ECE 353 HOMEWORK 3
Winter 2014
Due date: February 4, 2014 at 4 pm
1. A sequence of characters is transmitted over a channel that introduces errors with probability
p 0.01.
a) If N is the number of error-free characters until the first error, what is the p
HOMEWORK 6
Due date: Monday February 29 at 4 pm.
1. Find E cfw_ X Y if X and Y are independent exponential random variables with parameters x = 1
and y = 2 , respectively. Hint: Let Z= X Y , obtain the pdf of Z and then calculate Ecfw_| Z | .
2. Let K an
Gamma R.V.: Consider a Poisson process cfw_X (t ) : t 0 with parameter and cfw_Ti i1 be the
sequence of exponentially distributed independent increments between events (inter-occurrence
times), i.e.,
T2
T1
T3
T4
Tn
Time
1
0
1
2
3
4
n-1 n
t
T
Let T be the
1
Probability theory can be explained either from the axiomatic or the relative frequency points of
view. In this course we shall focus on the axiomatic approach.
Axiomatic Approach
Definition The sample space of an experiment with random outcomes is the
Introduction to Random Processes
Definition: Let (,P) be a probability space. Let X be the mapping from the
sample space to a space of functions called sample functions. Then X is called a
random process (r.p.) if at each time ti the mapping X is a random
HOMEWORK 2
Winter 2016
Due date: Monday February 1 at 4 pm.
1. A data source generates hexadecimal characters. Let X be the integer value corresponding to a
hexadecimal character. Suppose that the four binary digits in the character are independent and ea
HOMEWORK 1
Winter 2016
Due date: Monday January 25 at 4 pm.
1. A binary communication system transmits a signal X that is either +2 or 2 volts. A malicious
channel reduces the magnitude of the received signal by the number of heads it counts in two tosses
HOMEWORK 3
Winter 2016
Due date: Monday February 8 at 4 pm
1. A sequence of characters is transmitted over a channel that introduces errors with probability
p = 0.01 .
a) If N is the number of error-free characters until the first error, what is the pmf o
worksheet: Heaps Name:
Worksheet: Heap Practice - Answers
In Preparation: Read Chapter 11 on the Priority Queue ADT and Heaps
Insert the following values, in the order that they are given into a Min Heap. Show the
tree after each insertion.
1) 30,20,50,10
cs?61
Quiz
First Name:
Last Name:
1.
Show the tree that results from adding the following numbers, in the order given, to an
AVL tree. Please show the tree that results after each insertion and necessary rotations.
132,20,60,50,7 0,80,7 5l (10 pts)
<2
'uu
csz61
Quiz
First Namel
Last Name:
7.
Show the tree that results from adding the following numbers, in the order
given, to a Binary Search Tree [68, 100, 10, 42,70,56,22,16,95] (9 pts)
b8
btr
\
7*-.t\,^.
|rt,".
too
,/-_
'ao
/< ti'
,l
loo
qz io
ot
bs
,ra'
I
1
I. H OMEWORK 3
A. Problem 1
1) Roll 2 fair dice. Let event
A = the sum of the dice is 6
and event
B = first die equal 4
Are this events dependent or independent?
2) Roll 2 fair dice. Let event
A = the sum of the dice is 7
and event
B = first die equal 4
HOMEWORK 4
Due date: Monday February 15 at 4 pm.
1. A discrete-valued random variable X takes on values from the set A = cfw_1, 2,3, , 216 with probability
P( X= x=
)
1
, x A.
216
a) What is the mean value of X?
cfw_
b) What is the mean squared value of
HOMEWORK 5
Due date: Monday February 22 at 4 pm.
1. Compare the Chebyshev inequality and the exact probability of the event
cfw_ X m
X
> b
a) When X is an exponentially distributed random variable with = 0.5 and b = 3
b) When X is Binomial with n = 8 and