1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Discrete Random Variables and Probability
Distributions
Industrial and Systems and Engineering Management
Department
Fall 15
Random Variable
In any experiment, there

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Covariance and Correlation
Industrial and Systems and Engineering Management
Department
Fall 15
Covariance
When two or more random variables are
defined on a probabil

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Joint Probability Distributions
Industrial and Systems and Engineering Management
Department
Fall 15
Joint Probability Distributions
In Chapters 3 and 4, we developed

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Continuous Random Variable
Industrial and Systems and Engineering Management
Department
Fall 15
Uniform Distribution
Uniform (or Rectangular) pdf denoted
The
by U(a,

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Probability
Industrial and Systems and Engineering Management
Department
Fall 15
Introduction
The term probability refers to the study of
randomness and uncertainty.

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Continuous Random Variable
Industrial and Systems and Engineering Management
Department
Fall 15
Continuous Random Variables
In contrast to discrete random variables,

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Moments of a Random Variable
Industrial and Systems and Engineering Management
Department
Fall 15
Moments of a Random Variable
Moments are measures that tell us about

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Introduction
Industrial and Systems and Engineering Management
Department
Fall 15
Contact Information
Instructor:
Dr. Dilcu Helvaci Barnes
E-mail:
dh0066@uah.edu
P

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Discrete Probability Distributions
Industrial and Systems and Engineering Management
Department
Fallr 15
Bernoulli Distribution
Consider an experiment whose outcomes

1
ISE 690
Statistical Methods for Engineers
Dilcu Helvaci Barnes (Email:
dh0066@uah.edu)
Normal Distribution and Central Limit Theorem
Industrial and Systems and Engineering Management
Department
Fall 15
Normal Distribution
The normal distribution is the