VARIABEL ACAK DAN EKSPEKTASI (Random Variable and Expectation)

Slides:

Advertisements

Similar presentations

Ir. I Nyoman Setiawan, MT VARIABEL ACAK DAN EKSPEKTASI (Random Variable and Expectation) 1. Sheldon M Ross, Introduction Probability and Statistics for.

Advertisements

Let X 1, X 2,..., X n be a set of independent random variables having a common distribution, and let E[ X i ] = . then, with probability 1 Strong law.

PROBABILITY DISTRIBUTION BUDIYONO 2011 (distribusi peluang)

Continuous Random Variables Chapter 5 Nutan S. Mishra Department of Mathematics and Statistics University of South Alabama.

Sebaran Peluang Bersama

BAB V FUNGSI VARIABEL ACAK Ekspektasi dan Momen.

TURUNAN/ DIFERENSIAL.

Peubah Acak Kontinu Pertemuan 09 Matakuliah: L0104 / Statistika Psikologi Tahun : 2008.

1 Pertemuan 07 Variabel Acak Diskrit dan Kontinu Matakuliah: I Statistika Tahun: 2008 Versi: Revisi.

Engineering Statistics ECIV 2305 Chapter 2 Random Variables.

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

Review of Basic Probability and Statistics

Continuous Random Variables. For discrete random variables, we required that Y was limited to a finite (or countably infinite) set of values. Now, for.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Discrete random variables Probability mass function Distribution function (Secs )

Probability Distributions – Finite RV’s Random variables first introduced in Expected Value def. A finite random variable is a random variable that can.

Today Today: Chapter 5 Reading: –Chapter 5 (not 5.12) –Suggested problems: 5.1, 5.2, 5.3, 5.15, 5.25, 5.33, 5.38, 5.47, 5.53, 5.62.

1 Engineering Computation Part 6. 2 Probability density function.

1 Pertemuan 09 Peubah Acak Kontinu Matakuliah: I0134 – Metode Statistika Tahun: 2007.

TRANFORMASI PEUBAH ACAK DENGAN FUNGSI PAMBANGKIT MOMEN

Samples vs. Distributions Distributions: Discrete Random Variable Distributions: Continuous Random Variable Another Situation: Sample of Data.

Today Today: Chapter 5 Reading: –Chapter 5 (not 5.12) –Exam includes sections from Chapter 5 –Suggested problems: 5.1, 5.2, 5.3, 5.15, 5.25, 5.33,

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

1 Pertemuan 06 Sebaran Penarikan Contoh Matakuliah: I0272 – Statistik Probabilitas Tahun: 2005 Versi: Revisi.

Probability and Statistics Review

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

2. Random variables  Introduction  Distribution of a random variable  Distribution function properties  Discrete random variables  Point mass  Discrete.

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

1 Pertemuan 8 Variabel Acak-2 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1.

Ya Bao Fundamentals of Communications theory1 Random signals and Processes ref: F. G. Stremler, Introduction to Communication Systems 3/e Probability All.

1 Pertemuan 05 Peubah Acak Kontinu dan Fungsi Kepekatannya Matakuliah: I0262 – Statistik Probabilitas Tahun: 2007 Versi: Revisi.

LECTURE UNIT 4.3 Normal Random Variables and Normal Probability Distributions.

Distribution Function properties. Density Function – We define the derivative of the distribution function F X (x) as the probability density function.

CIS 2033 based on Dekking et al. A Modern Introduction to Probability and Statistics, 2007 Instructor Longin Jan Latecki Chapter 7: Expectation and variance.

Beberapa Distribusi Khusus

Functions of Random Variables. Methods for determining the distribution of functions of Random Variables 1.Distribution function method 2.Moment generating.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 5-1 2nd Lesson Probability and Sampling Distributions.

Functions of Random Variables. Methods for determining the distribution of functions of Random Variables 1.Distribution function method 2.Moment generating.

1 Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS Systems.

Probability and Statistics Dr. Saeid Moloudzadeh Random Variables/ Distribution Functions/ Discrete Random Variables. 1 Contents Descriptive.

