EXAM 1
Name: Jasen Shorter Start time: April 9, 2007 2:38am Time allowed: 48 hours Number of questions: 5 Finish Help
TO GET FULL CREDIT FOR A PROBLEM YOU MUST SHOW ALL THE WORK TO GET THE ANSWER. IF YOU GIVE ME JUST THE ANSWER I WILL GIVE YOU ONLY
Singh, Daljit ECE 315 Matlab #4b
Random Process #1
A Continuous Random Process 1 0.5 0 -0.5 y1 y2 y3 y4
-1
0
2
4
6 Time
8
10
12
14
RV average #2
Mean of the Random Variable 0.5
0
-0.5
0
2
4
6 Time
8
10
12
14
Mean of the Random V
Kevin Jon F. Figuracion
ECE 315
Dr. Clark
EXTRA CREDIT:
Write (that is type) a 2-3 page paper with references (in proper format) which describes
and illustrates the relationship between a Random Process and a Stochastic Process. Be
sure to include some ex
Fair Coin
This displays the result of 10 tosses of fair coin. 7 were heads and 3 were tails. No this
is not fair coin because the probability of tails and heads are not equal.
Our outcome has changed when trying the fair toss again. In ten tosses, 4 were
Down load PBRV2b.P to your PBRV directory, and make it the current directory
in MATLAB. Start MATLAB and in the command window enter PBRV2b and hit 'enter'.
This MATLAB assignment looks at some of the characteristics of a few
Continuous Random Variables.
Down load PBRV2a.P to your PBRV directory, and make it the current directory
in MATLAB. Start MATLAB and in the command window enter PBRV2a and hit 'enter'.
This MATLAB assignment looks at some of the characteristics of a few Discrete
Random Variables. As
Quiz 3t
Question 1
(5 points)
What is the standard error for a sample mean?
Student response: Standard Error for sample mean,(SE)=Standard Deviation(SD)s/sqrt(n); s is given as the SD
of the sample mean; derived from the Standard Error = sigma/sqrt(n); si
Kevin Figuracion
ECE 315
MATLAB 2
MATLAB 2A
BINOMIAL
The figure above displays the plot of the theoretical density and distribution functions for a
Binomial random variable.
Changing p to 0.5 and np to 1 gives the figure below
This could be described as a
You will need to type these equations in Yogi.i am not sure if these numbers are
right but I calculated them to the best of my knowledge)I have also attached the
excel file for the midterm, it has the calculations in it.
In this case the weight is the dep
Unit 5a
In this unit we will look it a sample function from a continuous-time (CT) WSS Ergodic
random process, simple linear time-invariant (LTI) system, and the output sample
function.
Figure 5a-1
The initial figure for Unit 5a
Now push the CT Signals bu
Unit 4a
In this unit we are working with the idea of a Random Process, and if the process is
stationary, and ergodic. In the MATLAB PBRV4a.p file we see examples of three
random processes. In MATLAB PBRV4b.p we see examples of two processes which are
stat
UNIT 4b
In this part of the unit we are going to revisit the three Random Processes from Unit 4a,
and discuss the concepts of STATIONARITY AND ERGODICITY.
Figure 4b-1
The initial figure of PBRV4b.p
Now push the Random Process #1 button
This is the same RP
Unit 4c
This is the third and final part of the Unit 4 Matlab Assignment. In this part of the
assignment we talk about the Power Spectral Density (PSD). The PSD is Fourier
transform of a Autocorrelation function. Sense the autocorrelation function that we
Figure 1a Start up Screen for PBRV2a
Figure 2a-1 Initial Display of the Binomial Theoretical
Density and Distribution Functions.
Figure 2a-2 Display after p=0.5 and np=1
This is like the basic probability example in which the probability of getting either
Side-by-side comparison of LaPlace and z- transforms
Since we want to learn to design continuous and sampled control systems simultaneously,
it is useful to emphasize how the mathematical transforms we use (LaPlace for
continuous systems and z-transforms
Practice Problems for Examination II
Solutions and Remarks
1. To function properly in a certain application an electrical resistor must have a resistance of
60 ohms, with a tolerance of 0.02 ohms. The present manufacturing process produces
resistors with
Syed Hasan
Ece 315
Assignment#3
Down load the Stat Data file. The data in the file is that which you and your classmates
submitted. You are to calculate the following: (1) the regression of height on weight; (2)
the goodness of fit of the day of week to a
These are the answers I put on mine: -Heenal
Question 1:
Two numbers are chosen at random from the numbers 1 to 10 without replacement. Find the probability that the
second number chosen is 7.
