Massachusetts nstitute 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 points)
(a) (7 points)
We start by recognizing that fX (x)
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 21 Solutions
November 23, 2010
1. (a) To use the Markov inequality, let X =
10
i=1 Xi .
Then,
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Final Exam Solutions | Fall 2009)
Problem 3. (25 points)
(a) (5 points)
The recurrent states are cfw_3,4.
(b) (5 points
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 19 Solutions: November 16, 2010
1. (a) The Markov chain is shown below.
1
1
15
9
1/2
1/8
1/8
1
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. (10 points) Let Ri be the amount of time Stephen spends
Massachusetts nstitute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Spring 2008)
Question 1
Multiple choice questions. CLEARLY circle the best answer for each question below. Each quest
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 18: Solutions
November 9, 2010
1. a) The number of remaining green sh at time n completely det
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 24: Solutions
December 7, 2010
1. (a) Normalization of the distribution requires:
1=
pK (k; )
Massachusetts nstitute of Technology
Department of Electrical Engineering & Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Spring 2009)
Question 1
Multiple Choice Questions: CLEARLY circle the appropriate choice. Scratch paper is available
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 20 Solutions: November 18, 2010
1. (a) Let Xi be a random variable indicating the quality of t
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 17 Solutions
November 4, 2010
1. (a) K has a Poisson distribution with average arrival time =
Massachusetts nstitute of Technology
Department of Electrical Engineering Computer Science
6 041/6 431: Probabilistic Systems Analysis
(Final Exam Solutions | Fall 2010)
4. 4 points) Is the sequence Yn a Markov chain? Justify your answer.
Solution: No. As
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 15 Solutions
October 28, 2010
1. (a) Let X be the time until the rst bulb failure. Let A (resp
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 13 Solutions
October 21, 2010
1. (a) We begin by writing the denition for E[Z | X, Y ]
E[Z | X
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Fall 2010)
Recitation 14 Solutions
October 26, 2010
1. (a) Let X = (time between successive mosquito bites) = (time
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(
)
Problem 1: True or False (2pts. each, 18 pts. total)
No partial credit will be given for individual questions in
Massachusetts nstitute 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. 80 points) In this problem:
(i) X is a (continuous) unifor