Stat Program
Introduction to Statistics & Probability Name:
Math & Physics Dept
Course #: STAT350
ID #:
CAS, QU
Oct 15, 2008
Time:75minutes
_
Exam 1
Show all your work! You could use the back of each page for more space
1.
a. Show that P(A)P(AUB) [Hint: A

ESE 326 Probability and Statistics for Engineering
HW 3: due on September 17, 2015
Total: 20 points
Problem 1. [5 pl In blasting soft rock such as limestone, the holes bored to hold the explosives
are drilled with at Kelly bar. This drill is designed so t

ESE 326 Probability and Statistics for Engineering
Lecture 7
Hypergeometric and Poisson Probability Distributions.
Outcomes of the lecture:
- hypergeometric probability distribution and its characteristics;
- Poisson probability distribution and its chara

ESE 326 Probability and Statistics for Engineering
Outcomes of the lecture:
— binomial probability distribution and its characteristics;
- calculating related binomial probabilities using tables;
— negative binomiai probability distribution and its ch

ESE 326 Probability and Statistics for Engineering
"General deﬁnition of probability and its properties. Conditional proba—
bility”.
Outcomes of the lecture:
— axiomatic deﬁnition of probability (due to A_N.Kolmogoroff, 1933);
— complement and a

ESE 326 Probability and Statistics for Engineering
Lecture 8
Continuous random variables (crvs) and their probability distributions.
General properties.
Outcomes of the lecture:
- probability density function (pdf) of a crv and its characteristic properti

ESE 326 Probability and Statistics for Engineering
Lecture 1
Introduction to probability. The simplest probability model: the case
with equally likely outcomes.
Outcomes of the lecture:
- sample space;
- events and the operations on them;
- denition of pr

ESE 326 Probability and Statistics for Engineering
.
Outcomes of the lecture:
— hypergeometric probability distribution and its characteristics;
— Poisson probability distribution and its characteristics;
— approximation of binomial distribu

ESE 326 Probability and Statistics for Engineering
Lecture 3
Independent events. Bayes formula.
Outcomes of the lecture:
- independent events and the formula for independent events;
- formula of the Total Probability;
- Bayes formula;
- various examples o

ESE 326 Probability and Statistics for Engineering
Lecture 4
Discrete random variables and their probability distributions. Numerical
characteristics.
Outcomes of the lecture:
- probability distribution of a discrete random variable (d.r.v.) X;
- probabil

ESE 326 Probability and Statistics for Engineering
Lecture 5
Moment-generating function (mgf) and its properties. Geometric probability distribution.
Outcomes of the lecture:
- some examples on general properties of a drv;
- moment-generating function (mg

ESE 326 Probability and Statistics for Engineering
HW 1: due on Thursday, September 3, 2015
Total: 20 points
Problem 1. [5 p.] Any home mortage is classied to be of xed rate (F) or variable rate (V).
Consider an experiment of randomly selecting a sample o

ESE 326 Probability and Statistics for Engineering
HW 1-Solutions
Total: 20 points
Problem 1. [5 points] Any home mortage is classied to be of xed rate (F) or variable rate
(V). Consider an experiment of randomly selecting a sample of four mortgages.
a) F

ESE 326 Probability and Statistics for Engineering
HW 7 - Solutions
Total: 20 points
Problem ? cfw_4 p.] Let E be a standard normal random variable and let Y m 232 1, Find the
pdf of Y.
Solution: We can use here the result extablished in lecture. In other

ESE 326 Probability and Statistics for Engineering
HW 9 - Solutions
Total: 20 points
Problem 1. [5 p.] Using a long rod that has length , you are going to lay out a square plot
in which the length of each side is . Thus the area of the plot will be 2 . Ho

ESE 326 Probability and Statistics for Engineering
HW 5 - Solutions
Total: 20 points
Problem 1. [5 p.] The weekly demand for propane gas (in 1000s of gallons) from a particular
facility is a crv X with pdf given by
f (x) = 2(1
1
) for 1 x 2
x2
(and 0 oth

ESE 326 Probability and Statistics for Engineering
HW 8 Solutions
Total: 20 points
Problem 1. [5 p.] Let X be a random variable with density
fX(:L') = 8, m > 0
and let Y = eX. Find the pdf of Y.
Solution: We see that Y = MX) Where Mac) 2 ex. Obviosly, h i

ESE 326 Probability and Statistics for Engineering
HW 11 - Solutions
Total: 20 points
Problem 1. [4 p.] A sample statistic of size 9 from a normal distribution with 2 = 25 is used
to test
H0 : = 20 against H1 : = 28.
Let us agree to reject H0 in favor of

ESE 326 Probability and Statistics for Engineering
HW 10 - Solutions
Total: 20 points
Problem 1. [5 p.] The late manifestation of an injury following exposure to a sufficient dose of
radiation is common. These data are obtained on the variable X, the time

ESE 326 Probability and Statistics for Engineering
HW 4-Solutions
Total: 20 points
Problem 1. [5 p.] Use the moment-generating function to show that E(X 2 ) =
rq
V ar(X) = p2 for the negative binomial distribution with parameters r and p.
(r2 +rq)
p2
and

ESE 326 Probability and Statistics for Engineering
HW 3 - Solutions
Total: 20 points
Problem 1. [5 p.] In blasting soft rock such as limestone, the holes bored to hold the explosives
are drilled with a Kelly bar. This drill is designed so that the explosi

Axioms of Probability
Let be a sample space for an experiment, and an event within . A function is called a
probability function if:
(1) 0 1 ,
;
(2) = 0 = 1
(3) If 1 , 2 , is a collection of mutually exclusive events in , then
1 2 = [ ]
=1
Properties of

ESE 326 Probability and Statistics
Instructor:
Dr. Jinsong Zhang
jinsong.zhang@wustl.edu
Green Hall, Room 1156B
Syllabus
General Information:
Office Hours: Monday and Wednesday 9:00AM to 10:00AM, Tuesday and Thursday
9:00AM to 11:30AM, and by appointment

Conditional Probability
Conditional probability: A sample space contains all the possible outcomes of an experiment. Sometimes,
we obtain some additional information about an experiment that tells us that the outcome comes from a
certain part of the sampl

April 15; 2014
ESE 326 Probability and Statistics for Engineering
Instructor: Vladimir Kurenok
EXAM 2
Name (Please print:
Total: 100 points
Instructions:
1. You must Show all work to completely justify your answers in order to receive any
credit.
2. Tab

October 7', 2014
ESE 326 Probability and Statistics for Engineering
Instructor: Vladimir Kurenok
EXAM I
Name (Please riri ): y .
p t S O l UL idol/13
Total: 100 points
Instructions:
1. You must show all work to completely justify your answers in order t

April 11, 2013
ESE 326 Probability and Statistics for Engineering
Instructor: Vladimir Kurenok
EXAM 2
Name (Please print): /
Total: 100 points
Instructions:
1. You must Show all work to completely justify your answers in order to receive any
credit.
2. Ta

ESE 326 Probability and Statistics for Engineering
Instructor: Vladimir Kurenok
EXAM 2
Name (Please print):
Total: 100 points
Instructions:
1. You must show all work to completely justify your answers in order to receive any
credit.
2. Tables are attached

l l
A new 8-bit microcomputer chip has been developed that can be reprogrammed without removal from the microcomputer. It
is claimed that a byte of memory can be programmed in less than 14 seconds.
A) Set up the appropriate null and aalternative hypothese