Lecture 2: Descriptive Statistics
12
Recap
What is statistics?
Why is it necessary for engineers?
Its all about the data.
13
Two Basic Concepts about Data
Population vs. Sample
E.g. what is the average height of students at
CSUS? Two options:
Measur

Lecture 20-21: Central Limit
Theorem
151
Chapter 5 and 6
Chapter 5 Sections 5.3, 5.4
Central Limit Theorem
Normal Approximation of Binomial, Poisson
Chapter 6 Section 6.1
Point Estimates
152
Recap (Sampling Distribution)
= =
Mean of means equals p

Lecture 23: Confidence Intervals
171
Chapter 7
Chapter 7 Section 7.1
Confidence Intervals
172
Confidence Intervals
Up to this point, the question was what is the
probability of a certain event, happening, or
occurrence
Now the question becomes, what i

Lecture 16-17: Uniform Distribution
/ Normal Distribution
118
Uniform Distribution (PDF)
Lets define a Continuous RV X
The probability is equally likely for all values of X
A Discrete RV with equally likely probabilities will have probability equal to

Lecture 19: Statistics and
Distributions
139
Chapter 5 and 6
Chapter 5 Sections 5.3, 5.4
Statistics and Distributions
Sampling Distributions
The Distribution of Mean
Central Limit Theorem
Normal Approximation of Binomial, Poisson
Chapter 6 Section

Lecture 22: Point Estimates
162
Chapter 6
Chapter 6 Section 6.1
Point Estimates
163
Point Estimate
Population
Sample
Point Estimate
Definition
Characteristics (parameters)
, 2 (statistics, parameters) describing the characteristics of the
population

Lecture 15: Continuous Random
Variables, PDF, CDF
101
Continuous Random Variable
Chapter 3 was all about Probability Distributions of Discrete Random
Variables, Chapter 4 related to Continuous Random Variables
A Continuous Random Variable is one which t

Lecture 14: Negative Binomial
and Poisson Distributions
145
Recap (Bernoulli and Binomial Random
Variables)
=
2 = (1 )
If X ~ Bernoulli(p), then
=
2 = (1 )
If X ~ Bin(n, p), then
n!
0,1,., n
p x (1 p ) n x , x =
= )
)
p ( x= P ( X x= x!(n x)!
0, o

Lecture 12/13: Binomial
Distribution
128
Distributions
Statistical Inference requires drawing a sample from a population, and
then analyzing the sample to learn about the population
The PMF and CDF of the sample is representative of the population
chara

Lecture 11: Expected Value and
Variance (Discrete Random Variable)
120
Expected Value (Discrete Random
Variable)
In Chapter 1, we learnt about mean and variance
(Descriptive Stastistics)
These are used in conjunction with PMF (PDF) to describe
the prope

Lecture 10: Discrete Random
Variables
111
Probability Mass Function (PMF) /
Probability Distribution Function (PDF)
Example: Flipping a single coin
Lets define a Random Variable X (Discrete) which represents the events of the experiment
(Bernoulli Random

Lecture 5: Rules of Probability
43
Rules of Probability
Set theory rules can be applied to develop probabilities
Probability can never be negative. A probability of 0 means an event
cannot happen ( = null event) so less than 0 would be meaningless
P(Xi

Lecture 9: Random Variables
101
Random Variable
Chapter 1, Summary Statistics, e.g. mean, standard deviation, histograms
Chapter 2, Probability
We now combine the 2 together
What is a variable?
x + 3 = 7, then x is a variable for which we can solve
x=4

Lecture 7 - 8: Conditional
Probability
67
Conditional Probability
Probability of an Event A =
Unconditional Probability, event with no conditions
What is the probability of a traffic jam tomorrow?
Conditional Probability, event with some condition

Lecture 3: Descriptive Statistics
21
Numerical Descriptive Statistics
Visual summaries are great, but for more formal analysis, we need
numbers
Measures of central tendency
Mean
Median
Mode
Measures of variability
Variance
Standard deviation
Range
M

Lecture 6: Permutations and
Combinations
55
Recap
Probability of an Event A =
Counting simple events is easy
Single coin flip
Counting compound events a bit more tricky
Two spades and two queens
Probability of significant levels of Cd or of Hg:

Lecture 4: Introduction to
Probability
33
Sample Space and Events
Sample Space is a set of all possible outcomes during an experiment
Events are individuals inside a sample space
An experiment is the process of observing the outcomes of a
chance event

ENGR 115: Statistics for
Engineers
Instructor: Dr. Ghazan Khan
ghazan.khan@csus.edu
1
Lecture 1: Introduction
2
Why are we here?
Introduce the concepts and application of probability and
statistics in engineering
Help you prepare for the Fundamentals of