployment
Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 00 (2015) 000 000 www.elsevier.com/locate/procedia The 2015 International Conference on Soft Computing and Software Engineering
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationEnvironmental report for Danish electricity and CHP
Environmental report for Danish electricity and CHP summary of the status year 2012 Energinet.dk is the transmission system operator for electricity and gas in Denmark. In accordance with the Danish Electricity
More informationPlumas Sierra Solar Rebate Program Guidebook 2015
Plumas Sierra Solar Rebate Program Guidebook 2015 Plumas Sierra Rural Electric Cooperative (PSREC) is offering rebates to encourage the installation of high quality solar photovoltaic (PV) systems in 2015.
More informationCLOUD computing, an emerging form of
CLOUD computing Mehmet Sahinoglu and Luis CuevaParra CLOUD computing (Grid or utility computing, computing ondemand) which was the talk of the computing circles at the end of 0s has become once again
More informationThe normal approximation to the binomial
The normal approximation to the binomial The binomial probability function is not useful for calculating probabilities when the number of trials n is large, as it involves multiplying a potentially very
More informationChoosing Probability Distributions in Simulation
MBA elective  Models for Strategic Planning  Session 14 Choosing Probability Distributions in Simulation Probability Distributions may be selected on the basis of Data Theory Judgment a mix of the above
More informationA reliable and experienced supplier
Email : aps@africapowersystems.com A reliable and experienced supplier A joint venture to increase efficiency Two CATERPILLAR dealers for more than 75 years decided to associate their experiences and skills
More informationATTACHMENT I TO IPN92041 RELATED TO LOAD TESTING AND,24 MONTH OPERATING CYCLES
ATTACHMENT I TO IPN92041 PROPOSED TECHNICAL SPECIFICATION CHANGE RELATED TO BATTERY LOAD TESTING AND,24 MONTH OPERATING CYCLES NEW YORK POWER AUTHORITY INDIAN POINT 3 NUCLEAR POWER PLANT DOCKET NO.
More information