Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 1 (Solutions)
Reading Assignment:
1. Chapter 1: Mathematical Review;
2. Chapter 2: Combinatorics.
Problems:
1. In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be arranged
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 2 (Solutions)
Reading Assignment:
1. Chapter 3: Basic Concepts of Probability
Problems:
1. Out of the students in a class, 60% are geniuses, 70% love chocolate, and 40% fall into both categories.
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 9 (Solutions)
Reading Assignment:
1. Chapter 9: Functions and Derived Distributions.
2. Chapter 10: Expectations and Bounds.
Problems:
1. (a) A re station is to be located along a road of length A
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 4 (Solutions)
Reading Assignment:
1. Chapter 5: Discrete Random Variables.
Problems:
1. In a certain community, 36 percent of the families own a dog, and 22 percent of the families that own
a dog
ECEN 303: Homework 9 Solutions
Problem 1:
(1) Let M denote the sum of NA and NB . We can nd the PMF of M by convolving the PMFs
of NA and NB . But we just need the probability M = 3, so it is easier to simply do an explicit
enumeration in this case
Pr(M =
ECEN 303: First Problem Assignment
Due in class at the beginning of lecture on Thursday, January 26, 2012.
Problem 1: (15 points) Fully explain your answers to the following questions.
(a) If events A and B are mutually exclusive and collectively exhausti
ECEN 303: Second Problem Assignment
Please give to Ms. Gayle Travis in ZEC 241 by noon on Fri. Feb 3, 2012.
Problem 1: (30 points) Bo and Cl are the only two people who will enter the Rover Dog Food
jingle contest. Only one entry is allowed per contestant
ECEN 303: Fourth Problem Assignment
Due in ZEC 241 by noon on Friday, February 17, 2012.
Problem 1: (25 points) 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
ECEN 303: Third Problem Assignment
Please give to Ms. Gayle Travis in ZEC 241 by noon on Feb. 10, 2012.
Problem 1: (35 points) Oscar has lost his dog in either forest A (with a priori probability 0.4) or
in forest B (with a priori prohability 0.6). If the
ECEN 303: Fifth Problem Assignment
Due in ZEC 241 by noon on February 24, 2012.
Problem 1: (24 points) Discrete random variable X is described by the PMF
(
x
K 12
, if x = 0, 1, 2
pX (x) =
0,
for all other values of x
Let D1 , D2 , . . . , DN represent N
ECEN 303: Eleventh Problem Assignment
Due by noon on April 27, 2012 in ZEC 241.
Problem 1: (18 points) Let X1 , X2 , . . . be independent, identically distributed random variables
with (unknown but finite) mean and positive variance. For i = 1, 2, . . . ,
ECEN 303: Seventh Problem Assignment
Due in ZEC 241 by noon on Friday, March 23, 2012.
Probiem ‘i: (24 points) Random' variables X and Y are independent and are described by the
probability density functions fx(x) and fY (y)
fx (X) fr (Y)
x (hours) y (hou
ECEN 303: Eighth Problem Assignment
Due by noon on Friday, March 30, 2012 in ZEC 241.
Problem 1: (17 points) A random variable X is known to be the sum of K independent and
identically distributed exponential random variables, each with an expected value
ECEN 303: Ninth Problem Assignment
Due by noon on Friday, April 13, 2012 in ZEC 241.
Problem 1: (21 points) The hitherto uncaught burglar is hiding in city A (with a priori probability
0.3) or in city B (with a priori probability 0.6), or he has left the
ECEN 401: Tenth Problem Assignment
Due by noon on Friday, April 20, 2012 in ZEC 241.
Problem 1: (18 points) The Markov chain with transition probabilities listed below is in state 3
immediately before the first trial.
p1,1 = p2,2 = 0.4, p1,2 = p2,1 = 0.6,
ECEN 303: Sixth Problem Assignment
Due in ZEC 241 by noon on Friday, March 9, 2012.
Problem 1: (30 points) Joe Lucky plays the lottery on any given week with probability p, inde
pendently of whether he piayed on any other week. Each time he plays, he has
Random Signals & Systems
ECEN303.501, Fall 2013
Exam 1
Date: October 3, 2013
Problems:
1. Assign one of the choices to each of the following denitions:
experiment, event, outcome, sample space, function, bijection, combination, permutation, partition,
pow
Random Signals & Systems
ECEN303.501, Fall 2013
Exam 2
Date: November 7, 2013
Problems:
1. True or False:
(a) 0.5 pt The variance of a random variable, if it exists, must always be nonnegative.
True.
(b) 0.5 pt If two random variables X and Y are independ
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 5 (Solutions)
Reading Assignment:
1. Chapter 6: Meeting Expectations.
Problems:
1. Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose
that we win $2
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 6 (Solutions)
Reading Assignment:
1. Chapter 7: Multiple Discrete Random Variables.
Problems:
1. A total of 4 buses carrying 148 students from the same school arrives at a football stadium. The bu
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 3 (Solutions)
Reading Assignment:
1. Chapter 4: Conditional Probability
Problems:
1. A system is composed of 5 components, each of which is either working or failed. Consider an experiment that co
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 8 (Solutions)
Reading Assignment:
1. Chapter 8: Continuous Random Variables.
Problems:
1. Consider a sequence of independent Bernoulli trials, each of which is a success with probability p. Let
X1
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 7 (Solutions)
Reading Assignment:
1. Review Chapters 1 to 7.
Problems:
1. A stock market trader buys 100 shares of stock A and 200 shares of stock B . Let X and Y be the
price changes of A and B ,
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 11 (Solutions)
Reading Assignment:
1. Chapter 12: Convergence, Sequences and Limit Theorems.
Problems:
1. We start with a stick of length . We break it at a point which is chosen according to a un
Random Signals & Systems
ECEN303.501, Fall 2013
Assignment 10 (Solutions)
Reading Assignment:
1. Chapter 11: Multiple Continuous Random Variables.
Problems:
1. Choose a number U from the unit interval [0, 1] with uniform distribution. Find the cumulative
Random Signals & Systems
ECEN303.501, Fall 2013
Final Exam
Date: December 9, 2013
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic
work.
Signature:
Name:
Table of important random variables:
Name
PMF or PDF
Be
Random Signals & Systems
ECEN303.501, Fall 2013
Quiz 1
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.
Signature:
Name:
Reading Question:
1. Describe in English what are Sample Space, Events, Outcomes of
Random Signals & Systems
ECEN303.501, Fall 2013
Quiz 5
Reading Question:
1. Consider a Gaussian random variable with PDF
x2
1
< x < .
fX (x) = e 2
2
(a) What is the mean and variance of X ?
You can recognize that this is a standard normal/Gaussian random
Random Signals & Systems
ECEN303.501, Fall 2013
Quiz 3
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.
Signature:
Name:
Reading Question:
1. The moments of a random variable X taking values in set X () a