ANS:
For the first number picked we are assuming that 7 is not
Write 2-3 page paper with references(in proper format) which describes and illustrates
the relationship between a Random Process and a Stochastic Process
STOCHASTIC PROCESS
A process of change governed by probabilities (see probability) at each step. E.g.
Figure 4b-1 Initial Display of pbrv4b.p
Figure 4b-2 Display of a Random Process # 1
Figure 4b-3 Display of the RV Average
The mean of the random variable changes with time.
Figure 4b-4 Display when both the angles are changed to pi.
To test the hypotheses
Micros oft Equation
3.0
Im not sure about # 4 but here it is:
Using the equation on page 51:
Fx ( x)
1
x
( a x ) 2
e
2 2
2 2
by squaring it so we have:
1
F ( x)
2 2
d
x
e
( a x ) 4
4 4
d
where ax=0, and =1
now go to page 52 of Peebles book:
plugging
You are to calculate the following:
(1) the regression of height on weight;
(2) the goodness of fit of the day of week to a uniform rv;
(3) Test to hypotheses at the .05 level that March is the most likely month of birth;
(4) Find the 95% confidence inter
4.3-15
r2 y2
fy(y)= f x , y ( x, y ) dx =
r2 y2
dx
r 2
2 r2 y2
(
,
y
r
=
r2
0, y r
r 2 x2
f x ( x ) f x , y ( x, y ) dy
r 2 x2
dy
r 2
2 2 2 2
r x / r , x r
=
0, x r
4.5-5
x
5
5
f x x f x , y ( x, y )dy x 2 ydy x 4 ,0 x 2
32
0 16
(a)
(and zero els
Figure 1-1
Fair Coin
Figure 2-1
When N=50
Figure 2-2
When N = 9000, The No. Of Heads = the No. Of Tails
Figure 2-3
Fair Die : 30 rolls of the fair die
Figure 3-1
60 rolls of the fair die
Figure 3-2
Figure 3-3
After 100,000 rolls the faces seem to be very
Syed Hasan
ECE 315
2/21/04
Matlab 4a
Random Process #1
The phases are uniform for the family of sine waves. They are orthogonal to each other
because they differ by pi/2.
RV #1 average-
this is not stationary in the mean.
editing the th4 phase angle to be
Figure 4a-1 Initial Display of pbrv4a.p
Figure 4a-2 Display of a Random Process # 1
The phases are uniform for the family of sine waves. They are orthogonal to each other because they
differ by pi/2.
Figure 4a-3 Display of RV # 1 Average
Figure 4a-4 Displ
Matlab Assignment # 2
PBRV2A
BINOMIAL
BINOMIAL WITH
np =1 AND p =.5
POISSON
UNIFORM
f x ( x)
1
ba
the uniform probability density function
dFx( x)
1
0
b 1 a
dx
ba
so for a=4, b=5 and it will look like the plot of a fair coin, here is the graph:
The Slop
Question 1
(6 points)
X(t) = A sin(Wot) is a random process with Wo a constant and A an uniform random
variable -0.5 to 0.5. Find E[X(t)].
Equation:
Equation editor
Save answer
Bottom of Form
Question 2
(6 points)
Y(t) = Bsin(Wot) is a random process Wo a
1.look at page 188 Peebles book
X(t)=A sin(w0*t),
E[ X (t )] E ( A sin( wo t ) sin( wo t ) * E ( A)
because only A is the random variable.
Where for a uniform random variable:
E( X )
a b 0.5 0.5
0
2
2
so E[X(t)]=sin(w0*t)*(0)=0
2.
the formula for the aut
YOGESH B ASUDANI
ASSIGNMENT # 2b
PBRV2B
UNIFORM TIME
Uniform Time with A= 0
Uniform Time with A= 2 and B = 4
Uniform time With A = 3 and B = 5
Uniform Time with A = 5 and B = 5
UNIFORM HISTOGRAM
Uniform Histogram with A =0
Uniform Histogram with A = 2 and