Moments of Random Variables
Chapter 3
Section 3.2: Expected Values
3.1
We are given the triangular PDF.
fX ( x )
1
-2
0
x
4
2
We have that
x
-4
fX ( x ) =
x
1 -4
0
0x<2
2x<4
otherwise
Thus,
E[X] =
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 7: Transform Methods
Oliver C. Ibe
1
Introduction
This lecture discusses how transform methods ar
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 3: Moments of Random Variables
Oliver C. Ibe
1
Introduction
When given the set of data X1, X2, ,
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 5: Multiple Random Variables
Oliver C. Ibe
1
Introduction
Some problems that we encounter in real
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 8: Introduction to Descriptive Statistics
Oliver C. Ibe
1
Introduction
Statistics deals with the
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 9: Introduction to Inferential Statistics
Oliver C. Ibe
1
Introduction
As discussed in Lecture 8,
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 1: Basic Probability Concepts
Oliver C. Ibe
1
Introduction
Probability deals with unpredictabili
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 4: Special Probability Distributions
Oliver C. Ibe
1
Introduction
In this lecture we describe the
University of Massachusetts Lowell
EECE.3630: Introduction to Probability and
Random Processes
Lecture 2: Random Variables
Oliver C. Ibe
1
Introduction
Lecture 1 dealt with outcomes of a random exper
CHAPTER 4
Special Probability Distributions
Section 4.3: Binomial Distribution
4.1
The probability of a six on a toss of a die is p = 1 6 . Let N(4) be a random variable that
denotes the number of six
Functions of Random Variables
Chapter 6
Section 6.2: Functions of One Random Variable
6.1
Given that X is a random variable and Y = aX b , where a and b are constants, then
y+b
y+b
F Y ( y ) = P [ Y y
Solutions to 16.363 Problem Set 2, Spring 2011
L40 We are given a game that consists of two successive trials in which the rst trial has
outcome A or B and the second trial has outcome C or D. The pro
University of Massachusetts, Lowell
Department of Electrical and Computer Engineering
Course 16.363: Introduction to Probability and Random Processes
Second Midterm Exam, April 4, 2011
Name: gqm Fi
I
Chapter 2
Random Variables
Section 2.4: Distribution Functions
2.1
We are given the following function that is potentially a CDF:
0
FX ( x ) =
( x 1 )
Bcfw_1 e
< x 1
1<x<
(a) For the function to be
Transform Methods
Chapter 7
Section 7.2: Characteristic Functions
7.1
We are given a random variable X with the following PDF:
1
-fX ( x ) = b a
0
a<x<b
otherwise
The characteristic function is give
Introduction to Statistics
Chapter 11
Section 11.2: Sampling Theory
11.1
A sample size of 5 results in the sample values 9, 7, 1, 4, and 6.
a.
9+7+1+4+6
-The sample mean is X = - = 27 = 5.4
b.
The sam
Introduction to Random Processes
Chapter 8
Section 8.3: Mean, Autocorrelation Function, and Autocovariance Function
8.1
Since the function
X(t) = A
0tT
is an aperiodic function, its autocorrelation fu
Multiple Random Variables
Chapter 5
Section 5.3: Bivariate Discrete Random Variables
5.1
kxy
p XY ( x, y ) =
0
a.
otherwise
To determine the value of k, we have that
x
b.
x = 1, 2, 3 ; y = 1, 2, 3
3