Size: px
Start display at page:

Download ""

Transcription

1 18-32 Question # 1 of 10 ( Start time: 12:11:21 AM ) Total Marks: 1 Let X be a random variable with binomial distribution, that is (X=0,1,, n). The expected value E[X] is p np np(1-p) Xnp Question # 2 of 10 Total Marks: 1 The sample mean is an unbiased estimator for the population mean. This means: The sample mean has a normal distribution mean The average sample mean, over all possible samples, equals the population The sample mean is always very close to the population mean The sample mean will only vary a little from the population mean Question # 3 of 10 Total Marks: 1 Probability of an impossible event is always: Less than one Greater than one Between one and zero

2 Zero Question # 4 of 10 ( Start time: 12:13:48 AM ) Total Marks: 1 The function abbreviated to d.f. is also called the... Probability density function Probability distribution function Commutative distribution function Discrete function Question # 5 of 10 ( Start time: 12:14:50 AM ) Total Marks: 1 The total area under the normal curve is: Question # 6 of 10 ( Start time: 12:15:12 AM ) Total Marks: 1 Two events A & B are said to be independent if... P (A) + P (B) P (B\A) = P (B) P (A) * P (B)

3 P (A\B) = P (A) Question # 7 of 10 ( Start time: 12:15:31 AM ) Total Marks: 1 When two coins are tossed the probability of at most one head is: 1/4 2/4 3/4 1 Question # 8 of 10 ( Start time: 12:16:33 AM ) Total Marks: 1 For exhaustive events, the P(AUBUC) is equal to: P(A) P(S) P(A) * P(B)* P(C) P(B) Question # 9 of 10 ( Start time: 12:17:46 AM ) Total Marks: 1 One card is drawn from a standard 52 card deck. In describing the occurrence of two possible events, an Ace and a King, these two events are said to be: independent randomly independent random variables

4 mutually exclusive Question # 10 of 10 ( Start time: 12:18:23 AM ) Total Marks: 1 The number of parameters in hypergeometric distribution is (are): State marks ka stem and leaf display tha probability main s bohy kam aya event ki def or population ki def ai thi IN another paper session Long Q is moments ka 10 marks ka and varience and SD ka 5 marks ka mcqs 2.one long question of mode 3.one question of chebychev's theorem jb kahein sy or information mely gi tu Inshallah zaroor share karon gi. My stats paper... Moment ratios - 10 marks probability - 5 marks calculate the harmonic mean - 3 marks definition of sample - 1 mark definition of population - 1 mark and 16 mcq's If X and Y are independent, then Var(X-Y) is equal to:

5 Zero Question No: 9 ( Marks: 1 ) Please choose one Which of the following is the class frequency The number of observations in each class The difference between consecutive lower class limits Always contains at least 5 observations Usually a multiple of the lower limit of the first class Question No: 10 ( Marks: 1 ) - Please choose one How to construct the class interval: Divide the class frequencies in half Divide the class frequency by the number of observations Find the difference between consecutive lower class limits Count the number of observations in the class Question No: 11 ( Marks: 1 ) - Please choose one Data in the Population Census Report is: Ungrouped data Secondary data Primary data Arrayed data chck these 4 current papers of sta301 1st paper 10 marks ka stem and leaf display tha probability main s bohy kam aya event ki def or population ki def ai thi moments ka 10 marks ka and varience and SD ka 5 marks ka another

6 sta301 paper 2 sta301 me22 question hy,17 mcq the. 1marks ki defnation aye the 2marsks ka reason pocha tha 3marks ka mean wala sawal tha. 5marks ka moment ratio k formula or explaination aye thi.. 10marks ki problem aye the solve ki the mene jo measure of dispersion se aye thi. sta301 paper 3 Q1) find the low quartile and median. marks = 10 Q2) find the Range marks = 3 Q3) what is meant by Sample? marks= 2 Q4) it what situation we use the Emperical rule and bays therom? marks = 5 Q5) find the standared deviation? marks= 1 Q6) i think, objective type marks = 15 objective type ziada tar theory main say hi aya tha, koi question solve karnay k liay nhi dia gya tha, e.g. mean > median > mode. i) positively skewed ii) negtively skewed iii) equal

7 sta301 paper 4 friends main b isi bhol bolaye main tha,par mera 80% paper probability main se aya,10 marks ka b 5 marks ka b,definatio 2 marks ki wo b prob se aur 11 mcqz from probability se

MIDTERM EXAMINATION (Spring 2011) STA301- Statistics and Probability

MIDTERM EXAMINATION (Spring 2011) STA301- Statistics and Probability STA301- Statistics and Probability Solved MCQS From Midterm Papers March 19,2012 MC100401285 Moaaz.pk@gmail.com Mc100401285@gmail.com PSMD01 MIDTERM EXAMINATION (Spring 2011) STA301- Statistics and Probability

