Introduction to Probability
2nd Edition
Problem Solutions
(last updated: 9/18/15)
c
Dimitri P. Bertsekas and John N. Tsitsiklis
Massachusetts Institute of Technology
WWW site for book information and
Lecture 1: Sets and Probabilistic Models
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konkuk University
Lecture 1
Probability and Statistics, Spring 2016
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Probability
In non-mathematical se
Probability and Statistics, S2016
Posted: March 23, 2016
Problem Set 2
Lecturer: Hyang-Won Lee
Due: March 30, 2015
1. Consider tossing a coin 100 times. Assume that each toss is independent of others.
Lecture 2: Conditional Probability
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konkuk University
Lecture 2
Probability and Statistics, Spring 2016
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Conditional Probability
In many probabilist
Lecture 4: Independence
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konkuk University
Lecture 4
Probability and Statistics, Spring 2016
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Independence
Independent events
P(A|B) captures the pa
Lecture 6: Discrete Random Variables
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konkuk University
Lecture 6
Probability and Statistics, Spring 2016
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Random Variables
Type of outcomes
Nume
Probability and Statistics, S2016
Posted: March 9, 2016
Problem Set 1
Lecturer: Hyang-Won Lee
Due: March 16, 2015
1. Use only the three probability axioms (and set algebra) to prove that for any event
Lecture 3: Total Probability Theorem and Bayes Rule
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konkuk University
Lecture 3
Probability and Statistics, Spring 2016
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Total Probability Theorem
Lecture 7: Mean, Variance and Joint PMFs
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konkuk University
Lecture 7
Probability and Statistics, Spring 2016
1 / 11
Expectation
It is sometimes desira
Lecture 5: Counting
Hyang-Won Lee
Dept. of Internet & Multimedia Eng.
Konuk Univresity
Lecture 5
Prboaility and Statistisc , Spring 2016
1/8
Counting
Calculation of probabilities often involves counti