ECEN 303: Homework 8 Solutions
Problem 1:
Let Xi denote the ith experimental value of X. Let Z = X1 +X2 +X3 +X4 , so that Z is the random
variable whose value we observe. For notation, let fZ|H0 (z|H0
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,
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,
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 ow
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
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 e
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 an
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)
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
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 h
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 fu
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 exp
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
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
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 fi
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 t
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
j
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
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.
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
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
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 . W
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:
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. Describ
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 r
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 mom
Random Signals & Systems
ECEN303.501, Fall 2013
Quiz 4
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this
academic work.
Signature:
Name:
Reading Question:
1. 1 pt Th