EE420/500 Class Notes
4/15/2008
John Stensby
Chapter 7 - Correlation Functions
Let X(t) denote a random process. The autocorrelation of X is defined as
R x ( t1, t 2 ) = E[X( t1 )X( t 2 )] =
zz
x x f ( x1, x 2 ; t1, t 2 ) dx1dx 2 . - - 1 2
(7-1)
The aut
EE420/500 HW #8 - All T196 II Summer 2007
1. (Type II) The random variables X and Y have a joint density of the form
ny, 0<Iygo<y<1j L1
ME
_._
i), otherwise . IE
fXY (BEE?
It
a) Find the constant K. a- "
b) Determine the correlation coefcient between X a
f John wms I 7 one C" The. +olwwmj bequwcm 0260'1-
7/ qaf an + t~ L
i, V
i+(%)z,& ()_6L+._
[l+(-)+ (-2-)Hm 1
0 1K " 1K
#203) = 212)
Km: k=o
= i = $15 * ,qug
3- 0/4)" 23055
m : 5); $95 NH]
P15- iJokv Mix-$3
Pm: PEAIMJPM +PMIE] pg
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EE420/500 HW # 7 Solutions
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available in the Library.
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1'. Let X and Y bejoi
EE42W5DD Hy; #4 xing anon
I1 Determine The win: utthn mnslnnt A.
In J Find the pmhnhilinr that I'm: :- 1 .
E Find the pmbahillty' that I] 1' 3": '5; l.
4. [T'pr II Lel I be H cuntmunun rnndum variable with knnwn Fx- LnL! = [1. m], where cfw_14:2 3!-
n.
EE420/500 HW # /0 Solutions
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Classmates need this information.
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1. In a radar syst
EE420/500 HW #Solutions
l/
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1. Let r and up be
EEJlIa'E
Lat X h: a cunmmus randnm variable with imam-n fgx. Let I = [xh Hg]. when: cfw_m :- le
dmt m1 iutmal. 111 team! nf knuwn f: and FE E I]. nd an expressiun fur the :unditiunal
density x [1 E I . Shaw all 01 1mm- work.
.Fx+ax1xe.r Fx|KE!I
1-1int: SL
EE420/500 HW # 1 Solutions
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1. The random variab
EE420/500 HW # 3 Solutions
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1, Let the moments b
EE420/500 HW # 6 Solutions
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1. c
EE420/500 HW # 5 Solutions
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t 1. Out of EDD fami
Poisson Approximation #3.doc
In transferring digital data over a channel, the bit error rate is found to be 104. Assume
that errors are made independently. Find the probability that 104 received bits contain
more than four errors (give a numerical answer
EE420/500 HW #7 Summer 2007
_,_._._._.-
I. Let X1 and X; be independent exponential random variables both with parameter 7t > 0 so that
fx1x2(xlax2)= K2 exp[Mx1+x2)], x12 0&x2 .20.
Define
Y1: X1+ X2
Y2=XIKX2
Determine the joint density for Y1 and Y2.
2. L
EE420/500 HW # 6 Solutions
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Madison Hall and the Library.
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classmates need this information.
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EEallt EIW #1 S rin euee
' . A hlt. eenteitts 20 red. 1t] white. 3!] leiue and 5E] green hells. An experiment eeneietn ef deeming :1 hell
Irem the hex and reeerding the hells ee'lrn. Then. the hall is rem-med te the hex. Suppeee the experiment
in repeated
EE4EDIUD HW #3 tting 2005
5. cfw_Tpr II A telepherie L'Illl enema at Tandem in the interval [,'|'], an the lime efthe mall is
deeeriheti by a tandem variable that 1'5 unithrmiy distributed an [111']- Find the |:Irelizlahjlit:_tr 171111 5
t 5 t. l LE 1] th
EE420/500 Class Notes
03/26/08
John Stensby
Chapter 6 - Random Processes
Recall that a random variable X is a mapping between the sample space S and the extended real line R+. That is, X : S R+. A random process (a.k.a stochastic process) is a mapping fro
EE420/500 Class Notes
03/13/08
John Stensby
Chapter 5 Moments and Conditional Statistics
Let X denote a random variable, and z = h(x) a function of x. transformation Z = h(X). We saw that we could express Consider the
E[Z] = E[h(X)] =
z
h( x )fx ( x ) dx
EE420/500 Class Notes Chapter 3: Multiple Random Variables
02/21/08
John Stensby
Let X and Y denote two random variables. The joint distribution of these random variables is defined as
FXY (x, y) = P[X x, Y y] .
(3-1)
This is the probability that (X,Y) li
EE420/500 Class Notes
02/04/09
John Stensby
Chapter 2 - Random Variables
In this and the chapters that follow, we denote the real line as R = (- < x < ), and the
extended real line is denoted as R+ Rcfw_. The extended real line is the real line with
thro
EE420/500 Class Notes
03/05/09
John Stensby
Chapter 4 - Function of Random Variables
Let X denote a random variable with known density fX(x) and distribution FX(x). Let y = g(x) denote a real-valued function of the real variable x. Consider the transforma
EE420/500 Class Notes
01/24/08
John Stensby
Chapter 1 - Introduction to Probability
Several concepts of probability have evolved over the centuries.
We discuss three
different approaches:
1) The classical approach.
2) The relative frequency approach.
3) T
Summer 2007
1313420500 HW #4
1. Two fair dice are tossed until the combination 1 and 1 (snake eyes) appear. Determine
the average (1'. e., expected) number of tosses required to hit snake eyes".
2. A coin is weighted so that P[l-I] 5 3/4 and P[T] = A. Sup
Summer 0?
[11111420500 Midterm Exam
m variable X(f;) = mi of the fair-die
nditional distribution F(x l M) of rando
script i denotes the number
1. Determine the co
experiment, where M=cfw_f2, f4, f6 is the event "even" has occurred (sub
and mm is 10 time t
EE420/500 HW # 5 Solutions
Please copy and return. Copiers are available
in the Engineering Building, Madison Hall and
the UAH Library.
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fellow classmates need access to this
information.
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