More information

MIDTERM EXAMINATION STA301- Statistics and Probability (Session - 4) Question No: 1 (Marks: 1) - Please choose one 10! =. 362880 3628800 362280 362800 Question No: 2 (Marks: 1) - Please choose one If a

More information

Come & Join Us at VUSTUDENTS.net

Come & Join Us at VUSTUDENTS.net Come & Join Us at VUSTUDENTS.net For Assignment Solution, GDB, Online Quizzes, Helping Study material, Past Solved Papers, Solved MCQs, Current Papers, E-Books & more. Go to http://www.vustudents.net and

More information

Statistics for Managers Using Microsoft Excel/SPSS Chapter 4 Basic Probability And Discrete Probability Distributions

Statistics for Managers Using Microsoft Excel/SPSS Chapter 4 Basic Probability And Discrete Probability Distributions Statistics for Managers Using Microsoft Excel/SPSS Chapter 4 Basic Probability And Discrete Probability Distributions 1999 Prentice-Hall, Inc. Chap. 4-1 Chapter Topics Basic Probability Concepts: Sample

More information

Statistics for Managers Using Microsoft Excel (3 rd Edition)

Statistics for Managers Using Microsoft Excel (3 rd Edition) Statistics for Managers Using Microsoft Excel (3 rd Edition) Chapter 4 Basic Probability and Discrete Probability Distributions 2002 Prentice-Hall, Inc. Chap 4-1 Chapter Topics Basic probability concepts

More information

STA301- Statistics and Probability Solved Subjective From Final term Papers. STA301- Statistics and Probability Final Term Examination - Spring 2012

STA301- Statistics and Probability Solved Subjective From Final term Papers. STA301- Statistics and Probability Final Term Examination - Spring 2012 STA30- Statistics and Probability Solved Subjective From Final term Papers Feb 6,03 MC004085 Moaaz.pk@gmail.com Mc004085@gmail.com PSMD0 STA30- Statistics and Probability Final Term Examination - Spring

More information

Note: Solve these papers by yourself This VU Group is not responsible for any solved content. Paper 1. Question No: 3 ( Marks: 1 ) - Please choose one

Note: Solve these papers by yourself This VU Group is not responsible for any solved content. Paper 1. Question No: 3 ( Marks: 1 ) - Please choose one Paper Composed & Solved STA30 Finalterm Papers 7 Papers Solved.. By Arman Makhani Statistic and Probability STA30 7Final term paper Question No: ( Marks: ) - Please choose one Mean deviation is always:

More information

EXAM. Exam #1. Math 3342 Summer II, July 21, 2000 ANSWERS

EXAM. Exam #1. Math 3342 Summer II, July 21, 2000 ANSWERS EXAM Exam # Math 3342 Summer II, 2 July 2, 2 ANSWERS i pts. Problem. Consider the following data: 7, 8, 9, 2,, 7, 2, 3. Find the first quartile, the median, and the third quartile. Make a box and whisker

More information

What is Probability? Probability. Sample Spaces and Events. Simple Event

What is Probability? Probability. Sample Spaces and Events. Simple Event What is Probability? Probability Peter Lo Probability is the numerical measure of likelihood that the event will occur. Simple Event Joint Event Compound Event Lies between 0 & 1 Sum of events is 1 1.5

More information

Binomial and Poisson Probability Distributions

Binomial and Poisson Probability Distributions Binomial and Poisson Probability Distributions Esra Akdeniz March 3, 2016 Bernoulli Random Variable Any random variable whose only possible values are 0 or 1 is called a Bernoulli random variable. What

More information

A Probability Primer. A random walk down a probabilistic path leading to some stochastic thoughts on chance events and uncertain outcomes.

A Probability Primer. A random walk down a probabilistic path leading to some stochastic thoughts on chance events and uncertain outcomes. A Probability Primer A random walk down a probabilistic path leading to some stochastic thoughts on chance events and uncertain outcomes. Are you holding all the cards?? Random Events A random event, E,

More information

Conditional Probability. CS231 Dianna Xu

Conditional Probability. CS231 Dianna Xu Conditional Probability CS231 Dianna Xu 1 Boy or Girl? A couple has two children, one of them is a girl. What is the probability that the other one is also a girl? Assuming 50/50 chances of conceiving

More information

Deep Learning for Computer Vision

Deep Learning for Computer Vision Deep Learning for Computer Vision Lecture 3: Probability, Bayes Theorem, and Bayes Classification Peter Belhumeur Computer Science Columbia University Probability Should you play this game? Game: A fair

More information

Learning Objectives for Stat 225

Learning Objectives for Stat 225 Learning Objectives for Stat 225 08/20/12 Introduction to Probability: Get some general ideas about probability, and learn how to use sample space to compute the probability of a specific event. Set Theory:

