Chemical Engineering/NanoEngineering 114
Probability and Statistical Methods in Engineering
Summer Session II 2015
Instructors:
TAs:
Justin Opatkiewicz
SME 241G
Eva Gonzalez Diaz, Meaghan Sullivan
[email protected]
Lectures:
MTuWTh 11:00AM - 12:20PM HSS

Discrete Random
Variables
Shyue Ping Ong
Readings
CENG114/NANO114
2
Chapters 2.4-2.6 and 4.1-4.4
Overview
In the next few lectures, we will introduce the concept
of a random variable, and specifically look at one
type of random variable the discrete rando

The Normal Distribution
Shyue Ping Ong
Normal Random Variable
Probably the most widely used model for a continuous random variable
Also known as the Gaussian distribution or the Bell curve
Sample mean for a large number of independent experiments follow

Populations, Samples and
Point Estimation
Shyue Ping Ong
Readings
CENG114/NANO114
2
Chapter 5
Key concept in inferential statistics
E.g., all voters, all potential samples of a material, etc.
Population
Sample
Sampling
Random or based on crosssectional se

Statistics
Shyue Ping Ong
Reading
CENG114/NANO114
2
Chapter 1 of Statistics for Engineers & Scientists,
4th edition
Types of Statistics
Descriptive Statistics
Organize and summarize data
Describe variability in data
Correlation, regression, etc.
Infere

Joint Discrete PMFs,
Conditioning and
Independence
Shyue Ping Ong
Alternative derivation of the mean and variance
of binomial distribution
A binomially distributed random variable, Z, with parameters n, p is
essentially a sum of a series of n independent

Counting
Shyue Ping Ong
A simpler example of a sample space and
probability model
Consider two flips of a coin, landing either heads
or tails.
What is a good sample space definition and
probability model
i.
If we are interested in the sequence of the two

Probability and Statistics,
and their Application to
Science and Engineering
Shyue Ping Ong
The Scientific Method
Modify
hypothesis
Develop
Hypothesis
Design and
conduct
experiments
There exists a force
acting between two
masses
Why does the apple
fall fr

Conditional Probability,
Bayes Rule and
Independence
Shyue Ping Ong
Conditional Probability
Reasoning about outcomes based on partial
information
If the sum of the roll of two dice is 10, how likely is it that one of
the dice shows a 6?
If the father ha

Analysis of Variance
(ANOVA)
Shyue Ping Ong
Readings
CENG114/NANO114
2
Chapter 9.1 and 9.2
Scenario
You are an engineer who has been tasked to know if a
particular commercial alloy is susceptible to corrosion.
Dutifully, you get a large number of equal we

Review Session
Example 1
A manufacturer of paper used for making grocery bags is interested in improving the products
tensile strength. Product engineering believes that tensile strength is a function of the hardwood
concentration in the pulp and that the

Normal distribution and Zscores, Correlation and
Regression
Shyue Ping Ong
The Normal Distribution Revisited
CENG114/NANO114
2
Gaussian distribution or Bell Curve
Central Limit Theorem
Let cfw_X1, X n be a random sample of size n of i.i.d.
random variabl

t test, confidence intervals and
p-values
Shyue Ping Ong
Readings
CENG114/NANO114
2
Chapter 6
Confidence intervals vs Hypothesis tests
Used when you
want to quantify the
uncertainty in an
estimate
Leads to a range of
plausible values for
your population

Review Session
Example 1
Specimen #
1
2
3
4
5
Fracture Toughness
(MPa m1/2)
77
51
43
36
59
i.
Estimate the population mean and standard deviation of the fracture toughness using the
sample above.
ii.
Assume that the fracture toughness is normally distribu

Continuous Random
Variables
Shyue Ping Ong
Discrete
Continuous
Takes fixed values (finite or
countably infinite)
Take any value in a range
(uncountably infinite)
Defined by probability mass
function (PMF)
Defined by probability distribution
function (PDF)

Bayes Rule Example
CENG/NANO114
1
The makers of a chemical test claim that it can detect
high levels of organic pollutants with 90% accuracy,
volatile solvents with 99% accuracy, and chlorinated
compounds with 95% accuracy. If a pollutant is not
present,

Geometric
i.
What is the probability that a successful alignment requires
exactly four tries?
ii.
What is the probability that a successful alignment requires at
most four tries?
iii.
What is the probability that a successful alignment requires at
least f

Chemical Engineering 114
Due: Tues. 8/18
Problem Set #2
1.) Section 2.3, Problem 28
2.) Section 2.3, Problem 32
3.) The level of impurity (in percent) in the product of a chemical process is a random variable with the
probability density function (PDF) of

Q1:
i.
X = 77 + 51+ 43 + 36 + 59 = 266
X 2 = 15156
(X)2
SS = X
= 1004.8
5
266
X=
= 53.2
5
SS
2 =
= 251.2
5 1
= 251.2 = 15.8
2
Make sure you are clear to the students about the factors of n-1 and n in the SS and std deviation
calculations.
ii.