Lecture 5 b Faten alamri.

Slides:

Advertisements

Similar presentations

Special random variables Chapter 5 Some discrete or continuous probability distributions.

Advertisements

Exponential Distribution. = mean interval between consequent events = rate = mean number of counts in the unit interval > 0 X = distance between events.

Log-linear and logistic models Generalised linear model ANOVA revisited Log-linear model: Poisson distribution logistic model: Binomial distribution Deviances.

Continuous Distribution. 1. Continuous Uniform Distribution f(x) 1/(b-a) abx Mean :  MIDPOINT Variance :  square length I(a,b) A continuous rV X with.

Lecture (10) Mathematical Expectation. The expected value of a variable is the value of a descriptor when averaged over a large number theoretically infinite.

Use of moment generating functions. Definition Let X denote a random variable with probability density function f(x) if continuous (probability mass function.

Review for Midterm Including response to student’s questions Feb 26.

STAT 270 What’s going to be on the quiz and/or the final exam?

Statistics for Financial Engineering Part1: Probability Instructor: Youngju Lee MFE, Haas Business School University of California, Berkeley.

Review of Basic Probability and Statistics

Chapter 1 Probability Theory (i) : One Random Variable

Estimation of parameters. Maximum likelihood What has happened was most likely.

Presenting: Assaf Tzabari

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Continuous random variables Uniform and Normal distribution (Sec. 3.1, )

Probability and Statistics Review

Engineering Probability and Statistics - SE-205 -Chap 3 By S. O. Duffuaa.

A random variable that has the following pmf is said to be a binomial random variable with parameters n, p The Binomial random variable.

The moment generating function of random variable X is given by Moment generating function.

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 4 Continuous Random Variables and Probability Distributions.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference.

Week 51 Relation between Binomial and Poisson Distributions Binomial distribution Model for number of success in n trails where P(success in any one trail)

Chapter 21 Random Variables Discrete: Bernoulli, Binomial, Geometric, Poisson Continuous: Uniform, Exponential, Gamma, Normal Expectation & Variance, Joint.

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

Moment Generating Functions 1/33. Contents Review of Continuous Distribution Functions 2/33.

Random variables Petter Mostad Repetition Sample space, set theory, events, probability Conditional probability, Bayes theorem, independence,

MTH 161: Introduction To Statistics

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Review of Exam 2 Sections 4.6 – 5.6 Jiaping Wang Department of Mathematical Science 04/01/2013, Monday.

Continuous Random Variables and Probability Distributions

CPSC 531: Probability Review1 CPSC 531:Distributions Instructor: Anirban Mahanti Office: ICT Class Location: TRB 101.

4.2 Variances of random variables. A useful further characteristic to consider is the degree of dispersion in the distribution, i.e. the spread of the.

Statistics for Engineer Week II and Week III: Random Variables and Probability Distribution.

Moment Generating Functions

Lecture 4 1 Discrete distributions Four important discrete distributions: 1.The Uniform distribution (discrete) 2.The Binomial distribution 3.The Hyper-geometric.

Continuous Distributions The Uniform distribution from a to b.

Probability & Statistics I IE 254 Summer 1999 Chapter 4  Continuous Random Variables  What is the difference between a discrete & a continuous R.V.?

Chapter 12 Probability. Chapter 12 The probability of an occurrence is written as P(A) and is equal to.

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 6 Some Continuous Probability Distributions.

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

1 Since everything is a reflection of our minds, everything can be changed by our minds.

STA347 - week 31 Random Variables Example: We roll a fair die 6 times. Suppose we are interested in the number of 5’s in the 6 rolls. Let X = number of.

MATH 4030 – 4B CONTINUOUS RANDOM VARIABLES Density Function PDF and CDF Mean and Variance Uniform Distribution Normal Distribution.

Lecture 10 Image restoration and reconstruction 1.Basic concepts about image degradation/restoration 2.Noise models 3.Spatial filter techniques for restoration.

Methodology Solving problems with known distributions 1.

Stats Probability Theory Summary. The sample Space, S The sample space, S, for a random phenomena is the set of all possible outcomes.

Math 4030 Midterm Exam Review. General Info: Wed. Oct. 26, Lecture Hours & Rooms Duration: 80 min. Close-book 1 page formula sheet (both sides can be.

Engineering Statistics - IE 261

INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2011 Pearson Education, Inc. Chapter 16 Continuous Random.

Exam 2: Rules Section 2.1 Bring a cheat sheet. One page 2 sides. Bring a calculator. Bring your book to use the tables in the back.

IE 300, Fall 2012 Richard Sowers IESE. 8/30/2012 Goals: Rules of Probability Counting Equally likely Some examples.

Topic 5: Continuous Random Variables and Probability Distributions CEE 11 Spring 2002 Dr. Amelia Regan These notes draw liberally from the class text,

Chap 5-1 Chapter 5 Discrete Random Variables and Probability Distributions Statistics for Business and Economics 6 th Edition.

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

Chapter 14 Fitting Probability Distributions

Ch3.5 Hypergeometric Distribution

Random Variable 2013.

The Exponential and Gamma Distributions

Lecture 5 Faten alamri.

CONTINUOUS RANDOM VARIABLES

Chapter 7: Sampling Distributions

The Bernoulli distribution

Moment Generating Functions

Moment Generating Functions

Part 2: Named Discrete Random Variables

Chapter 5 Some Discrete Probability Distributions.

Chapter 6 Some Continuous Probability Distributions.

Functions of Random variables

3. Random Variables Let (, F, P) be a probability model for an experiment, and X a function that maps every to a unique point.

Chapter 3 : Random Variables

Continuous Distributions

Moments of Random Variables

Presentation transcript:

Lecture 5 b Faten alamri

Common families of distribution Discrete distribution 1.discrete uniform distribution 2.hypergeometric distribution 3.binomial distribution 4.poisson distribution 5.negative binomial distribution

Continues distribution 1.uniform distribution 2.gamma distribution 3.normal distribution Exponential families Binomial exponential family Normal exponential family

Location and scale families There are three types of families are called Location families, scale families and location scale families Theorem 3.5.1 Let f(x) be any pdf and let and Be any given constants then the function is a pdf

Definition 3.5.2 Let f(x) be any pdf then the family of pdf f(s- ) Indexed by the parameter Is called the location family with standard pdf f(x) and is called the location parameter for the family Exponential location family

Definition 3.5.4 Let f(x) be any pdf. Then for any The family of pdf , indexed by the parameter ,is called the scale family with standard pdf f(x) and is called the scale parameter of family

Definition 3.5.5 Let f(x) be any pdf. Then for any And any ,the family of pdfs , indexed by parameter is called a location-scale family with standard pdf f(x); is called a location parameter and is called a scale parameter