Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

1 Page

q1_sol

Course: ESE 520, Fall 2009
School: Washington University...
Rating:

Word Count: 316

Document Preview

1 Quiz of ESE 520: Probability and Stochastic Processes Problem 1. Caculate the probability: Pr(2 Z 4), where Z is a geometric distribution with p = 1/2, i.e., PZ (k) = 2k , k = 1, 2, . . .. Sol: Pr(2 Z 4) =Pr(Z = 2)+Pr(Z = 3)+Pr(Z = 4) = PZ (2) + PZ (3) + PZ (4) = 1/4 + 1/8 + 1/16 = 7/16. Problem 2. A communication channel has three states: A, B or C. The error probability for a bit transmitted through the...

Register Now

Unformatted Document Excerpt

Coursehero >> Missouri >> Washington University in St. Louis >> ESE 520

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
1 Quiz of ESE 520: Probability and Stochastic Processes Problem 1. Caculate the probability: Pr(2 Z 4), where Z is a geometric distribution with p = 1/2, i.e., PZ (k) = 2k , k = 1, 2, . . .. Sol: Pr(2 Z 4) =Pr(Z = 2)+Pr(Z = 3)+Pr(Z = 4) = PZ (2) + PZ (3) + PZ (4) = 1/4 + 1/8 + 1/16 = 7/16. Problem 2. A communication channel has three states: A, B or C. The error probability for a bit transmitted through the channel is 0.05 when the channel is in state A, 0.02 when the channel is in state B, and 0.04 when the channel is in state C. Suppose that the channel is in state A, B, C with probablities 0.2, 0.3, 0.5 respectively. Compute the error probability when a bit is transmitted through this channel. Sol: Since the error is from A, B, or C, Pr(err) = Pr(err, A) + Pr(err, B) + Pr(err, C) = Pr(err|A)Pr(A) + Pr(err|B)Pr(B) + Pr(err|C)Pr(C) = 0.02 0.2 + 0.05 0.3 + 0.04 0.5 = 0.036 Problem 3. Suppose a pair of dice are rolled. (i) compute the probability that sum the of the two numbers is 4; Sol: Possible outcomes: (1, 3), (2, 2), (3, 1); Total outcomes: 6*6=36 Therefore, Pr(sum = 4) = 3/36 = 1/12. (ii) compute the probability that the sum of the two numbers is not less than 4; Sol: Use the formula: Pr(sum 4) = 1 Pr(sum 3) = 1 3/36 = 11/12 since the possible outcomes for the sum 3 are: (1, 1), (1, 2), (2, 1). (iii) compute the (conditional) probability that the sum of the two numbers is not less than 4 given that the number on the rst die is not greater than 2. (Hint: use the denition of conditional probability.) Sol: Let d1...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Washington University in St. Louis - JTB - 1
http:/aimediaserver.com/studiodaily/harvard/harvard.swf Parameter Estimation in biochemical systems models with alternating regressionI-Chun Chou, Harald Martens, and Eberhard O Voit Justin Brown Comp Genetics Discussion Group Washington Univ
Washington University in St. Louis - JTB - 1
Justin T. Brown jtb1@cec.wustl.eduCAMPUS: PERMANENT:Campus Box 7358 6985 Snow Way Dr. St. Louis, MO 63130 (314) 954 - 7117OBJECTIVE: SUMMARY:4615 E. Diamond Woods Lane Springfield, MO 65809 (417) 868 - 8891Career in Computational Sciences/Mat
Washington University in St. Louis - GWH - 2
Agimone: Middleware Support for Seamless Integration of Sensor and IP NetworksGregory Hackmann, ChienLiang Fok, GruiaCatalin Roman, and Chenyang Lu Mobile Computing Laboratory and Center for Distributed Object Computing Department of Computer Sci
Washington University in St. Louis - BMW - 3
CS535 Final Project:ATAPI (aka IDE) Interface within an FPX ModuleNovember 14, 2001Benjamin WestComputer Communications Research Center (CCRC)Qiong ZhangMagnetic Information Sciences Center (MISC)http:/zeus.doc.wustl.edu/cs535.shtmlATAPI
Washington University in St. Louis - CS - 333
TORA RevisitedVanessa Clark 10/29/02TORA Temporally-Ordered Routing Algorithm Routing Algorithm - finds paths between multiple users in an ad hoc network Destination-oriented DAG (Directed Acyclic Graph) Logically separate version of protocol
Washington University in St. Louis - TEAMA - 436
Vandal 1.0CS436: Team AAmy Fan Brian Kelly Brandon Harris Christopher Baker Dave Franco Kris Georgiev Kory Postma Last Week: Basic Object TrackingUse frame by frame data to attempt to track objects. Last Week: Linear Prediction
Washington University in St. Louis - AJM - 2
Feature Detection Using Genetic Programming With Multiple Sensors Andrew J. Marek Advisor William D. Smart Outline Task Martin's work motivation Genetic Programming Related Work Crossenvironment + performance Sensor Fusion Pr
