Gowthama Thangamathesvaran, Probability
Homework 4, ggt7, 164000006
%#1
t=linspace(3,3,1000);
y=normcdf(t);
figure;
hold on;
plot(t,y);
title('Normal CDF from closed form expression')
hold off;
%#2
for i=1:4 %Calculates the Zn values for n=4
x = 1+2*1*r
%#1
q=linspace(3,3,1000);
k=normcdf(q);
figure;
hold on;
plot(q,k);
title('Normal CDF of the function')
hold off;
%#2
for i=1:4 %This loop will calculate the Zn values for when n=4
b = 1+2*1*rand(4,1);
l = sum(b);
f(i)=l./(sqrt(4)*(2)/sqrt(12);
end
for
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Probability and Stochastic Processes
May 7, 2015
Final Examination
You have 180 minutes to answer the following questions in the notebooks provided. Make sure that you have
included your name, RU NetID and signature at the
PROBABILITY AND STOCHASTIC PROCESSES
A FRIENDLY INTRODUCTION FOR ELECTRICAL AND COMPUTER ENGINEERS
Third Edition
Chapter 3 Viewgraphs
Roy D. Yates & David J. Goodman
Yates & Goodman 3e
62
Discrete Random Variables
In this chapter and for most of the rema
Yates & Goodman 3e
Theorem 2.2
The number of kpermutations of n distinguishable objects is
(n)k = n(n
1)(n
2) (n
k + 1) =
n!
(n
k)!
.
41
Yates & Goodman 3e
42
Theorem 2.3
The number of ways to choose k objects out of n distinguishable objects
is
n
k
=
(
Yates & Goodman 3e
Section 3.5
Averages and Expected Value
80
Yates & Goodman 3e
80
Example 3.23 Problem
For one quiz, 10 students have the following grades (on a scale of 0 to
10):
X
,
Xn
X2
9, 5, 10, 8, 4, 7, 5, 5, 8, 7

.
(1)

57
Find the mean, the m
Formula Sheet Probability and Random Processes
Continuous Sample Space:
The Cumulative Distribution Function (CDF):
F X ( x )=P [ X x ]
(Less Than Or Equal To!)
For any random variable X,
F X ( )=0, F X ( )=1, P[ x 1< X < x 2=F X ( x 2 )F X ( x 1 ) ]
Prob
Yates & Goodman 3e
11
Denition 1.4 Axioms of Probability
A probability measure P[] is a function that maps events in the sample
space to real numbers such that
Axiom 1 For any event A, P[A]
0.
Axiom 2 P[S] = 1.
Axiom 3 For any countable collection A1, A2,
Yates & Goodman 3e
Section 2.1
Tree Diagrams
35
Yates & Goodman 3e
Problem 2.1.5
57
Suppose that for the general population, 1 in 5000 people carries the human immunodeciency virus (HIV). A test for the presence of HIV yields
either a positive (+) or nega
Yates & Goodman 3e
20
Theorem 1.8
For a partition B = cfw_B1, B2, . . . and any event A in the sample space, let
Ci = A \ Bi. For i 6= j, the events Ci and Cj are mutually exclusive and
A = C1 [ C2 [ .
Yates & Goodman 3e
Theorem 1.9
For any event A, and p
PROBABILITY AND STOCHASTIC PROCESSES
A FRIENDLY INTRODUCTION FOR ELECTRICAL AND COMPUTER ENGINEERS
Third Edition
Chapter 7 Viewgraphs
Roy D. Yates & David J. Goodman
Yates & Goodman 3e
Section 7.1
Conditioning a Random Variable
by an Event
242
Yates & Goo
PROBABILITY AND STOCHASTIC PROCESSES
A FRIENDLY INTRODUCTION FOR ELECTRICAL AND COMPUTER ENGINEERS
Third Edition
Chapter 3 Viewgraphs
Roy D. Yates & David J. Goodman
Yates & Goodman 3e
62
Discrete Random Variables
In this chapter and for most of the rema
Yates & Goodman 3e
66
Probability Mass Function
Denition 3.3 (PMF)
The probability mass function (PMF) of the discrete random variable X
is
PX (x) = P [X = x]
Yates & Goodman 3e
68
Families of Random Variables
In practical applications, certain families
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Probability and Stochastic Processes
February 28, 2013
Examination 1
You have 110 minutes to answer the following questions in the notebooks provided. This is
a closed book exam; neither notes nor calculators are permitted.
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Probability and Stochastic Processes
April 18, 2013
SOLUTION (VERSION 1)
(The solution for version 2 starts on page 7.)
Examination 2
You have 110 minutes to answer the following questions in the notebooks provided. This
is a closed book exam; nei
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February 26, 2015
Examination 1
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neither notes nor calculators are permitted.
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Probability and Stochastic Processes
February 28, 2013
SOLUTION
Examination 1A
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a closed book exam; neither notes nor calculators are permitted. Make sure tha

,.,.
A
.i
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Prob?bility and Stochastic Processes
February 26, 2015
Examination 1
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neither notes nor calculator
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April 18, 2013
Examination 2
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notes nor calculators are permitted. Ma
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April 15, 2015
Examination 2A Solution
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book exam; neither notes nor calculators are per
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Final Examination
May 9, 2013
MAKE SURE TO READ BOTH SIDES OF THIS EXAM PAPER.
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Calculus Prerequisite Quiz
Quiz 0
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Jan 2630, 2009
Quiz 1
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