Probability distributions Carola Wenk 11/13/13 CMPS/MATH 2170 - PowerPoint PPT Presentation

Nov 23, 2023 •160 likes •218 views

CMPS/MATH 2170 -- Fall 2013 Discrete Mathematics Probability distributions Carola Wenk 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 1 Rolling two dice Sum of two fair six-sided dice: S = {1,2,3,4,5,6} x {1,2,3,4,5,6} X((s 1 ,s

CMPS/MATH 2170 -- Fall 2013 Discrete Mathematics Probability distributions Carola Wenk 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 1
Rolling two dice Sum of two fair six-sided dice: S = {1,2,3,4,5,6} x {1,2,3,4,5,6} X((s 1 ,s 2 )) = s 1 +s 2 x P(X=x) {X=x} P(X=x) 2 1/36 {(1,1)} 0.18 3 2/36 {(1,2),(2,1)} 0.16 4 3/36 {(1,3),(2,2),(3,1)} 0.14 5 4/36 {(1,4),(2,3),(3,2),(4,1)} 0.12 6 5/36 {(1,5),(2,4),(3,3),(4,2),(5,1)} 0.10 7 6/36 {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} 0.08 0.06 8 5/36 {(2,6),(3,5),(4,4),(5,3),(6,2)} 0.04 9 4/36 {(3,6),(4,5),(5,4),(6,3)} 0.02 10 3/36 {(4,6),(5,5),(6,4)} 0.00 11 2/36 {(5,6),(6,5)} 1 2 3 4 5 6 7 8 9 10 11 12 1/36 {(6,6)} Probability function or probability distribution: p(x) = P(X=x) 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 2
Rolling two dice x 2 p(x) x p(x) x p(x) 2 1/36 2/36 4/36 3 2/36 6/36 18/36 4 3/36 12/36 48/36 5 4/36 20/36 100/36 6 5/36 30/36 180/36 P(X=x) 7 6/36 42/36 294/36 0.18 8 5/36 40/36 320/36 0.16 9 4/36 36/36 324/36 0.14 10 3/36 30/36 300/36 0.12 0.10 11 2/36 22/36 242/36 0.08 12 1/36 12/36 144/36 0.06 0.04 Sum 36/36 252/36 1974/36 0.02 = 1 = 7 = 54.833 0.00 1 2 3 4 5 6 7 8 9 10 11 Probability function or probability distribution: p(x) = P(X=x) 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 3
Binomial Distribution 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 4
Geometric Distribution 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 5

Download Presentation

Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Common Probability Distributions Several simple probability distributions are useful in may

Deep Learning Srihari Common Probability Distributions Several simple probability distributions are useful in may contexts in machine learning Bernoulli over a single binary random variable Multinoulli distribution over a variable

305 views • 17 slides

Chapter II.2: Basic Probability Theory and Statistics 1. What is a probability? 1.1. Probability

Chapter II.2: Basic Probability Theory and Statistics 1. What is a probability? 1.1. Probability spaces, events, and random variables 2. Distributions 2.1. Discrete distributions 2.2. Continuous distributions 3. Moments, independence, and

355 views • 34 slides

Unit 2: Probability and distributions Lecture 1: Probability and conditional probability

Unit 2: Probability and distributions Lecture 1: Probability and conditional probability Statistics 101 Thomas Leininger May 21, 2013 Announcements Announcements 1 Probability 2 Randomness Defining probability Law of large numbers

1.36k views • 76 slides

Outline Discrete Probability Distributions The Binomial Distribution (3.1) The

12/7/2006 219323 Probability y and Statistics for Software and Knowledge Engineers Lecture 4: Discrete and Continuous Probability Distributions Monchai Sopitkamon, Ph.D. Outline Discrete Probability Distributions The Binomial

171 views • 14 slides

Unit 2: Probability and distributions 1. Probability and conditional probability GOVT 3990 -

Unit 2: Probability and distributions 1. Probability and conditional probability GOVT 3990 - Spring 2017 Cornell University Dr. Garcia-Rios Slides posted at http://garciarios.github.io/govt_3990/ Outline 1. Main ideas 1. Disjoint and

451 views • 21 slides

Unit 2: Probability and distributions 3. Normal and binomial distributions GOVT 3990 - Spring

Unit 2: Probability and distributions 3. Normal and binomial distributions GOVT 3990 - Spring 2020 Cornell University Outline 1. Housekeeping 2. Main ideas 1. Two types of probability distributions: discrete and continuous 2. Normal

893 views • 63 slides

Outline Continuous Probability Distributions The Uniform Distribution (4.1) ( ) The

12/14/2006 219323 Probability y and Statistics for Software and Knowledge Engineers Lecture 5: Continuous Probability Distributions Monchai Sopitkamon, Ph.D. Outline Continuous Probability Distributions The Uniform Distribution

280 views • 15 slides

Outline 1. Bayes Law L7: Probability Basics 2. Probability distributions CS 344R/393R:

Outline 1. Bayes Law L7: Probability Basics 2. Probability distributions CS 344R/393R: Robotics Benjamin Kuipers 3. Decisions under uncertainty Probability Probability Theory For a proposition A , the probability p ( A ) is p (

399 views • 5 slides

Unit 2: Probability and distributions 3. Normal and binomial distributions PS: Explain your

Announcements Unit 2: Probability and distributions 3. Normal and binomial distributions PS: Explain your reasoning + show your work will result in STA 104 - Summer 2017 point deductions next time RA 3 tomorrow Duke University,

