ECE450
Mid-Term#1 Exam (100 points)
(M. Youssef)
Problem 1 (25 points):
A telephone switching center survey indicates that one of four calls is a business call (B),
that one-tenth of business calls ar
ECE450
Mid-Term#2 Exam (100 points)
(M. Youssef)
Problem 1 (35 points):
In a digital communication system, messages are encoded into binary symbols 0 and 1.
Because of noise in the system, an incorrec
1. Royal flush
A, K, Q, J, 10, all the same suit.
A K G J 10
O O O O O Q Q
. 0.
0,0
2. Straight flush
Five cards in a sequence, all in the same suit.
8 7 6 5 4
.0.0 90.0 .00 .00 .00
0. o. o. o
99 99
ECE450: Extra Credit 3, Due Sunday February 12 (Midnight)
1. The CSUN IEEE chapter is to choose a President, Treasurer and secretary, all
different, from a group of 10 students. How many different cho
ECE 450 - Lecture #9
Pairs of Random Variables - Overview
Introduction to Pairs (X, Y) of Random Variables
The joint CDF for the pair X, Y
The joint PDF for the pair X, Y
Examples
Independence of
ECE 450 - Lecture # 7
Overview
Review
Transformations of RVs
Alternate approach to finding fY(y), using definition
of FY(y), the cdf
Expected values, moments of RVs
1
Review
Exponential pdf for R
Using the F-Table for
Gaussians An Example
Recall: For an arbitrary (non-standard)
Normal RV, X: N(m, s)
0
Pr(X < x0) = F(
s
)
Example: Say X is N(2, 4); to find
Pr(X < 3), we need
0
Pr(X < 3) =F(
s
ECE 450 - Lecture # 8
Review
Mean: X E( X) x fX ( x ) dx
Mean of Y = g(X) : E(Y) = g( x ) fX ( x ) dx
Overview
Mean & (More Generally) Moments of RVs, continued
Conditional Averages
Characteristi
ECE 450 - Lecture #9, Part 1
Pairs of Random Variables, continued - Overview
Joint PDFs A Discrete Example (PDF for Pair of Discrete RVs)
Jointly Gaussian RVs
Conditional Probability Density Functi
ECE 450 Lecture 3
Overview:
Randomly Selected Experiments & Hypothesis Testing
Digital Communications Examples
Many General Probability Examples
D. van Alphen
1
Review & Practice:
Conditional Proba
ECE450, Spring 2017, Zahid
Extra Credit #2, worth 3 points
Due: Sunday, Feb 5, Midnight
Please read the following notes carefully:
1. Extra credit assignments will be assigned periodically throughout
ECE450: Solutions 1'0 X4
1. Eighf people hold reservorions for Travel in o 5-possenger limousine from LA To
SFV Let X be The number of persons who aciuaiiy show up to 'ir-ovei, The
probabiiiry +hc+ a
ECE450, Spring 2017, Zahid
Extra Credit #5, worth 3 points
Due: Sunday, February 26, Midnight
Please read the following notes carefully:
1. Extra credit assignments will be assigned periodically throu
I. Royal Flush
ail of the
same suit
All four cards of
the same rank
Any five cards of
the same suit.
but not in
sequence
Three cards of
the same rank
Two cards of
the same rank
Poker Hand Rankings
2.
ECE 450
Quiz 1
Study Sheet
Know the following, by heart (i.e., memorize, for the closed-book, closed notes part of the
exam). A few questions in the closed-book, closed-notes part will just ask you to
Milefoot.com
Mathematics
Playing Card Frequencies
A standard deck of 52 playing cards consists of 4 suits, with 13 kinds in each suit. In many card
games, the kinds are ranked, and are often referred
ECE 450 Homework #3
0. Consider the random variables X and Y, whose values are a function of the number
showing when a single die is tossed, as show below:
Exp. Outcome 1
X
2
Y
0
2
2
1
3
3
2
4
3
3
5
4
ECE 450 1
Sp 15
Homework Set 2
Solve these problems after Lecture #4:
1. Two dice are tossed; let X be the sum of the numbers appearing.
a. Graph the CDF, FX(x), and the pdf, fX(x).
b. Use the CDF to
ECE 450 1
Sp 15
Homework Set #1
Instructions: Circle your answer for each problem.
MATLAB Instructions: Write a single m-file for all problems that require the use of
MATLAB. In your code, use MATLABs
ECE450: Extra Credit 3, Due Sunday February 12 (Midnight)
1. The CSUN IEEE chapter is to choose a President, Treasurer and secretory, all
different, from a group of 10 students. How many different cho
ECE450, Spring 2017 Zahid
Extra Credit #4, worth 3 points
Due: Sunday, February 19, Midnight
Please read the following notes carefully:
1. Extra credit assignments will be assigned periodically throug
EE450, Spring-2017, Zahid
Extra Credit #1, worth 2 points
Due: Sunday, Jan 29, Midnight
Please read the following notes carefully. You must write your name on every page of
your submission.
1. Extra c
ECE 450 - Lecture #10
Overview
Introduction to Random Vectors
CDF, PDF
Mean Vector, Covariance Matrix
Jointly Gaussian RVs: vector form of pdf
Introduction to Random (or Stochastic) Processes
De
ECE 450 - Lecture 4
Overview
Simulation & MATLAB
Random Variables: Concept and Definition
Cumulative Distribution Functions (CDFs)
Examples & Properties
Probability Distribution Functions (pdfs)
ECE 450 - Lecture # 6
Overview
Review
Conditional Distributions
Conditioning on Events
Conditioning on Event in Terms of RVs
Functions of a Random Variable
D. van Alphen
1
Review
Gaussian pdf: f
ECE 450 - Lecture #9, Part 1
Pairs of Random Variables, continued - Overview
Joint PDFs A Discrete Example (PDF for Pair of Discrete RVs)
Jointly Gaussian RVs
Conditional Probability Density Functi
ECE 450 - Lecture #9 Part 2 Overview
Bivariate Moments
Mean or Expected Value of Z = g(X, Y)
Correlation and Covariance of 2 RVs
Functions of 2 RVs: Z = g(X, Y); finding fZ(z)
Method 1: First fin
ECE 450 Review for Exam 1
Homework Questions?
Requested #s from HW Sets 1 & 2
From HW Set 1, Part 1:
_
From HW Set 1, Part 2:
_
From HW Set 2:
_
Problem 1 No notes allowed
(No notes allowed) Complete
ECE 450 - Lecture #9
Pairs of Random Variables - Overview
Introduction to Pairs (X, Y) of Random Variables
The joint CDF for the pair X, Y
The joint PDF for the pair X, Y
Examples
Independence of