Homework 2 Solution Key
ECI 114 - SSII 2015
Show all work explicitly and explain your answers. Write your name on the top of each page of your assignment,
number each page, and staple all pages together in order (problems should be presented in the order
Homework 1 Solution Key
ECI 114 - SSII 2015
Show all work explicitly and explain your answers. Write your name on the top of each page of your assignment,
number each page, and staple all pages together in order (problems should be presented in the order
ECI114 HW3 Due 5p.m Wed, Oct. 26th
Q1.
a) Here cylinders are selected without replacement. And n/N = 5/15 > 0.1.
Thus, X is a hypergeometric random variable, i.e. it uses the multiple
combinations rule.
r N r 6 15 6
x n x x 5 x
=
p ( x) =
where
ECI 114
Fall 2009
Name
Solutions
Midterm 1 (100 points)
Wednesday, October 28, 2009
Show your work. Its not necessary to give a final numerical answer unless speci fically asked, but you
need to provide all the information necessary to compute the final a
ECI 114 University of California, Davis Department of Civil and Environmental Engineering Homework Assignment 3 (62 points) Due 5:00 p.m. Wednesday, October 30, 2002
Fall 2002
Show all work and explain your answers; no credit will be given for solutions o
Gil Tal ECI 114 Homework Assignment 1
1. Problem 6-8 (a), (b), p. 195
a. Mean:
Y=
y
i =1
N
i
= 2.173333
N
2 s =
b. Sample Variance:
( Y
i=1
N
i
- Y )2 =
0.4303
N -1
Standard variation: s = s2 = 0.656011 c. maximum 3.0200 minimum 1.1500 range 1.87
median
2
ECI 114
Fall 2011
NAME: _
Final Examination (Solutions)
Monday, December 5, 2011, 10:30 a.m. - 12:30 p.m.
100+5 bonus points
Show your work. Its not necessary to give a final numerical answer unless specifically asked, but you need to
clearly provide all
1
ECI 114:
PROBABILISTIC SYSTEMS ANALYSIS
LECTURES 4-6
INSTRUCTOR: Kaveh Zamani
2
Lecture 4
Random Variables
Probability Density Functions (PDF)
Cumulative Distribution Functions (CDF)
Mean and Variance
Random Variables
3
Because the particular outcome of
31
Lecture 2
Interpretation of Probability
Addition Rules
Counting techniques
Conditional Probability
Multiplication and Total Probability Rules
Probability
32
Probability is used to quantify the likelihood, or chance,
that an outcome of a random experime
1
ECI 114:
PROBABILISTIC SYSTEMS ANALYSIS
LECTURES 1-3
INSTRUCTOR: Kaveh Zamani
2
Lecture 1
The Role of Statistics in Engineering
Sample Spaces and Events
The Engineering Method
3
Usual steps in the Engineering Method are:
Develop a clear and concise desc
1
Two Discrete Random Variables
The probability mass function (pmf) of a single discrete
random variable X specifies how much probability mass is
placed on each possible X value.
The joint PMF of two discrete random variables X and Y
describes how much
1
ECI 114:
PROBABILISTIC SYSTEMS ANALYSIS
MOMENTS AND MOMENT
GENERATING FUNCTIONS
INSTRUCTOR: Kaveh Zamani
2
Lecture 1
Moments
Moment Generating Functions
Characteristic functions (not in the exam)
Moments
3
The rth moment of a random variable X about the
Homework 3
ECI 114 - SSII 2015
1- (10 points) A synthetic fiber used in manufacturing carpet has tensile strength that is normally
distributed with mean 75.5 psi and standard deviation 3.5 psi. Find the probability that a random sample
of n=6 fiber specim
Homework 5
ECI 114 - SSII 2015
Due to: Tuesday, September 8, 8:00 AM in class
1- A random sample has been taken from a normal distribution and the following confidence
intervals constructed using the same data: (38.02, 61.98) and (39.95, 60.05)
a) What is
70
Lecture 3
Independence
Bayes Theorem
Independence
71
In some cases, we might have that
P(AB) = P(A)
e.g., the probability of failure of a building in the US given that
an earthquake occurred in Italy
In this special and important case, we have
P(A B) =
1
Conditional Probability Distribution
When two random variables are defined in a random experiment,
knowledge of one can change the probabilities that we associate to the
others
Conditional probability density function of Y given X=x is
() ,
| =
for
Applied Statistics and Probability for Engineers, 5th edition
July 2, 2010
CHAPTER 2
Section 2-1
Let e and o denote a bit in error and not in error (o denotes okay), respectively.
2-2.
eeee, eoee, oeee, ooee,
eeeo, eoeo, oeeo, ooeo,
S=
eeoe, eooe, oeoe,
nobsmaw mom! b9 x.,x:, xn=>msampw mean-w ~
X: XvHCy-t" *ISn =1"ng - _ ’ ' .
Lﬂ .
won? 50mm (WM? Comm. 0L nWmM a rwmm value 0% m
M WWW mean M : ﬂ .
'wM‘h - row esmw‘ . ,. v .4
‘ ”148' asmm probably dim . 5mm .\
a wild a A '2
m'jm random “
III. Random Variables
Miguel Jaller, Ph.D.
Assistant Professor
Department of Civil and Environmental Engineering
University of California, Davis
2
Today
BayesTheorem (From last lecture)
Random variables
Probability Density Functions (PDF)
Cumulative Distr
II. Probability
Miguel Jaller, Ph.D.
Assistant Professor
Department of Civil and Environmental Engineering
University of California, Davis
Today
2
Permutations and Combinations
Independence
BayesTheorem
3
Permutations and Combinations
Special Thanks to Pr
JWCL232_c02_017-065.qxd
28
1/7/10
9:45 AM
Page 28
CHAPTER 2 PROBABILITY
EXERCISES FOR SECTION 2-1
Provide a reasonable description of the sample space for each
of the random experiments in Exercises 2-1 to 2-17. There can
be more than one acceptable inter
III. Probability Distribution
Miguel Jaller, Ph.D.
Assistant Professor
Department of Civil and Environmental Engineering
University of California, Davis
2
Today
Review examples:
Random variables
Probability Density Functions (PDF)
Cumulative Distribution
UNIVERSITY OF CALIFORNIA DAVIS
Department of Civil and Environmental Engineering
Probabilistic Systems Analysis for Civil Engineers (ECI 114)
Fall 2012
Midterm (1)
Monday, October 29, 2012
1) (8 points) For each of the following statements, define if they
ECI 114
Random Variables
RANDOM VARIABLES Reading: Section 2.8
At this point, we have a complete probability structure: we have discussed a random experiment,
sample points (or outcomes of the experiment), a set of outcomes that define the sample space,
c
ECI 114
Probability
For the next few weeks, we will be studying basic principles of probability. How does that relate to
the statistical ideas we presented in the introduction? In probability, we draw conclusions about a
sample based on knowledge (or assu
ECI 114
Winter 2017
University of California, Davis
Department of Civil and Environmental Engineering
Homework Assignment 2 (55 points)
Due in class Tuesday, January 24, 2017
Show all work and explain your answers; no credit will be given for solutions on
ECI 114
Introduction
INTRODUCTION Reading Assignment: Chapter 1; Sections 6.1, 6.2, 6.4
The science of statistics is concerned with:
1.
2.
3.
The description of data sets;
Inferences about the parameters characterizing the system, "population", phenomenon