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

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
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

Estimation
A statistical problem:
We wish to study the performance of the lithium batteries used in a particular model of pocket calculator. The purpose
of the study is to determine the mean effective life span of these batteries so that we can place a li

Meanings of random sampling
Let 1 , 2 , . be a random sample of size from a random variable with mean and variance 2 .
Then,
1 , 2 , . are random variables with the same distribution of . i.e., = , = 2 , = 1,2, ,
1
The sample mean = =1 is a random vari

Estimation
Point estimation:
A sample-based statistics is used to approximate or estimate a population parameter , is called a point estimator for
and is denoted by .
2. Maximum likelihood estimate: steps
Obtain a random sample 1 , 2 , , from the distrib

Estimation
Point estimation:
A sample-based statistics is used to approximate or estimate a population parameter , is called a point estimator for
and is denoted by .
1. The moments-based estimator
Consider a random variable with n samples , = 1,2,3, , .

Joint Distribution
Correlation:
Let be random variables with means and variances 2 2 respectively. The correlation
coefficient between , denoted by is given by
,
=
()()
What is possible value range of ?
Example: The joint density of a discrete 2D rando

Random Variables
A random variable assigns a numerical value to each outcome in a sample space with associated probabilities.
Example: Suppose that an electrical engineer has on hand six resistors. Three of them are labeled 10 and the
other three are labe

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 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
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

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
Lecture 6
drv X with values in the set {0, 1, 2.1., n} where n 2 1
is a xed integer is said to have:Winona;astrategistsaerial;titanwith
parameters 72 and p (O < p < 1) if its pdf is given by

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