ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 6
Due: April 2, 2015
Exercise 1. Total Probability, Geometric Random Variables, and Expectation
Independent trials, resulting in one of the outcome

Math S21a: Multivariable calculus
Oliver Knill, Summer 2011
1: Geometry and Distance
The arena for multivariable calculus is the two-dimensional plane and the three dimensional
space.
A point in the plane has two coordinates P = (x, y). A point in space i

Computer Science 141
Computing Hardware
Fall 2015
Harvard University
Instructor: Prof. David Brooks
dbrooks@eecs.harvard.edu
Outline
Course admin
CS141 webpage (http:/www.eecs.harvard.edu/cs141/)
TF and Avis Office Hours will be available by end of wee

ES 173 MIDTERM 2015
Engineering Sciences 173
MIDTERM DESIGN PROJECT
Due: Tuesday, March 31, 2015 by 1:00 p.m.
(Upload using CANVAS, must be a DOC, DOCX, or PDF file, any hand made
drawing must be scanned, NO PHONE PICTURES, Camscanner, etc.)
In Chapter 4

Electron mobilities in modulation-doped semiconductor
heterojunction superlattices
R. Dingle, H. L. StOrmer,a) A. C. Gossard, and W. Wiegmann
Bell Laboratories. Murray Hill. New Jersey 07974
(Received 19 June 1978; accepted for publication 27 July 1978)
G

The Innite Resistor Chain
Background to Morseman Column, November-December 2007
Gary ZL1AN, g.bold@auckland.ac.nz
Figure 1 (a) shows the original network of the problem set in the column. This string of 1 resistors
is innitely long. What is the resistance

1.
ELECTRICAL CIRCUITS
Jaan Kalda
1
CIRCUITS WITH RESISTORS, BATTERIES, AMMETERS AND VOLTMETERS.
Version: 1st January 2014
Circuits with resistors, batteries, ammeters
and voltmeters.
The fundamental physics of circuits of resistors, batteries,
ammeters a

chapter
3
Amplitude Modulation
Fundamentals
I
n the modulation process, the baseband voice, video, or digital signal modifies
another, higher-frequency signal called the carrier, which is usually a sine wave.
A sine wave carrier can be modified by the int

ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 5
Due: March 26, 2015
Exercise 1. Playing Cards
Suppose a standard deck of 52 playing cards is thoroughly shued and a single card is
drawn. An ace

TXW XSXEP
TXW FSRYW XSXEP
ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 4
Due: March 12, 2015
Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closed-book,
with no electro

ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 4
Due: March 12, 2015
Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closed-book,
with no electronics allowed. However, you

8SXEP
TXW
ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Solution 3
Date: February 28, 2015
TXW XSXEP
Exercise 1. Probability Models
Consider two events A and B dened on a common sample space .
(a) Expre

ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 3
Due: February 26th, 2015
Exercise 1. Probability Models
Consider two events A and B dened on a common sample space .
(a) Express each of the foll

TXW XSXEP
TXW FSRYW
ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Solution 2
Date: February 25, 2015
TXW XSXEP
TXW FSRYW
Exercise 1. Conditional Probability and the Total Probability Formula
Alice and B

ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 2
Due: Feb. 19, 2015
Exercise 1. Conditional and Total Probabilities
Alice and Bob play the following game of dice. Each round of the game consists

TXW XSXEP
ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Solution 1
Date: February 18, 2015
TXW XSXEP Exercise 1.
TX
TX
TXW
a. A (B C) = (A B) (A C) is true by distributive property of sets.
b. A (B C) =

ES 150: Introduction to Probability with Engineering Applications
Spring 2015
Professor: Yue M. Lu
Homework 1
Due: Feb. 12, 2015
Note: Due to the extended due date, this homework contains more problems (8) than a
typical homework might contain (5-6). Plea