STAT 155
Sections 3.4: The Binomial Probability Distribution_
Binomial Experiment
n independent, identical Bernoulli trials
Each trial results in one of two possible outcomes,
success and failure.
The probability of success, p is the same from trial to
STAT 155
Section 4.4: The Exponential and Gamma Distributions_
There are many practical situations in which the variable
of interest to an investigator might have a skewed
distribution. One family of distributions that has this
property is the gamma famil
STAT 155
Section 5.3: Statistics and Their Distributions_
By suitably sampling from a population and analyzing the
sampled items, one hopes to be able to draw some
conclusions about the population.
The values of the individual sample observations vary
fro
@997
1. A system contains two components, C and D, connected in parallel as shown in the diagram.
E 3
Assume C and D function independently. For the system to function, either C or D must
function. If the probability that C fails is 0.08 and the probabili
COURSE SYLLABUS
Statistics 155, Fall 2013
Probability and Statistics for Science and Engineering
Course Description_
_
This is a 4 unit course composed of 3 lecture units per week and 1 discussion unit per week.
The prerequisite for this course is MATH 00
STAT 155
Section 5.2: Expected Values, Covariance, and Correlation_
Expected Values
Let X and Y be jointly distributed rvs with pmf p(x, y) or
pdf f(x, y) according to whether the variables are discrete
or continuous. Then the expected value of a function
STAT 155
Chapter 6: Point Estimation
Section 6.1: Some General Concepts of Point Estimation_
When discussing general concepts and methods of
inference, it is convenient to have a generic symbol for
the parameter of interest. We will use the Greek letter
STAT 155
Chapter 8: Tests of Hypotheses Based on a Single Sample
Section 8.1: Hypotheses and Test Procedures_
Null Hypothesis, H0: a statement that a parameter takes a
particular value. The null hypothesis is assumed true until
evidence indicates otherwis
Formula Sheet for Statistics 155
I.
Descriptive Statistics
density =
x=
x
s=
n
IQR = Q3  Q1
relative frequency of the class
class width
2
(xx)
n1
LF = Q1 1.5(IQR)
=
2
x 
x
2
n
n1
UF = Q3 + 1.5(IQR)
II. Probability
Complement Rule: P(A) = 1 P(A)
Gen
STAT 155
Section 4.3: The Normal Distribution_
The normal or bellshaped distribution is the
cornerstone of most methods of estimation and hypothesis
testing developed in the rest of this course.
The probabilitydensity function (pdf) of the continuous
ra
STAT 155
Chapter 4: Continuous Random Variables and Probability Distributions
Section 4.1: Probability Density Functions_
Continuous Probability Distributions
The graph of f(x) is often referred to as the density curve.
P(a X b) the area under the density
STAT 155
Section 6.2: Methods of Point Estimation_
Method of Moments
Let X1, , Xn be a random sample from a pmf or pdf.
For k = 1, 2, 3, ,
the kth population moment is E(Xk)
n
th
the k sample moment is
X
i=1
n
k
i
.
Let X1, , Xn be a random sample from a
STAT 155
Chapter 7: Statistical Intervals Based on a Single Sample
Section 7.1: Basic Properties of Confidence Intervals_
Inferential Statistics: 1) Estimation
and
2) Hypothesis Testing
Both types of inference are based on the sampling
distributions of st
Statistics 155 Formula Sheet for Midterm 2 Fall 2013
Probability Distribution of a Discrete Random Variable:
E(X) = = xP(x)
V(X) = 2 = x 2 P(x)  2
Probability Distribution of X~B(n, p):
n
P(x) = p x q nx , x = 0, 1, 2, ., n
x
E(X) = np
V(X) = npq
Probab
701!
1. The weight distribution (in lb) of parcels sent in a certain manner is normal with
mean value p = 15 and standard deviation 0' = 2.8. A surcharge is applied to
parcels weighing more than 21 lb. What is the probability that among three
W231 5:,v~31
Statistics 155 Midterm 1 Formula Sheet Fall 2013
I. Descriptive Statistics
density =
relative frequency of the class
class width
x=
x
n
s=
2
(x
x)
n1
=
x
2

( x)2
n
n1
IQR = Q3  Q1
LF = Q1 1.5(IQR)
UF = Q3 + 1.5(IQR)
II. Probability
Complement Rule: P
8W
1. An individual who has automobile insurance from a certain company is randomly
selected. Let Y be the number of moving violations for which the individual was
cited during the last 3 years. The pmf of Y is shown below. Suppose an
individual with Y vi
STAT 155
Section 1.3: Measures of Location
Measures of Location
mean
median
quartiles & percentiles
trimmed mean
arithmetic mean sum of all the observations divided by
the number of observations.
sample mean: x =
_
For reporting x, it is recommended t
STAT 155
Chapter 2: Probability
Section 2.1: Sample Spaces and Events_
Probability allows us to make the inferential jump
from a sample to a population.
In this chapter, probability is defined and some rules
for working with probabilities are introduced
STAT 155
Chapter 1: Overview and Descriptive Statistics
What is Statistics?
The discipline of statistics teaches us how to make
intelligent judgments and informed decisions in the
presence of uncertainty and variation.
Without the presence of uncertainty
STAT 155
Sections 2.3: Counting Techniques
Basic Principle of Counting
If the first element of an ordered pair can be selected in n1
ways, and for each of these n1 ways the second element of
the pair can be selected in n2 ways, then the number of
pairs is
STAT 155
Chapter 1: Overview and Descriptive Statistics
STAT 155
Section 1.1: Populations, Samples, and Processes
What is Statistics?
Introduction to Basic Terms
The discipline of statistics teaches us how to make
intelligent judgments and informed decisi
STAT 155
Chapter 3: Discrete Random Variables and Probability Distributions
Sections 3.1: Random Variables_ _
random variable a numerical measurement of the
outcome of a random phenomenon, so its value is
determined by chance. Random variables are denoted
STAT 155
Section 4.4: The Exponential and Gamma Distributions_
There are many practical situations in which the variable
of interest to an investigator might have a skewed
distribution. One family of distributions that has this
property is the gamma famil
STAT 155
Sections 2.3: Counting Techniques
Basic Principle of Counting
If the first element of an ordered pair can be selected in n1
ways, and for each of these n1 ways the second element of
the pair can be selected in n2 ways, then the number of
pairs is
f(x) 
STAT 155
Section 4.3: The Normal Distribution_

The normal or bellshaped distribution is the
cornerstone of most methods of estimation and hypothesis
testing developed in the rest of this course.
The probabilitydensity function (pdf) of the cont
STAT 155
Sections 3.4: The Binomial Probability Distribution_
Binomial Experiment
n independent, identical Bernoulli trials
Each trial results in one of two possible outcomes,
success and failure.
Example: A satellite system consists of 4 components and
STAT 155
Chapter 1: Overview and Descriptive Statistics
STAT 155
Section 1.1: Populations, Samples, and Processes
What is Statistics?
Introduction to Basic Terms
The discipline of statistics teaches us how to make
intelligent judgments and informed decisi
STAT 155
Section 1.3: Measures of Location
median the middle position in a ranked data set.
Measures of Location
The sample median ( x ) is in the (n+1)/2 position.
mean
median
Steps to find the sample median:
quartiles & percentiles
1. Rank the data s
STAT 155
Chapter 3: Discrete Random Variables and Probability Distributions
Sections 3.1: Random Variables_ _
random variable a numerical measurement of the
outcome of a random phenomenon, so its value is
determined by chance. Random variables are denoted