PROBABILITY AND STATISTICS FOR SCIENTISTS AND
ENGINEERS
Discrete Probability
Distributions
Discrete Random Variables
Probability Distributions
Jerrell T.Stracener Ph.D
1
Random Variable
Definition - A random variable is a mathematical function that
associ

Homework 2 Solution
a) Rare disease
Only 1 in 1000 adults is afflicted with a rare disease for
which a diagnosis test has been developed. The test is
such that, when an individual actually has the disease,
a positive result will occur 99% of the time, whe

Sample Questions
Part 1
Levent Kaan, PhD
1
Dinner Party
A person giving dinner party. His current wine supply includes 8
bottles of Zinfandel, 10 of Merlot, and 12 of Cabernet ( only red
wine).
a) He wants to serve 3 bottles of Z and serving order is impo

Probability and Statistics for Scientists and Engineers
ProbabilityBasic Concepts and
Approaches
Levent Kaan Ph.D
1
Probability-Basic Concepts and Approaches
)Basic Terminology & Notation
)Basic Concepts
)Approaches to Probability
Levent Kaan Ph.D
2
Basic

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS
Special Continuous
Probability Distribution
Lognormal Distribution
Levent Kaan, Ph.D.
1
Lognormal Distribution
Alognormal distributionis a continuousprobability
distributionof arandom variablewhoselo

Probability and Statistics for Scientists and Engineers
Introduction
to
Probability and
Statistics
Levent Kaan Ph.D
1
Objective
Introduction to fundamental probabilistic and statistical
concepts, methods and techniques
for application to engineering and s

Probability and Statistics for Scientists and Engineers
Probability
Independence and
Fundamental Rules
Levent Kaan, Ph.D
1
ni
n
P
i1Ai
A
P
i1
Definition - Independence
Definition
Two events A and B in S are independent if, and only if,
P(A B) = P(A)P(B)

PROBABILITY AND STATISTICS FOR SCIENTISTS AND
ENGINEERS
Special Continuous
Probability Distributions
Weibull Distribution
Levent Kaan, Ph.D.
1
x
x
x
1
x
e
f(x)
0
Weibull Distribution Probability Density Function
A random variable X is said to have the Wei

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS
Special Continuous
Probability Distributions
Normal Distribution
Levent Kaan, Ph.D.
1
Normal Distribution Probability Density Function
A random variable X is said to have a normal (or Gaussian)
distr

Probability and Statistics for Scientists and Engineers
Discrete Probability
Distributions
Hypergeometric &
Poisson Distributions
Levent Kaan - Ph.D.
1
HYPERGEOMETRIC
DISTRIBUTION
Levent Kaan - Ph.D.
2
Hypergeometric Distribution - Conditions
Population

Probability and Statistics for Scientists and Engineers
Discrete Probability
Distributions
Hypergeometric &
Poisson Distributions
Levent Kaan - Ph.D.
1
HYPERGEOMETRIC
DISTRIBUTION
Levent Kaan - Ph.D.
2
Hypergeometric Distribution - Conditions
Population

Probability and Statistics for Scientists and Engineers
Probability
Conditional Probability
and
Bayes Theorem
Levent Kaan, Ph.D
1
Conditional Probability
Definition
Basic Concept
Reduced Sample Space
Rules
Bayes Rule
Levent Kaan, Ph.D
2
(P(A
P
A
B
)
|B
)

Probability and Statistics for Scientists and Engineers
Continuous Probability
Distributions
Continuous Random
Variables & Probability
Distributions
Levent Kaan, Ph.D.
1
Continuous Random Variable
Definition - A random variable is a mathematical function

PROBABILITY AND STATISTICS FOR SCIENTISTS AND
ENGINEERS
Discrete Probability
Distributions
Discrete Random Variables
Probability Distributions
Levent Kaan - Ph.D.
1
Random Variable
Definition - A random variable is a mathematical function that
associates

Probability And Statistics For Scientists And Engineers
Discrete Probability
Distributions
Binomial, Negative
Binomial, Geometric
Distributions
Levent Kaan - Ph.D.
1
BINOMIAL DISTRIBUTION
Levent Kaan - Ph.D.
2
Binomial Model - Conditions
Let X be the numb

