Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chap 11 Sums of Independent Random Variables and Limit Theorem Ghahramani 3rd edition 2019/5/16.

Published byEmre Sağlık Modified over 5 years ago

Similar presentations

Presentation on theme: "Chap 11 Sums of Independent Random Variables and Limit Theorem Ghahramani 3rd edition 2019/5/16."— Presentation transcript:

1 Chap 11 Sums of Independent Random Variables and Limit Theorem Ghahramani 3rd edition
2019/5/16

2 Outline 11.1 Moment-generating functions
11.2 Sums of independent random variables 11.3 Markov and Chebyshev inequalities 11.4 Laws of large numbers 11.5 Central limit theorem

3 Skip 11.1 Moment-generating functions 11.2 Sum of independent random variables

4 11.3 Markov and Chebyshev inequalities

5 Markov and Chebyshev inequalities

6 Markov and Chebyshev inequalities

7 Markov and Chebyshev inequalities

8 Markov and Chebyshev inequalities

9 Markov and Chebyshev inequalities

10 Markov and Chebyshev inequalities

11 Markov and Chebyshev inequalities

12 Markov and Chebyshev inequalities

13 Markov and Chebyshev inequalities

14 Markov and Chebyshev inequalities

15 Markov and Chebyshev inequalities

16 Markov and Chebyshev inequalities

17 Markov and Chebyshev inequalities

18 11.4 Laws of large numbers

19 Laws of large numbers

20 Laws of large numbers

21 Laws of large numbers

22 Laws of large numbers

23 Laws of large numbers

24 Laws of large numbers

25 Laws of large numbers

26 Laws of large numbers

27 11.5 Central limit theorem

28 Central limit theorem

29 Central limit theorem

30 Central limit theorem

31 Central limit theorem

Download ppt "Chap 11 Sums of Independent Random Variables and Limit Theorem Ghahramani 3rd edition 2019/5/16."

Similar presentations

Ordinary Least-Squares

Ordinary Least-Squares
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.

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.
Functions of Random Variables Notes of STAT 6205 by Dr. Fan.

Functions of Random Variables Notes of STAT 6205 by Dr. Fan.
Occupancy Problems m balls being randomly assigned to one of n bins. (Independently and uniformly) The questions: - what is the maximum number of balls.

Occupancy Problems m balls being randomly assigned to one of n bins. (Independently and uniformly) The questions: - what is the maximum number of balls.
ENGG 2040C: Probability Models and Applications Andrej Bogdanov Spring 2014 8. Limit theorems.

ENGG 2040C: Probability Models and Applications Andrej Bogdanov Spring Limit theorems.
Important Random Variables Binomial: S X = { 0,1,2,..., n} Geometric: S X = { 0,1,2,... } Poisson: S X = { 0,1,2,... }

Important Random Variables Binomial: S X = { 0,1,2,..., n} Geometric: S X = { 0,1,2,... } Poisson: S X = { 0,1,2,... }
Statistics 1: Introduction to Probability and Statistics Section 3-3.

Statistics 1: Introduction to Probability and Statistics Section 3-3.
Randomized Algorithms Randomized Algorithms CS648 Lecture 8 Tools for bounding deviation of a random variable Markov’s Inequality Chernoff Bound Lecture.

Randomized Algorithms Randomized Algorithms CS648 Lecture 8 Tools for bounding deviation of a random variable Markov’s Inequality Chernoff Bound Lecture.
Probability Theory Part 2: Random Variables. Random Variables  The Notion of a Random Variable The outcome is not always a number Assign a numerical.

Probability Theory Part 2: Random Variables. Random Variables  The Notion of a Random Variable The outcome is not always a number Assign a numerical.
1 Chap 5 Sums of Random Variables and Long-Term Averages Many problems involve the counting of number of occurrences of events, computation of arithmetic.

1 Chap 5 Sums of Random Variables and Long-Term Averages Many problems involve the counting of number of occurrences of events, computation of arithmetic.
Time Series Basics Fin250f: Lecture 3.1 Fall 2005 Reading: Taylor, chapter 3.1-3.3.

Time Series Basics Fin250f: Lecture 3.1 Fall 2005 Reading: Taylor, chapter
Rules for means Rule 1: If X is a random variable and a and b are fixed numbers, then Rule 2: If X and Y are random variables, then.

Rules for means Rule 1: If X is a random variable and a and b are fixed numbers, then Rule 2: If X and Y are random variables, then.
CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Multiple random variables Transform methods (Sec. 4.1-4.2, 4.5.7)

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Multiple random variables Transform methods (Sec , 4.5.7)
Chap 10 More Expectations and Variances Ghahramani 3rd edition

Chap 10 More Expectations and Variances Ghahramani 3rd edition
4. Convergence of random variables  Convergence in probability  Convergence in distribution  Convergence in quadratic mean  Properties  The law of.

4. Convergence of random variables  Convergence in probability  Convergence in distribution  Convergence in quadratic mean  Properties  The law of.
Standard Normal Distribution

Standard Normal Distribution
2003/04/23 Chapter 3 1頁1頁 3.6 Expected Value of Random Variables.

2003/04/23 Chapter 3 1頁1頁 3.6 Expected Value of Random Variables.
Math Camp 2: Probability Theory Sasha Rakhlin. Introduction  -algebra Measure Lebesgue measure Probability measure Expectation and variance Convergence.

Math Camp 2: Probability Theory Sasha Rakhlin. Introduction  -algebra Measure Lebesgue measure Probability measure Expectation and variance Convergence.
The moment generating function of random variable X is given by Moment generating function.

The moment generating function of random variable X is given by Moment generating function.
2003/04/24 Chapter 5 1頁1頁 Chapter 5 : Sums of Random Variables & Long-Term Averages 5.1 Sums of Random Variables.

2003/04/24 Chapter 5 1頁1頁 Chapter 5 : Sums of Random Variables & Long-Term Averages 5.1 Sums of Random Variables.

Similar presentations

Ads by Google