Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2007)
Tutorial 11
Week of May 1, 2009
1. Problem 7.37 on p.404
Empty taxis pass by a street corner at a Poiss
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2009)
Tutorial 8
April 10, 2009
1. Example 11, textbook p304
In each minute of basketball play, Alicia commit
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2009)
Tutorial 7
Week of April 3, 2009
1. (Problem 3.34)
A defective coin minting machine produces coins whos
Descriptor HowTo Guide
Release 2.7.1
Guido van Rossum
Fred L. Drake, Jr., editor
January 10, 2011
Python Software Foundation
Email: docs@python.org
Contents
1
Abstract
ii
2
Denition and Introduction
ii
3
Descriptor Protocol
ii
4
Invoking Descriptors
iii
5
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 2
September 14, 2010
1. Problem 1.15, page 56-57 in the text.
A coin is tossed twice. Alice cl
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 2: Solutions
September 14, 2010
1. Let A be the event that the rst toss is a head and let B be
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
Transcript Recitation: The Monty Hall Problem
Hi. In the session, we'll be solving the Monty Hall problem. And this problem is based on an old
game show that was called "Let's Make
LECTURE 2
Review of probability models
Readings: Sections 1.3-1.4
Sample space
Mutually exclusive
Collectively exhaustive
Lecture outline
Right granularity
Review
Event: Subset of the sample space
Conditional probability
Allocation of probabiliti
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Tutorial 1
September 16/17, 2010
1. Let A and B be events such that A B. Can A and B be independent?
2. A
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
Transcript Lecture 2
The following content is provided under a Creative Commons license. Your support will help
MIT OpenCourseWare continue to offer high quality educational resourc
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
Transcript Recitation: Conditional Probability Example
Hi. Today we're going to do another fun problem that involves rolling two dice. So if you guys
happen to frequent casinos, thi
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
Transcript Recitation: A Coin Tossing Puzzle
Hi. In this problem, we'll be going over practice with the calculation of conditional probabilities.
We'll start with a game where our f
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Problem Set 2
Due September 22, 2010
1. Most mornings, Victor checks the weather report before deciding w
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Problem Set 2: Solutions
Due September 22, 2010
1. (a) The tree representation during the winter can be d
LECTURE 3
Models based on conditional
probabilities
Readings: Section 1.5
3 tosses of a biased coin:
P(H) = p, P(T ) = 1 p
Review
Independence of two events
p
1- p
HHT
p
Independence of a collection of events
HHH
HTH
p
Review
p
1- p
1- p
P(A B)
P(A |
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 1: Solutions
September 9, 2010
1. Since the events A B c and Ac B are disjoint, we have, using
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2010)
Problem Set 1
Due: September 15, 2010
1. Express each of the following events in terms of the events A,
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 1
September 11, 2015
1. Venn Diagrams
In this problem, you are given descriptions in words of ce
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 3
September 25, 2015
(1) (MITx Unit 3 Solved Problem 2.)
Rooks on a chessboard. Eight rooks are
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 4
October 2, 2015
1. (MITx Unit 4 Solved Problem 8.)
Joint PMF drill. The joint PMF of the rando
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 2
September 18, 2015
1. (MITx Unit 2 Solved Problem 2.)
The Chess Problem. This years Belmont ch
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 1
September 11, 2015
1. Venn Diagrams
In this problem, you are given descriptions in words of ce
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 7
October 23, 2015
1. (Textbook Problem 4.18, page 249.)
Correlation coecients. Consider four ra
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 8
October 30, 2015
1. (MITx, Unit 7, Lecture 14, Exercise 5)
Continuous unknown and observation.
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 6
October 16, 2015
(1) (MITx Unit 5 , Lecture 10, Exercise 10.)
Let K be a discrete random varia
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Tutorial 5
October 9, 2015
(1) Consider a normal random variable X with mean 3 and variance 4. Find the e
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2015)
Recitation 1
September 10, 2015
1. The probability of the dierence of two events.
(MITr Unit 1 Solved Pro
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Problem Set 1: Solutions
Due: September 15, 2010
1. (a) A B C
(b) (A B c C c ) (Ac B C c ) (Ac B c C) (Ac
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 3: September 16, 2010
1. Example 1.20, page 37 in the text.
Consider two independent fair coin
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 3: Solutions
September 16, 2010
1. See the textbook, Example 1.20, page 37.
2. (a) In order t