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
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
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Question 2
(6 points)
Y(t) = Bsin(Wot) is a random process Wo a
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
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
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
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
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
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
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
No
birth month
color of eyes
1
12 blue
2 February
Brown
3 August
brown
4 march
dark brown
5 september
brown
6 July
brown
7 June
Brown
8 august
brown
9 October
black
10 may
brown
11 August
Blue
12 April
Brown
13 January
brown
14 june
brown
15
4 black
16 ap
Exam 2
Name: Syed Hasan
Start time: January 29, 2004 9:49am
Time allowed: 72 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 2 POIN
Question 1
(5 points)
If evens A and B are independent what is the probability of their INTERSECTION?
Student response: P(AnB) = P(A) P(B) it is the product of the two independent events
Score:
Question 2
5/5
(5 points)
Find the probability that a single
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
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
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
ECE315: Introduction to Probability and Statistics for
Electrical Engineers
Thomas Ketseoglou
Electrical and Computer Engineering
CalPoly Pomona
February 10, 2012
Ketseoglou (ECE315 #6)
ECE315: Introduction to Probability and Statistics for Electrical Eng
Figure 4c-1 Initial Display of pbrv4c.p
Figure 4c-2 Display of the Random Process #1
Figure 4c-3 Display of the RV Autocorrelation
Figure 4c-4 Display of the Time Autocorrelation
Figure 4c-4 Display of the Power Spectrum
The maximum value is supposed to o
Problem#4- the answer to both the different versions is the same
Please change the wording
The autocorrelation is given by:
Rxx(u )
w(t) * w(t u)du =4*(width of the overlap)
if a constant is autocorrelated it returns c^2
in this case if the signal shift
CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA
COLLEGE OF ENGINEERING
ECE 315
Spring 2004
Instructor: Dr. T. Ketseoglou
HW #1
Problems 1-4.3, 1-4.5, 1-4.8, 1-7.1, 1-7.5, 1-7.8. Due one week from today.
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