More information

2011 Pearson Education, Inc

2011 Pearson Education, Inc Statistics for Business and Economics Chapter 3 Probability Contents 1. Events, Sample Spaces, and Probability 2. Unions and Intersections 3. Complementary Events 4. The Additive Rule and Mutually Exclusive

More information

Probability Dr. Manjula Gunarathna 1

Probability Dr. Manjula Gunarathna 1 Probability Dr. Manjula Gunarathna Probability Dr. Manjula Gunarathna 1 Introduction Probability theory was originated from gambling theory Probability Dr. Manjula Gunarathna 2 History of Probability Galileo

More information

CHAPTER - 16 PROBABILITY Random Experiment : If an experiment has more than one possible out come and it is not possible to predict the outcome in advance then experiment is called random experiment. Sample

More information

Binomial random variable

Binomial random variable Binomial random variable Toss a coin with prob p of Heads n times X: # Heads in n tosses X is a Binomial random variable with parameter n,p. X is Bin(n, p) An X that counts the number of successes in many

More information

If S = {O 1, O 2,, O n }, where O i is the i th elementary outcome, and p i is the probability of the i th elementary outcome, then

If S = {O 1, O 2,, O n }, where O i is the i th elementary outcome, and p i is the probability of the i th elementary outcome, then 1.1 Probabilities Def n: A random experiment is a process that, when performed, results in one and only one of many observations (or outcomes). The sample space S is the set of all elementary outcomes

More information

Presentation on Theo e ry r y o f P r P o r bab a il i i l t i y

Presentation on Theo e ry r y o f P r P o r bab a il i i l t i y Presentation on Theory of Probability Meaning of Probability: Chance of occurrence of any event In practical life we come across situation where the result are uncertain Theory of probability was originated

More information

STP 226 ELEMENTARY STATISTICS

STP 226 ELEMENTARY STATISTICS STP 226 ELEMENTARY STATISTICS CHAPTER 5 Probability Theory - science of uncertainty 5.1 Probability Basics Equal-Likelihood Model Suppose an experiment has N possible outcomes, all equally likely. Then

More information

Counting principles, including permutations and combinations.

Counting principles, including permutations and combinations. 1 Counting principles, including permutations and combinations. The binomial theorem: expansion of a + b n, n ε N. THE PRODUCT RULE If there are m different ways of performing an operation and for each

More information

Example. If 4 tickets are drawn with replacement from ,

Example. If 4 tickets are drawn with replacement from , Example. If 4 tickets are drawn with replacement from 1 2 2 4 6, what are the chances that we observe exactly two 2 s? Exactly two 2 s in a sequence of four draws can occur in many ways. For example, (

More information

STAT 430/510 Probability

STAT 430/510 Probability STAT 430/510 Probability Hui Nie Lecture 3 May 28th, 2009 Review We have discussed counting techniques in Chapter 1. Introduce the concept of the probability of an event. Compute probabilities in certain

More information

Axioms of Probability

Axioms of Probability Sample Space (denoted by S) The set of all possible outcomes of a random experiment is called the Sample Space of the experiment, and is denoted by S. Example 1.10 If the experiment consists of tossing

More information

Probability Year 9. Terminology

Probability Year 9. Terminology Probability Year 9 Terminology Probability measures the chance something happens. Formally, we say it measures how likely is the outcome of an event. We write P(result) as a shorthand. An event is some

More information

Name: Exam 2 Solutions. March 13, 2017

Name: Exam 2 Solutions. March 13, 2017 Department of Mathematics University of Notre Dame Math 00 Finite Math Spring 07 Name: Instructors: Conant/Galvin Exam Solutions March, 07 This exam is in two parts on pages and contains problems worth

More information

University of Jordan Fall 2009/2010 Department of Mathematics

University of Jordan Fall 2009/2010 Department of Mathematics handouts Part 1 (Chapter 1 - Chapter 5) University of Jordan Fall 009/010 Department of Mathematics Chapter 1 Introduction to Introduction; Some Basic Concepts Statistics is a science related to making

More information

Statistics for Business and Economics

Statistics for Business and Economics Statistics for Business and Economics Basic Probability Learning Objectives In this lecture(s), you learn: Basic probability concepts Conditional probability To use Bayes Theorem to revise probabilities

More information

2.6 Tools for Counting sample points

2.6 Tools for Counting sample points 2.6 Tools for Counting sample points When the number of simple events in S is too large, manual enumeration of every sample point in S is tedious or even impossible. (Example) If S contains N equiprobable

More information

Lecture 2: Repetition of probability theory and statistics

Lecture 2: Repetition of probability theory and statistics Algorithms for Uncertainty Quantification SS8, IN2345 Tobias Neckel Scientific Computing in Computer Science TUM Lecture 2: Repetition of probability theory and statistics Concept of Building Block: Prerequisites:

More information

STAT Chapter 3: Probability

STAT Chapter 3: Probability Basic Definitions STAT 515 --- Chapter 3: Probability Experiment: A process which leads to a single outcome (called a sample point) that cannot be predicted with certainty. Sample Space (of an experiment):

More information

UNIT 5 ~ Probability: What Are the Chances? 1

UNIT 5 ~ Probability: What Are the Chances? 1 UNIT 5 ~ Probability: What Are the Chances? 1 6.1: Simulation Simulation: The of chance behavior, based on a that accurately reflects the phenomenon under consideration. (ex 1) Suppose we are interested

More information

Stat 2300 International, Fall 2006 Sample Midterm. Friday, October 20, Your Name: A Number:

Stat 2300 International, Fall 2006 Sample Midterm. Friday, October 20, Your Name: A Number: Stat 2300 International, Fall 2006 Sample Midterm Friday, October 20, 2006 Your Name: A Number: The Midterm consists of 35 questions: 20 multiple-choice questions (with exactly 1 correct answer) and 15

More information

Probability and random variables. Sept 2018

Probability and random variables. Sept 2018 Probability and random variables Sept 2018 2 The sample space Consider an experiment with an uncertain outcome. The set of all possible outcomes is called the sample space. Example: I toss a coin twice,

More information

STAT509: Probability

STAT509: Probability University of South Carolina August 20, 2014 The Engineering Method and Statistical Thinking The general steps of engineering method are: 1. Develop a clear and concise description of the problem. 2. Identify

More information

Distribusi Binomial, Poisson, dan Hipergeometrik

Distribusi Binomial, Poisson, dan Hipergeometrik Distribusi Binomial, Poisson, dan Hipergeometrik CHAPTER TOPICS The Probability of a Discrete Random Variable Covariance and Its Applications in Finance Binomial Distribution Poisson Distribution Hypergeometric

More information

S2 QUESTIONS TAKEN FROM JANUARY 2006, JANUARY 2007, JANUARY 2008, JANUARY 2009

S2 QUESTIONS TAKEN FROM JANUARY 2006, JANUARY 2007, JANUARY 2008, JANUARY 2009 S2 QUESTIONS TAKEN FROM JANUARY 2006, JANUARY 2007, JANUARY 2008, JANUARY 2009 SECTION 1 The binomial and Poisson distributions. Students will be expected to use these distributions to model a real-world

More information

Today we ll discuss ways to learn how to think about events that are influenced by chance.

Today we ll discuss ways to learn how to think about events that are influenced by chance. Overview Today we ll discuss ways to learn how to think about events that are influenced by chance. Basic probability: cards, coins and dice Definitions and rules: mutually exclusive events and independent

More information

Probability Year 10. Terminology

Probability Year 10. Terminology Probability Year 10 Terminology Probability measures the chance something happens. Formally, we say it measures how likely is the outcome of an event. We write P(result) as a shorthand. An event is some

More information

Sampling Distribution: Week 6

Sampling Distribution: Week 6 Sampling Distribution: Week 6 Kwonsang Lee University of Pennsylvania kwonlee@wharton.upenn.edu February 27, 2015 Kwonsang Lee STAT111 February 27, 2015 1 / 16 Sampling Distribution: Sample Mean If X 1,

More information

The enumeration of all possible outcomes of an experiment is called the sample space, denoted S. E.g.: S={head, tail}

The enumeration of all possible outcomes of an experiment is called the sample space, denoted S. E.g.: S={head, tail} Random Experiment In random experiments, the result is unpredictable, unknown prior to its conduct, and can be one of several choices. Examples: The Experiment of tossing a coin (head, tail) The Experiment

More information

Relationship between probability set function and random variable - 2 -

Relationship between probability set function and random variable - 2 - 2.0 Random Variables A rat is selected at random from a cage and its sex is determined. The set of possible outcomes is female and male. Thus outcome space is S = {female, male} = {F, M}. If we let X be

More information

MIT Arts, Commerce and Science College, Alandi, Pune DEPARTMENT OF STATISTICS. Question Bank. Statistical Methods-I

MIT Arts, Commerce and Science College, Alandi, Pune DEPARTMENT OF STATISTICS. Question Bank. Statistical Methods-I Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 MIT Arts, Commerce and Science College, Alandi, Pune DEPARTMENT OF STATISTICS Question Bank Statistical Methods-I Questions for 2 marks Define the following terms: a. Class limits

More information

STA301- Statistics and Probability. A Mega File for MiD Term Papers &Quizzes.