Probability and Statistics for Scientists and Engineers
EMIS/CSE 7370 /STAT 4341
Course Information and
Administration
Levent Kaan, PhD
1
Course Overview
) Contact Information
) About the Instructor
) About the Course
) Objectives
) Canvas
) Course Websit

Homework 1 Solution
1) Graduation
In a high school class of 100 students, 42 studies mathematics,
68 studies psychology, 54 studies history, 22 studies both
mathematics and history, 25 studies both mathematics and
psychology, 7 studies history and neith

EMIS 7370 & CSE 7370 & STAT 4341
Homework 2
a) Rare disease
Only 1 in 1000 adults is afflicted with a rare disease for
which a diagnosis test has been developed. The test is
such that, when an individual actually has the disease,
a positive result will oc

Supplementary
Examples
Levent Kaan - Ph.D.
1
Questions
GAS STATION PAY
Customers at a gas station pay with a credit card (A), debit
card (B), or cash (C). Assume that successive customers make
independent choices as P(A)=0.5 P(B)=0.2, and P(C)=0.3
a)Among

Probability and Statistics for Scientists and Engineers
EMIS 7370
Course Information and
Administration
Jerrell Stracener, PhD
1
Course Overview
) Contact Information
) About the Course
) Objectives
) Canvas
) Course Website
) Homework
) Exams
) Info
) As

EMIS / CSE 7370
Homework 4
Tires / Defectives/Demo
1. In testing a certain kind of truck over rough terrain, it is found
that 15% of the front wheel tires have a blowout. What is the
probability that of the next four trucks tested, at most 3 tires
will bl

Probability and Statistics for Scientists and Engineers
Introduction
to
Probability and
Statistics
Jerrell T.Stracener Ph.D
1
Objective
Introduction to fundamental probabilistic and statistical
concepts, methods and techniques
for application to engineeri

Probability And Statistics For Scientists And Engineers
Discrete Probability
Distributions
Binomial, Negative
Binomial, Geometric
Distributions
Jerrell T.Stracener Ph.D
1
BINOMIAL DISTRIBUTION
Jerrell T.Stracener Ph.D
2
Binomial Model - Conditions
Let X b

PROJECT PLAN
QUEUEING THEORY
EMIS 7370
Yavuz SAHIN
Scope :
In depth overview of Queueing Theory and its an application
to my professional job
Motivation :
This theory is applicable to nearly all part of life; in the hospital,
in the bank etc. I would li

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS
Special Continuous
Probability Distribution
Lognormal Distribution
Jerrell T. Stracener , Ph.D.
1
1
f(x)
e
2
0
12lnx2
2
Lognormal Distribution Probability Density Function
A random variable X is said

Probability and Statistics for Scientists and Engineers
Special Continuous
Probability Distributions
Exponential Distribution
Jerrell T. Stracener, Ph.D.
1
EXPONENTIAL DISTRIBUTION
Jerrell T. Stracener, Ph.D.
2
1
x
e
0
f(x)
x
Exponential Definition- Proba

PROBABILITY AND STATISTICS FOR SCIENTISTS AND
ENGINEERS
Special Continuous
Probability Distributions
Gamma Distribution
Beta Distribution
Jerrell T.Stracener , Ph.D.
1
GAMMA DISTRIBUTION
Jerrell T.Stracener , Ph.D.
2
Family of Gamma Distributions
A famil

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS
Special Continuous
Probability Distribution
Lognormal Distribution
Jerrell T. Stracener , Ph.D.
1
1
f(x)
e
2
0
12lnx2
2
Lognormal Distribution Probability Density Function
A random variable X is said

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS
Special Continuous
Probability Distributions
Normal Distribution
Jerrell T. Stracener, Ph.D.
1
Normal Distribution Probability Density Function
A random variable X is said to have a normal (or Gaussi

PROBABILITY AND STATISTICS FOR SCIENTISTS AND
ENGINEERS
Special Continuous
Probability Distributions
Weibull Distribution
Jerrell T. Stracener, Ph.D.
1
x
x
x
1
x
e
f(x)
0
Weibull Distribution Probability Density Function
A random variable X is said to hav