Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
6.041/6.431 Fall 2010 Final Exam Solutions
Wednesd
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
6.041/6.431 Fall 2010 Quiz 2 Solutions
Problem 1.
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2009)
Quiz 2 Solutions:
November 3, 2009
Problem 2. (49
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
6.041/6.431 Spring 2009 Quiz 1
Wednesday, March 11, 7:30  9:30 PM.
SOLUTIONS
Question
0
1
2
Name:
3
Recitation Instructor:
Part
Score
all
a
b
c
d
e
f
a
b
c
d
e
f
g
h
Total
Out of
2
40
5
2
5
5
5
5
2
2
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2009)
Quiz 1 Solutions:
October 13, 2009
1. (10 p oints)
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Quiz 1 Solutions:
October 12, 2010
Problem 1.
1.
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
LECTURE 5
Random variables
Readings: Sections 2.12.3, start 2.4
An assignment of a value (number) to
every possible outcome
Lecture outline
Mathematically: A function
from the sample space to the
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
LECTURE 4
Discrete uniform law
Readings: Section 1.6
Let all sample points be equally likely
Then,
Lecture outline
P(A) =
Principles of counting
number of elements of A
A
=
total number of sampl
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
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 collec
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
LECTURE 2
Review of probability models
Readings: Sections 1.31.4
Sample space
Mutually exclusive
Collectively exhaustive
Lecture outline
Right granularity
Review
Event: Subset of the sample sp
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
6.041 Probabilistic Systems Analysis
6.431 Applied Probability
Coursework
Quiz 1 (October 12, 12:0512:55pm)
Turn in recitation and tutorial scheduling form
(last sheet of course information hand
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
6.041/6.431 Spring 2009 Final Exam
Thursday, May 21, 1:30  4:30 PM.
Question
0
1
2
3
4
Name:
Recitation Instructor:
5
6
7
Part
Score
all
all
a
b
c
a
b
c
a
b
a
b
c
d
e
a
b
Total
Write your solutions
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2009)
Final Solutions:
December 15, 2009
Problem 2. (20
Probabilistic Systems Analysis and Applied Probability
EECS 6.041

Fall 2010
6.041/6.431 Spring 2008 Quiz 2
Wednesday, April 16, 7:30  9:30 PM.
SOLUTIONS
Name:
Question
0
1
2
Recitation Instructor:
TA:
3
6.041/6.431:
Part
Score
all
a
b
c
d
e
f
a
b
c
d
e
Total
Out of
3
36
4
5