'Random variable' diaporamas de présentation

Chapter 3, Section 9 Discrete Random Variables. Moment-Generating Functions.  John J Currano, 12/15/2008. æ. ö. k. (  c ) k  j E [ Y j ]. E [ ( Y – c ) k ]. k. =. å. ç. ÷. j. è. ø. =. j. 0. E [ ( Y – E ( Y ) ) k ] = E [ ( Y –  ) k ]. m. =. k.

Section Duration Data Introduction Sometimes we have data on length of time of a particular event or ‘spells’ Time until death Time on unemployment Time to complete a PhD

RANDOM VARIABLES, EXPECTATIONS, VARIANCES ETC. Variable. Recall: Variable: A characteristic of population or sample that is of interest for us. Random variable: A function defined on the sample space S that associates a real number with each outcome in S. DISCRETE RANDOM VARIABLES.

S TATISTICS. E LEMENTARY. Chapter 4 Probability Distributions. M ARIO F . T RIOLA. E IGHTH. E DITION. Chapter 4 Probability Distributions. 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions

Stats for Engineers: Lecture 4. Summary from last time. Standard deviation – measure spread of distribution. Variance = (standard deviation) 2. Discrete Random Variables. Binomial distribution – number of successes from independent Bernoulli (YES/NO) trials.

Random Processes Introduction. Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering E-mail: rslab@ntu.edu.tw. Introduction.

The Invisible Academy: nonlinear effects of linear learning. Mark Liberman University of Pennsylvania myl@cis.upenn.edu. Outline. An origin myth: naming without Adam a computer-assisted thought experiment

Chapter 5: Continuous Random Variables. Where We’ve Been. Using probability rules to find the probability of discrete events Examined probability models for discrete random variables. Where We’re Going. Develop the notion of a probability distribution for a continuous random variable

5-1 Random Variables and Probability Distributions. The Binomial Distribution. Random Variables. Discrete – These variables take on a finite number of values, or a countable number of values Number of days absent Number of students taking a course

Continuous random variables. Continuous random variable Let X be such a random variable Takes on values in the real space (-infinity; +infinity) (lower bound; upper bound) Instead of using P(X= i ) Use the probability density function f X (t) Or f X (t) dt.

4.2 (cont.) Expected Value of a Discrete Random Variable. A measure of the “middle” of the values of a random variable. Center. The mean of the probability distribution is the expected value of X, denoted E(X) E(X) is also denoted by the Greek letter µ (mu) . Economic Scenario. Profit

CS498-EA Reasoning in AI Lecture #9. Instructor: Eyal Amir Fall Semester 2011. Previously. First-Order Logic Syntax: Well-Founded Formulas Semantics: Models, Satisfaction, Entailment Models of FOL: how many, sometimes unexpected Resolution in FOL Resolution rule Unification Clausal form

Chapter 4.2. Variance and Covariance. Variance and Covariance. The mean or expected value of a random variable X is important because it describes the center of the probability distribution.

4.7 Brownian Bridge. 報告者 : 劉彥君. 4.7.1 Gaussian Process. Definition 4.7.1:

DATA 220 Mathematical Methods for Data Analysis September 17 Class Meeting. Department of Applied Data Science San Jose State University Fall 2019 Instructor: Ron Mak www.cs.sjsu.edu/~mak. Some Counting Principles.

45-733: lecture 6 (chapter 5). Continuous Random Variables. Joint continuous distributions. The joint continuous distribution is a complete probabilistic description of a group of r.v.s Describes each r.v. Describes the relationship among r.v.s. Joint continuous distributions.

Review. Lecture 42 Tue, Dec 12, 2006. Chapter 1. Sections 1.1 – 1.4. Be familiar with the language and principles of hypothesis testing. Given two explicit hypotheses, be able to calculate  and  . Given a value of the “test statistic,” be able to calculate the p -value. Etc.

Chapter 5 Discrete Probability Distributions. 5.3 EXPECTATION 5.3.1 The Mean and Expectation (Expected Value) 5.3.2 Some Applications 5.4 VARIANCE AND STANDARD DEVIATION. 5.3 EXPECTATION. 5.3.1 The Mean and Expectation (Expected Value) Experimental approach

5.3 Martingale Representation Theorem. 報告者：顏妤芳. 5.3.1 Martingale Representation with One Brownian Motion. Corollary 5.3.2 is not a trivial consequence of the Martingale Representation Theorem , Theorem 5.3.1, with replacing W(t)

Selection --Medians and Order Statistics (Chap. 9). The i th order statistic of n elements S={ a 1 , a 2 ,…, a n } : i th smallest elements Also called selection problem Minimum and maximum Median, lower median, upper median Selection in expected/average linear time