Seventh Problem Assignment
EECS 401
Problem 1 Random variables X and Y are independent and are described by the probability density functions fX (x) and fY (y)
fX (x)
0
fY ( y )
1
x (hours)
0
y (hours)
1
Stations A and B are connected by two parallel mess
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Spring 2014
Final Exam
Solutions
Please write your name and discussion section number clearly at top of first page. N
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Homework 2
Solutions
1. You have a fair coin, you toss it 5 times.
(a) What is the probability that you g
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Homework 4
Solutions
1. Compute the following expectations
(a) What is the expected value when we roll a
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Discussion 8
Friday May 29
1. Alice is playing a repeated game of Rock Paper Scissors. In an attempt to b
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Discussion 7
Solutions
1. A certain component is critical to the operation of an electrical system and mu
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Discussion3
Notes
1. [regaring to quiz question 1]
Find the number n of distinct permutations that can be
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Homework 3
Solutions
1. A casino is considering a dice game that would pay the winner of the game $10. Th
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Homework 8
Solutions
Note: The first problem is 20 points and the others are 10 points.
1. [20 pts]You ar
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Quiz 7
Solutions
Please write your name and discussion section number clearly at top of first page.
1. [3
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Spring 2015
Discussion 2
Friday April 10
1. Students who attend discussion are more likely to pass ECE 139. A student
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Discussion Week 4
1. A stick of length 1 is split at a point U that is uniformly distributed over (0, 1).
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Homework 8
due Monday June 1 at 8:00pm in submission box in HFH 3120
(please write your name and discussi
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2014
Common Distributions
5. Pascal (k, p) distribution
x 1 pk (1 p)xk ,
k1
PX (x) =
0
Discrete Distributions
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Homework 7
due Wednesday May 27 at 8:00pm in submission box in HFH 3120
(please write your name and discu
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Spring 2015
Midterm Study Guide
The purpose of this study guide is to outline many of the topics that might appear in
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Discussion Week 6 - Problem 4
1. Random variables X and Y have the joint PDF
fX,Y (x, y) =
2x
0
0 x, y 1
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
Prof. P. Sen
ECE 139 Probability and Statistics
Spring 2015
Sunday Discussion Section #7 Notes
1. Gaussian Random Vectors
From the book, X is the Gaussian random vec
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Homework 1
Solutions
1. In an experiment, C and D are independent events with probabilities P [C] =
Determine:
1
5
an
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Spring 2015
ECE 139 Discussion Examples: Week 8
1. Consider the random process Y (t) = at + X, where a is a constant
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Spring 2015
Homework 6
Solutions
1
1. Consider an exponential random variable X whose pdf fx (x) = 2
exp(x y)2 /2). T
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139 Probability and Statistics
Prof. P. Sen
Spring 2015
Midterm
Solutions
Please write your name and discussion section number clearly at top of first page. No c
ECE 139: Discussion examples: Week 1
1. In an experiment, A and B are mutually exclusive events with probabilities P [A B] = 5/8 and
P [A] = 3/8.
(a) Find P [B], P [A B c ], and P [A B c ].
Soln: Since AB=, P [AB]=0. To find P [B], we can write P [AB]=P [
Sixth Problem Assignment
EECS 401
Problem 1 An ambulance travels back and forth, at a constant speed, along a road of
length L. At a certain moment of time an accident occurs at a point uniformly distributed on the road. (That is, its distance from one of
Fifth Problem Assignment
EECS 401
Problem 1 Discrete random variable X is described by the PMF
pX (x) =
K
0,
x
12 ,
if x = 0, 1, 2
for all other values of x
Let D1 , D2 , . . . , DN represent N successive independent experimental values of random variable
Fourth Problem Assignment
EECS 401
Problem 1 Joe and Helen each know that the a priori probability that her mother will
be home on any given night is 0.6. However, Helen can determine her mothers plan
for the night at 6 P.M., and then, at 6:15 P.M., she h
Third Problem Assignment
EECS 401
Problem 1 Oscar has lost his dog in either forest A (with a priori probability 0.4) or
in forest B (with a priori probability 0.6). If the dog is alive and not found by the Nth
day of the search, it will die that evening
Second Problem Assignment
EECS 401
Problem 1 Bo and Ci are the only two people who will enter the Rover Dog Fod jingle
contest. Only one entry is allowed per contestant, and the judge (Rover) will declare
the one winner as soon as he receivers a suitably
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 139
Probability and Statistics
Spring 2011
Homework Assignment #5
(Due on Tuesday 5/10/2011 by 8 pm in the Homework Box)
Solve the following problems in the text