Washington University in St. Louis - JAP - 1
WUGLEJacob Perkins BS/MS Student, Washington University in St Louis jap1@wustl.eduWUGLE is a novel visualization and configuration tool for manipulating allowable transformations of abstract relations. We have applied WUGLE to a wide range of soft
Washington University in St. Louis - MJH - 3
Informed AllocationMain Questions:1. If you are given a stream of allocation requests. What would be the best way to prepare the allocator? 2. What is the best way to determine phases in a program's stream of allocation requests?Progress:1. Init
Washington University in St. Louis - CSE - 545
CSE545 Project Proposal Vanessa Clark Oct 20, 2005 For my CSE545 project, I am going to implement the suggested project Decision tree exploration. Input: DIMACS CNF formatted propositional formula Output: Display(s) of simplified clauses Implementati
Washington University in St. Louis - DGW - 333
Washington University in St. Louis - DGW - 333
* Communication Models: Evolution(1) Unreliable datagrams(2) Steams(3) Remote Procedure(4) Distributed Object Computing(5) Distributed Shared Memory* Tutorial RequirementsAssume: Wire (or medium) that carries a signal.Problem: Noisy
Washington University in St. Louis - JAP - 1
Jacob A. Perkins609 Clara Ave, Apt 9St. Louis, MO, 63112314-367-4332jap1@cec.wustl.eduobjective:CEC consultant position.summary:-7 years experience as computer technician, consultant, and hobbyist.-Working towards B.S. in CS.-Pro
Washington University in St. Louis - JAP - 1
pvqp^qpxqp&gt;q
Washington University in St. Louis - JAP - 1
Above is a screenshot of WUGLE doing 'flat' expression manipulation. During the fall of 2003, we added graph technology to WUGLE. Using graphs makes the expression trees more visual. Below is a screenshot of WUGLE doing tree-like expression manipu
Penn State - ASTRO - 485
Penn State - ASTRO - 485
Penn State - ASTRO - 130
Today in Astronomy 102: observations of stellarmass black holes Summary of distinctive features of celestial black holes. The search for stellarmass black holes: Xray and ray emission. Mass from orbital motion: the Doppler effect. Results fo
Penn State - ASTRO - 20
The Astronomical Journal, 131:8499, 2006 January# 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.ASPECTRAL DECOMPOSITION OF BROAD-LINE AGNs AND HOST GALAXIESDaniel E. Vanden Berk,1 Jiajian Shen,1 Ching-Wa Yip,2 D
Penn State - ASTRO - 480
The Uses of Gravitational Lenses Gravitational lenses are extremely interesting for three reasons. 1) Because the magnification properties of lenses depend on the mass of the lensing object, microlensing experiments, such as the MACHO experiment of m
Penn State - AERSP - 401
TelecommunicationsAERSP 401BCommunication System Designers' Goal Maximize information transfer Minimize errors/interference Minimize required power Minimize required system bandwidth Maximize system utilization Minimize costUseful Relation
Penn State - PHIL - 012
Satisfiability &amp; Logical TruthPHIL 012 - 2/16/2001Outline Test Scores Homework Reminder Satisfiability Logical Truth Complex Truth Tables Sample ProblemsSatisfiability A sentence is said to be satisfiable IFF under some circumstances it c
Penn State - PHIL - 012
Symbolic Logic April 4, 2001 The System F' Announcements Homework 9 will be returned on Monday Homework 10 is due Monday Exam 3 is next Wednesday I'll post a study sheet for Exam 3 soon I'll hand back Exam 2 at the end of class If you didn't receiv
Penn State - IST - 250
T3L9DHTMLIntroductionThis lesson is designed for you to gain some basic information about Dynamic HTML, or DHTML. When you finish this lesson, you should be able to: Describe what DHTML is. Describe what technologies DHTML is composed of. Exp
Penn State - FIN - 406
Solutions to Assignment 5 Chapter 16 2. 4. Only statement C is correct Call option with X=75 cost = 8 1/8 ; payoff = 5; profit = -3 3/8 Put option with X=75 Cost = 3; payoff = 0; profit = -3 Walmart stock price = 100 Call option with X=100; six month
Penn State - PHIL - 012
Solutions to Homework #9, Problems 1-22 (not 15, 17 or 21) Problem 1. Construct a truth table for the sentence (A B) (B A). Show that its final column is the same as that for A B (A T T F F T F T T B) T F T F T F F T (B T F T F T T F T A) T T F
Penn State - ART - 122