STA301- Statistics and Probability. A Mega File for MiD Term Papers &Quizzes. STA301- Statistics and Probability Composed By Faheem Saqib A Mega File for MiD Term Papers &Quizzes For more Help Rep At Faheem_saqib2003@yahoo.com Faheem.saqib2003@gmail.com 0334-6034849 Student Info

More information

Elementary Discrete Probability

Elementary Discrete Probability Elementary Discrete Probability MATH 472 Financial Mathematics J Robert Buchanan 2018 Objectives In this lesson we will learn: the terminology of elementary probability, elementary rules of probability,

More information

Review of Probabilities and Basic Statistics

Review of Probabilities and Basic Statistics Alex Smola Barnabas Poczos TA: Ina Fiterau 4 th year PhD student MLD Review of Probabilities and Basic Statistics 10-701 Recitations 1/25/2013 Recitation 1: Statistics Intro 1 Overview Introduction to

More information

Review Basic Probability Concept

Review Basic Probability Concept Economic Risk and Decision Analysis for Oil and Gas Industry CE81.9008 School of Engineering and Technology Asian Institute of Technology January Semester Presented by Dr. Thitisak Boonpramote Department

More information

CIVL Why are we studying probability and statistics? Learning Objectives. Basic Laws and Axioms of Probability

CIVL Why are we studying probability and statistics? Learning Objectives. Basic Laws and Axioms of Probability CIVL 3103 Basic Laws and Axioms of Probability Why are we studying probability and statistics? How can we quantify risks of decisions based on samples from a population? How should samples be selected

More information

TOPIC 12 PROBABILITY SCHEMATIC DIAGRAM

TOPIC 12 PROBABILITY SCHEMATIC DIAGRAM TOPIC 12 PROBABILITY SCHEMATIC DIAGRAM Topic Concepts Degree of Importance References NCERT Book Vol. II Probability (i) Conditional Probability *** Article 1.2 and 1.2.1 Solved Examples 1 to 6 Q. Nos

More information

STA301- MCQs: Page No.1. STA301 Solved MCQz by Muhammad Ishfaq. Question No: 21 ( Marks: 1 ) 1 8 = 3 8 = and.

STA301- MCQs: Page No.1.   STA301 Solved MCQz by Muhammad Ishfaq. Question No: 21 ( Marks: 1 ) 1 8 = 3 8 = and. No. STA30- MCQs: Question No: ( Marks: ) P X 0 8 P X 3 8 P X =, =, Then find F () 3 8 = and P( X 3) 8 = If Question No: ( Marks: ) the formula of mathematical expectation. Write down e=(w * p) + (-v *).

More information

Dover- Sherborn High School Mathematics Curriculum Probability and Statistics

Dover- Sherborn High School Mathematics Curriculum Probability and Statistics Mathematics Curriculum A. DESCRIPTION This is a full year courses designed to introduce students to the basic elements of statistics and probability. Emphasis is placed on understanding terminology and

More information

Part (A): Review of Probability [Statistics I revision]

Part (A): Review of Probability [Statistics I revision] Part (A): Review of Probability [Statistics I revision] 1 Definition of Probability 1.1 Experiment An experiment is any procedure whose outcome is uncertain ffl toss a coin ffl throw a die ffl buy a lottery

More information

Set/deck of playing cards. Spades Hearts Diamonds Clubs

Set/deck of playing cards. Spades Hearts Diamonds Clubs TC Mathematics S2 Coins Die dice Tale Head Set/deck of playing cards Spades Hearts Diamonds Clubs TC Mathematics S2 PROBABILITIES : intuitive? Experiment tossing a coin Event it s a head Probability 1/2

More information

If the objects are replaced there are n choices each time yielding n r ways. n C r and in the textbook by g(n, r).

If the objects are replaced there are n choices each time yielding n r ways. n C r and in the textbook by g(n, r). Caveat: Not proof read. Corrections appreciated. Combinatorics In the following, n, n 1, r, etc. will denote non-negative integers. Rule 1 The number of ways of ordering n distinguishable objects (also

More information

Random Signals and Systems. Chapter 1. Jitendra K Tugnait. Department of Electrical & Computer Engineering. James B Davis Professor.

Random Signals and Systems. Chapter 1. Jitendra K Tugnait. Department of Electrical & Computer Engineering. James B Davis Professor. Random Signals and Systems Chapter 1 Jitendra K Tugnait James B Davis Professor Department of Electrical & Computer Engineering Auburn University 2 3 Descriptions of Probability Relative frequency approach»

More information

MATH MW Elementary Probability Course Notes Part I: Models and Counting

MATH MW Elementary Probability Course Notes Part I: Models and Counting MATH 2030 3.00MW Elementary Probability Course Notes Part I: Models and Counting Tom Salisbury salt@yorku.ca York University Winter 2010 Introduction [Jan 5] Probability: the mathematics used for Statistics

More information

Topic 3: Introduction to Probability

Topic 3: Introduction to Probability Topic 3: Introduction to Probability 1 Contents 1. Introduction 2. Simple Definitions 3. Types of Probability 4. Theorems of Probability 5. Probabilities under conditions of statistically independent events

