Probabilistic Systems Analysis and Applied Probability

Lecture 19: Weak Law of Large Numbers

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Lecture Topics

The sample mean A tool: Chebyshev’s inequality Convergence “in probability” Convergence of the sample mean (weak law of large numbers)

Lecture Activities

• Watch the Lecture 19 Video by Prof. Tsitsiklis (00:50:13)
• Review the Lecture 19: Weak Law of Large Numbers Slides (PDF)
• Read Sections 5.1–5.3 and start Section 5.4 in the textbook

Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Two of the problems have an accompanying video where a teaching assistant solves the same problem.

• Recitation 20 Problems (PDF)
• Recitation 20 Solutions (PDF)

Recitation Help Videos

PROBLEM #	PROBLEM TITLE	PROBLEM SOLVED BY
2	Convergence in Probability and in the Mean Part 1 Convergence in Probability and in the Mean Part 2	Kuang Xu Kuang Xu
3	Convergence in Probability Example	Kuang Xu

Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

• Tutorial 10 Problems (PDF) Do ONLY Problem 1
• Tutorial 10 Solutions (PDF)

Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 9 covers Lectures 18 and 19.

• Problem Set 9 (PDF)
• Problem Set 9 Solutions (PDF)

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