170 views • 5 slides

Input Distributions Reading: Chapter 6 in Law Input Distributions Overview Probability Theory

Input Distributions Reading: Chapter 6 in Law Input Distributions Overview Probability Theory for Choosing Distributions Peter J. Haas Data-Driven Approaches Other Approaches to Input Distributions CS 590M: Simulation Spring Semester 2020

463 views • 6 slides

Probability Distributions. Conditional Probability Russell Impagliazzo and Miles Jones Thanks to

Probability Distributions. Conditional Probability Russell Impagliazzo and Miles Jones Thanks to Janine Tiefenbruck http://cseweb.ucsd.edu/classes/sp16/cse21-bd/ May 16, 2016 In probability, we want to reason about the likelihood of

605 views • 49 slides

AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS Parametric Distributions Basic

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS Parametric Distributions Basic building blocks: Need to determine given Representation: or ? Recall Curve Fitting Binary Variables (1) Coin

1.09k views • 86 slides

Lecture 6 : Discrete Random Variables and Probability Distributions 0/ 31 Go to BACKGROUND

Lecture 6 : Discrete Random Variables and Probability Distributions 0/ 31 Go to BACKGROUND COURSE NOTES at the end of my web page and download the file distributions . Today we say goodbye to the elementary theory of probability and start

1.21k views • 32 slides

Lecture 6 : Discrete Random Variables and Probability Distributions 0/ 32 Go to BACKGROUND

Lecture 6 : Discrete Random Variables and Probability Distributions 0/ 32 Go to BACKGROUND COURSE NOTES at the end of my web page and download the file distributions . Today we say goodbye to the elementary theory of probability and start

708 views • 33 slides

Unit 2: Probability and distributions 3. Normal and binomial distributions Sta 101 - Spring 2019

Announcements Unit 2: Probability and distributions 3. Normal and binomial distributions Sta 101 - Spring 2019 RA 3 on Tuesday PS 2 due Friday, PA 2 due Sunday Duke University, Department of Statistical Science Dr. Abrahamsen Slides

250 views • 5 slides

Statistics for Business Random Variables and Probability Distributions, Special Discrete and

Statistics for Business Random Variables and Probability Distributions, Special Discrete and Continuous Probability Distributions Panagiotis Th. Konstantinou MSc in International Shipping, Finance and Management , Athens University of Economics

702 views • 67 slides

Order statistics of Matrix-Geometric distributions Azucena Campillo Navarro 1 , Bo Friis Nielsen 1

Motivation Order statistics for independent Matrix-geometric distributions Conclusion Order statistics of Matrix-Geometric distributions Azucena Campillo Navarro 1 , Bo Friis Nielsen 1 , Mogens Bladt 2 . 1 Technical University of Denmark

1.16k views • 70 slides

The Geometric Distribution of Ranks and Selmer Groups of Elliptic Curves over Function Fields

The Geometric Distribution of Ranks and Selmer Groups of Elliptic Curves over Function Fields Aaron Landesman (Stanford) Tony Feng (MIT) Eric Rains (Caltech) Special Session on Geometry and Topology in Arithmetic Madison, WI Slides available

481 views • 25 slides

A Denotational Semantics for Low-Level Probabilistic Programs with Nondeterminism Di Wang 1 Jan

A Denotational Semantics for Low-Level Probabilistic Programs with Nondeterminism Di Wang 1 Jan Hoffmann 1 Thomas Reps 2,3 1 Carnegie Mellon University 2 University of Wisconsin 3 GrammaTech, Inc. Probabilistic Programs Draw random data from

914 views • 72 slides

Pair HMM based gap statistics for re-evaluation of indels in alignments with affine gap penalties

Guideline Introduction Methods Results Pair HMM based gap statistics for re-evaluation of indels in alignments with affine gap penalties Alexander Schnhuth, Raheleh Salari Cenk Sahinalp Centrum Wiskunde & Informatica Amsterdam

601 views • 42 slides

On the R enyi Entropy of Log-Concave Sequences James Melbourne University of Minnesota

On the R enyi Entropy of Log-Concave Sequences On the R enyi Entropy of Log-Concave Sequences James Melbourne University of Minnesota melbo013@umn.edu Tomasz Tkocz Carnagie Mellon University ttkocz@andrew.cmu.edu ISIT June 8, 2020 On

394 views • 21 slides

Non-Parametric Priors For Generative Adversarial Networks Rajhans Singh 1 , Pavan Turaga 1,2 ,

Non-Parametric Priors For Generative Adversarial Networks Rajhans Singh 1 , Pavan Turaga 1,2 , Suren Jayasuriya 1,2 , Ravi Garg 3 , Martin W. Braun 3 1 School of Electrical, Computer, and Energy Engineering, Arizona State University 2 School of

201 views • 8 slides

Statistical Inference Lecture 3: Common Families of Distributions MING GAO DASE @ ECNU (for

Statistical Inference Lecture 3: Common Families of Distributions MING GAO DASE @ ECNU (for course related communications) mgao@dase.ecnu.edu.cn Mar. 24, 2020 Outline Discrete Distributions 1 Continuous Distributions 2 Exponential Family

715 views • 58 slides

Chapter 3: Common Families of Distributions STK4011/9011: Statistical Inference Theory Johan

Chapter 3: Common Families of Distributions STK4011/9011: Statistical Inference Theory Johan Pensar STK4011/9011: Statistical Inference Theory Chapter 3: Common Families of Distributions 1 / 8 Overview Exponential Families 1 Location and

194 views • 8 slides