More information

STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6. With SOLUTIONS

STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6. With SOLUTIONS STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6 With SOLUTIONS Mudunuru Venkateswara Rao, Ph.D. STA 2023 Fall 2016 Venkat Mu ALL THE CONTENT IN THESE SOLUTIONS PRESENTED IN BLUE AND BLACK

More information

Conditional Probability

Conditional Probability Conditional Probability Idea have performed a chance experiment but don t know the outcome (ω), but have some partial information (event A) about ω. Question: given this partial information what s the

More information

Introduction and basic definitions

Introduction and basic definitions Chapter 1 Introduction and basic definitions 1.1 Sample space, events, elementary probability Exercise 1.1 Prove that P( ) = 0. Solution of Exercise 1.1 : Events S (where S is the sample space) and are

More information

Probability (10A) Young Won Lim 6/12/17

Probability (10A) Young Won Lim 6/12/17 Probability (10A) Copyright (c) 2017 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later

More information

Notation: X = random variable; x = particular value; P(X = x) denotes probability that X equals the value x.

Notation: X = random variable; x = particular value; P(X = x) denotes probability that X equals the value x. Ch. 16 Random Variables Def n: A random variable is a numerical measurement of the outcome of a random phenomenon. A discrete random variable is a random variable that assumes separate values. # of people

More information

LECTURE NOTES by DR. J.S.V.R. KRISHNA PRASAD

LECTURE NOTES by DR. J.S.V.R. KRISHNA PRASAD .0 Introduction: The theory of probability has its origin in the games of chance related to gambling such as tossing of a coin, throwing of a die, drawing cards from a pack of cards etc. Jerame Cardon,

More information

n N CHAPTER 1 Atoms Thermodynamics Molecules Statistical Thermodynamics (S.T.)

n N CHAPTER 1 Atoms Thermodynamics Molecules Statistical Thermodynamics (S.T.) CHAPTER 1 Atoms Thermodynamics Molecules Statistical Thermodynamics (S.T.) S.T. is the key to understanding driving forces. e.g., determines if a process proceeds spontaneously. Let s start with entropy

More information

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 2 MATH00040 SEMESTER / Probability

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 2 MATH00040 SEMESTER / Probability ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 2 MATH00040 SEMESTER 2 2017/2018 DR. ANTHONY BROWN 5.1. Introduction to Probability. 5. Probability You are probably familiar with the elementary

More information

Suppose that you have three coins. Coin A is fair, coin B shows heads with probability 0.6 and coin C shows heads with probability 0.8.

Suppose that you have three coins. Coin A is fair, coin B shows heads with probability 0.6 and coin C shows heads with probability 0.8. Suppose that you have three coins. Coin A is fair, coin B shows heads with probability 0.6 and coin C shows heads with probability 0.8. Coin A is flipped until a head appears, then coin B is flipped until

More information

Chapter 2.5 Random Variables and Probability The Modern View (cont.)

Chapter 2.5 Random Variables and Probability The Modern View (cont.) Chapter 2.5 Random Variables and Probability The Modern View (cont.) I. Statistical Independence A crucially important idea in probability and statistics is the concept of statistical independence. Suppose

More information

Week 2: Probability: Counting, Sets, and Bayes

Week 2: Probability: Counting, Sets, and Bayes Statistical Methods APPM 4570/5570, STAT 4000/5000 21 Probability Introduction to EDA Week 2: Probability: Counting, Sets, and Bayes Random variable Random variable is a measurable quantity whose outcome

More information

Sets and Set notation. Algebra 2 Unit 8 Notes

Sets and Set notation. Algebra 2 Unit 8 Notes Sets and Set notation Section 11-2 Probability Experimental Probability experimental probability of an event: Theoretical Probability number of time the event occurs P(event) = number of trials Sample

More information

[ 1] ST301(AKI) Mid1 2010/10/07. ST 301 (AKI) Mid 1 PLEASE DO NOT OPEN YET! TURN OFF YOUR CELL PHONE! FIRST NAME: LAST NAME: STUDENT ID:

[ 1] ST301(AKI) Mid1 2010/10/07. ST 301 (AKI) Mid 1 PLEASE DO NOT OPEN YET! TURN OFF YOUR CELL PHONE! FIRST NAME: LAST NAME: STUDENT ID: [ 1] ST301(AKI) Mid1 2010/10/07 ST 301 (AKI) Mid 1 PLEASE DO NOT OPEN YET! TURN OFF YOUR CELL PHONE! FIRST NAME: LAST NAME: STUDENT ID: [ 2] ST301(AKI) Mid1 2010/10/07 Choose one answer for each question.

More information

STAT 302 Introduction to Probability Learning Outcomes. Textbook: A First Course in Probability by Sheldon Ross, 8 th ed.