Statistics 3502/6304 Prof. Eric A. Suess Chapter 4.

Lecture 14 Prof. Dr. M. Junaid Mughal Mathematical Statistics 1.

Math 4030 – 6a Joint Distributions (Discrete)

Point Estimation of Parameters and Sampling Distributions Outlines:  Sampling Distributions and the central limit theorem  Point estimation  Methods.

Random Variables. Numerical Outcomes Consider associating a numerical value with each sample point in a sample space. (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

Chapter 3 Discrete Random Variables and Probability Distributions  Random Variables.2 - Probability Distributions for Discrete Random Variables.3.

PENDAHULUAN Dalam matematika, deret Taylor adalah representasi fungsi matematika sebagai jumlahan tak hingga dari suku-suku yang nilainya dihitung dari.

Statistics and Probability Theory Lecture 12 Fasih ur Rehman.

Anifuddin Azis UNCERTAINTY. 2 Introduction The world is not a well-defined place. There is uncertainty in the facts we know: What’s the temperature? Imprecise.

Random Variables By: 1.

Probability Distribution for Discrete Random Variables

Chapter 7 Sampling and Sampling Distributions

Peubah Acak Diskrit Pertemuan 07

Statistics Lecture 19.

Pertemuan 5 Probabilitas-1

Lecture 3 B Maysaa ELmahi.

Cumulative distribution functions and expected values

Probability for Machine Learning

Random Variables and their Properties

Variabel Acak – Distribusi Probabilitas

Dasar-Dasar Pemrograman

Bab 5 Distribusi Normal © 2002 Prentice-Hall, Inc.

AP Statistics: Chapter 7

TM 605: Probability for Telecom Managers

Probability & Statistics Probability Theory Mathematical Probability Models Event Relationships Distributions of Random Variables Continuous Random.

POPULATION (of “units”)

Statistics Lecture 12.

... DISCRETE random variables X, Y Joint Probability Mass Function y1

Introduction to Probability: Solutions for Quizzes 4 and 5

MATH 3033 based on Dekking et al

Presentation transcript:

VARIABEL ACAK DAN EKSPEKTASI (Random Variable and Expectation) Sheldon M Ross, Introduction Probability and Statistics for Engineers and Scientists, 2004 Oliver C. Ib, Fundamentals of Applied Probability and Random Proceses, 2005 John A Gubner, Probability and random Processes for Electrical and Computer Engineers, 2006 KA Stroud, Engineering Mathematics ,2001 Ir. I Nyoman Setiawan, MT

Pengertian Variabel Acak (Random Variable) Variabel acak (Random Variable) adalah suatu fungsi yang mengaitkan suatu bilangan real pada setiap unsur ruang sampel Ir. I Nyoman Setiawan, MT

Ir. I Nyoman Setiawan, MT

Ir. I Nyoman Setiawan, MT

Fungsi Distribusi Kumulatif (Cumulatif Distribution Function /CDF) Ir. I Nyoman Setiawan, MT

Properties Fx(x) Ir. I Nyoman Setiawan, MT

Contoh : Ir. I Nyoman Setiawan, MT

Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Variabel Acak Diskret (Discrete Random Variable) Fungsi Masa Probabilitas (Probability Mass Function/PMF) Ir. I Nyoman Setiawan, MT

Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Variabel Acak Kontinu (Continuous Random Variable) Fungsi Padat Probabilitas (Probability Dencity Function/PDF) Ir. I Nyoman Setiawan, MT

Properties dari fx (x) Ir. I Nyoman Setiawan, MT

Contoh : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Ekspektasi (Expectation) Ir. I Nyoman Setiawan, MT

Ir. I Nyoman Setiawan, MT

Contoh : Ir. I Nyoman Setiawan, MT

Moment Ir. I Nyoman Setiawan, MT

Central Moment ke n Ir. I Nyoman Setiawan, MT

Contoh : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT

Contoh : Ir. I Nyoman Setiawan, MT

Penyelesaian : Ir. I Nyoman Setiawan, MT