STAT 302 Introduction to Probability Learning Outcomes. Textbook: A First Course in Probability by Sheldon Ross, 8 th ed. STAT 302 Introduction to Probability Learning Outcomes Textbook: A First Course in Probability by Sheldon Ross, 8 th ed. Chapter 1: Combinatorial Analysis Demonstrate the ability to solve combinatorial

More information

2.4. Conditional Probability

2.4. Conditional Probability 2.4. Conditional Probability Objectives. Definition of conditional probability and multiplication rule Total probability Bayes Theorem Example 2.4.1. (#46 p.80 textbook) Suppose an individual is randomly

More information

Chapter 2 Class Notes

Chapter 2 Class Notes Chapter 2 Class Notes Probability can be thought of in many ways, for example as a relative frequency of a long series of trials (e.g. flips of a coin or die) Another approach is to let an expert (such

More information

Independence. P(A) = P(B) = 3 6 = 1 2, and P(C) = 4 6 = 2 3.

Independence. P(A) = P(B) = 3 6 = 1 2, and P(C) = 4 6 = 2 3. Example: A fair die is tossed and we want to guess the outcome. The outcomes will be 1, 2, 3, 4, 5, 6 with equal probability 1 6 each. If we are interested in getting the following results: A = {1, 3,

More information

Announcements. Lecture 5: Probability. Dangling threads from last week: Mean vs. median. Dangling threads from last week: Sampling bias

Announcements. Lecture 5: Probability. Dangling threads from last week: Mean vs. median. Dangling threads from last week: Sampling bias Recap Announcements Lecture 5: Statistics 101 Mine Çetinkaya-Rundel September 13, 2011 HW1 due TA hours Thursday - Sunday 4pm - 9pm at Old Chem 211A If you added the class last week please make sure to

More information

Notes for Math 324, Part 17

Notes for Math 324, Part 17 126 Notes for Math 324, Part 17 Chapter 17 Common discrete distributions 17.1 Binomial Consider an experiment consisting by a series of trials. The only possible outcomes of the trials are success and

More information

2. AXIOMATIC PROBABILITY

2. AXIOMATIC PROBABILITY IA Probability Lent Term 2. AXIOMATIC PROBABILITY 2. The axioms The formulation for classical probability in which all outcomes or points in the sample space are equally likely is too restrictive to develop

More information

Lecture 10: Probability distributions TUESDAY, FEBRUARY 19, 2019

Lecture 10: Probability distributions TUESDAY, FEBRUARY 19, 2019 Lecture 10: Probability distributions DANIEL WELLER TUESDAY, FEBRUARY 19, 2019 Agenda What is probability? (again) Describing probabilities (distributions) Understanding probabilities (expectation) Partial

More information

STA301 Statistics and Probability. Composed By Faheem Saqib Sta 301 Solved Questions

STA301 Statistics and Probability. Composed By Faheem Saqib Sta 301 Solved Questions STA301 Statistics and Probability Composed By Faheem Saqib Current & Past Final Term Solved Questions For more Help Rep At Faheem_saqib2003@yahoo.com Faheem.saqib2003@gmail.com 0334-6034849 Sta 301 Solved

More information

Notes 12 Autumn 2005

Notes 12 Autumn 2005 MAS 08 Probability I Notes Autumn 005 Conditional random variables Remember that the conditional probability of event A given event B is P(A B) P(A B)/P(B). Suppose that X is a discrete random variable.

More information

Fault-Tolerant Computer System Design ECE 60872/CS 590. Topic 2: Discrete Distributions

Fault-Tolerant Computer System Design ECE 60872/CS 590. Topic 2: Discrete Distributions Fault-Tolerant Computer System Design ECE 60872/CS 590 Topic 2: Discrete Distributions Saurabh Bagchi ECE/CS Purdue University Outline Basic probability Conditional probability Independence of events Series-parallel

More information

Intro to Probability Day 3 (Compound events & their probabilities)

Intro to Probability Day 3 (Compound events & their probabilities) Intro to Probability Day 3 (Compound events & their probabilities) Compound Events Let A, and B be two event. Then we can define 3 new events as follows: 1) A or B (also A B ) is the list of all outcomes

More information

Higher Secondary - First year STATISTICS Practical Book

Higher Secondary - First year STATISTICS Practical Book Higher Secondary - First year STATISTICS Practical Book th_statistics_practicals.indd 07-09-08 8:00:9 Introduction Statistical tools are important for us in daily life. They are used in the analysis of

More information

Dr. Babasaheb Ambedkar Marathwada University, Aurangabad. Syllabus at the F.Y. B.Sc. / B.A. In Statistics

Dr. Babasaheb Ambedkar Marathwada University, Aurangabad. Syllabus at the F.Y. B.Sc. / B.A. In Statistics Dr. Babasaheb Ambedkar Marathwada University, Aurangabad Syllabus at the F.Y. B.Sc. / B.A. In Statistics With effect from the academic year 2009-2010 Class Semester Title of Paper Paper Per week Total

More information

STA 2023 EXAM-2 Practice Problems. Ven Mudunuru. From Chapters 4, 5, & Partly 6. With SOLUTIONS

STA 2023 EXAM-2 Practice Problems. Ven Mudunuru. From Chapters 4, 5, & Partly 6. With SOLUTIONS STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6 With SOLUTIONS Mudunuru, Venkateswara Rao STA 2023 Spring 2016 1 1. A committee of 5 persons is to be formed from 6 men and 4 women. What

More information

Econ 325: Introduction to Empirical Economics

Econ 325: Introduction to Empirical Economics Econ 325: Introduction to Empirical Economics Lecture 2 Probability Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 3-1 3.1 Definition Random Experiment a process leading to an uncertain

More information

STAT 311 Practice Exam 2 Key Spring 2016 INSTRUCTIONS

STAT 311 Practice Exam 2 Key Spring 2016 INSTRUCTIONS STAT 311 Practice Exam 2 Key Spring 2016 Name: Key INSTRUCTIONS 1. Nonprogrammable calculators (or a programmable calculator cleared in front of the professor before class) are allowed. Exam is closed

More information

Venn Diagrams; Probability Laws. Notes. Set Operations and Relations. Venn Diagram 2.1. Venn Diagrams; Probability Laws. Notes

Venn Diagrams; Probability Laws. Notes. Set Operations and Relations. Venn Diagram 2.1. Venn Diagrams; Probability Laws. Notes Lecture 2 s; Text: A Course in Probability by Weiss 2.4 STAT 225 Introduction to Probability Models January 8, 2014 s; Whitney Huang Purdue University 2.1 Agenda s; 1 2 2.2 Intersection: the intersection

More information

9/6/2016. Section 5.1 Probability. Equally Likely Model. The Division Rule: P(A)=#(A)/#(S) Some Popular Randomizers.

9/6/2016. Section 5.1 Probability. Equally Likely Model. The Division Rule: P(A)=#(A)/#(S) Some Popular Randomizers. Chapter 5: Probability and Discrete Probability Distribution Learn. Probability Binomial Distribution Poisson Distribution Some Popular Randomizers Rolling dice Spinning a wheel Flipping a coin Drawing

More information

Discrete Probability

Discrete Probability Discrete Probability Counting Permutations Combinations r- Combinations r- Combinations with repetition Allowed Pascal s Formula Binomial Theorem Conditional Probability Baye s Formula Independent Events

More information

Discrete Random Variables

Discrete Random Variables Discrete Random Variables An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2014 Introduction The markets can be thought of as a complex interaction of a large number of random

More information

Introduction to Statistical Data Analysis Lecture 3: Probability Distributions

Introduction to Statistical Data Analysis Lecture 3: Probability Distributions Introduction to Statistical Data Analysis Lecture 3: Probability Distributions James V. Lambers Department of Mathematics The University of Southern Mississippi James V. Lambers Statistical Data Analysis

More information

CHAPTER 14 THEORETICAL DISTRIBUTIONS

CHAPTER 14 THEORETICAL DISTRIBUTIONS CHAPTER 14 THEORETICAL DISTRIBUTIONS THEORETICAL DISTRIBUTIONS LEARNING OBJECTIVES The Students will be introduced in this chapter to the techniques of developing discrete and continuous probability distributions

More information

Properties of Probability

Properties of Probability Econ 325 Notes on Probability 1 By Hiro Kasahara Properties of Probability In statistics, we consider random experiments, experiments for which the outcome is random, i.e., cannot be predicted with certainty.

More information

Introduction to Probability and Statistics Slides 3 Chapter 3

Introduction to Probability and Statistics Slides 3 Chapter 3 Introduction to Probability and Statistics Slides 3 Chapter 3 Ammar M. Sarhan, asarhan@mathstat.dal.ca Department of Mathematics and Statistics, Dalhousie University Fall Semester 2008 Dr. Ammar M. Sarhan

More information

Intermediate Math Circles November 8, 2017 Probability II

Intermediate Math Circles November 8, 2017 Probability II Intersection of Events and Independence Consider two groups of pairs of events Intermediate Math Circles November 8, 017 Probability II Group 1 (Dependent Events) A = {a sales associate has training} B

More information

Review of Statistics

Review of Statistics Review of Statistics Topics Descriptive Statistics Mean, Variance Probability Union event, joint event Random Variables Discrete and Continuous Distributions, Moments Two Random Variables Covariance and

More information

Statistics. Joe Erickson

Statistics. Joe Erickson Statistics Joe Erickson Contents 1 Introduction to Statistics 1 1.1 Basic Definitions.................................. 1 1.2 Data and Measurement.............................. 3 1.3 Experimental Design................................

More information

Probabilistic models

Probabilistic models Probabilistic models Kolmogorov (Andrei Nikolaevich, 1903 1987) put forward an axiomatic system for probability theory. Foundations of the Calculus of Probabilities, published in 1933, immediately became

More information