Visual Mapping ExerciseIn &quot;Intuitive Stories,&quot; James Elkins suggests that the mental &quot;maps&quot; we form about our experiences with art and art history tell more than just what we think about art. He notes that they can reveal much about who we are, wher
Penn State - IST - 110
IST 110 13 Sept 99On Your Own/Team Work Assignment #1Part I On Your Own On your own, complete the following: Scavenger Hunt pg 526 #1 thru #10 Appendix B Provide the web address for each answer as shown in the text. Part II Teamwork Assignment
Penn State - IST - 110
IST110 LabProjectI Baseball DSSPhase II Creating the Database 1) Start up MS Access. 2) Create a BLANK database and name it IST Baseball Database. 3) Import each of the Baseball Statistics worksheet AS ITS OWN DATABASE Table. Naming each table afte
Penn State - IST - 250
IST 250 Online PBL Case #1 Customer Letter Note from Harold Kern: This letter is the best example of customer comments we've received over the past year or so. It contains all of the complaints we've been hearing. Dear InstaBook: I been using InstaBo
Penn State - IST - 250
IST 250 Online PBL Case #4 Narrative Introduction This case covers the fourth and final contact between the PBL Team and a fictional company named InstaBook. InstaBook has developed technology that allows a customer to purchase chapters from differen
Penn State - IST - 4
IST 250 Online PBL Case #4 Narrative Introduction This case covers the fourth and final contact between the PBL Team and a fictional company named InstaBook. InstaBook has developed technology that allows a customer to purchase chapters from differen
Penn State - IST - 2
IST 250 Online PBL #2 Goals and Objectives Goal You will develop a web site prototype from a previously developed storyboard for a proposed company web site. Objectives You will be able to utilize a development plan for web site development that meet
Penn State - IST - 250
IST 250 Online PBL #2 Goals and Objectives Goal You will develop a web site prototype from a previously developed storyboard for a proposed company web site. Objectives You will be able to utilize a development plan for web site development that meet
Penn State - IST - 256
&quot;We are 'your' company and will strive to find you aplace to call 'home'. We will take the time to find youa property to meet your needs. If looking for a businessproperty, we will also ensure it is a good business decision.&quot;
Penn State - IST - 256
table {border:double; border-color:grey}td.left {font:bold; font-family:times New Roman; padding: 3px;}td.right {background-color:#B7B774; font: bolder; font-family:Arial; padding: 3px;}
Penn State - IST - 247
&lt;%@ Language=VBScript %&gt;&lt;% Response.Buffer = True %&gt;&lt;html&gt;&lt;head&gt;&lt;title&gt;Registration Response&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;center&gt;&lt;H1&gt;User Registration Response&lt;/h1&gt;&lt;/center&gt;&lt;center&gt;&lt;p&gt;The information you entered: &lt;br&gt;&lt;ul&gt;&lt;li&gt;First Name: &lt;%=Re
Penn State - FOR - 466
334F Vairo Blvd. State College, PA 16803 814-867-4175 January 21, 2003 Ms. Karen Lutz ATC-MARO P.O. Box 625 Boiling Springs, PA 17007 Dear Ms. Lutz: My strong background in natural resources and recreation makes me an excellent candidate for to the r
Penn State - FOR - 410
&quot;Helping western forests heal&quot; William Wallace CovingtonCandace M. Sabol FOR 410 Article CritiqueWilliam Wallace Covington's article located in edition 408 of Nature entitled, &quot;Helping western forests heal,&quot; discusses the effects and concerns reg
Penn State - PHYS - 202
Physics Lab 202P-6 Resistance &amp; Ohm's Law NAME: LAB PARTNERS: _ _ _LAB SECTION:_LAB INSTRUCTOR: _ DATE: EMAIL ADDRESS: _ _Penn State UniversityCreated by nitin samarthPhysics Lab 202P-6Page 1 of 14Physics Lab 202P-5Software list Micr
Penn State - PHYS - 202
Physics Lab 202P-2 Charges in Motion I: How Electric Charges Move In Electric Fields (A Virtual Lab) NAME: LAB PARTNERS: _ _ _LAB SECTION: LAB INSTRUCTOR: DATE: EMAIL ADDRESS:_ _ _ _ Penn State UniversityCreated by nitin samarthPhysics Lab
Penn State - GEOSC - 001
Volcanism: Creating the Earth's SurfaceGoals 1. describe the types of volcanic cones 2. identify the recent volcanic centers of the western United States 3. review the vo lcanic provinces of the world Introduction For a significant number of people,
Penn State - GEOSC - 001
Seismicity of the Hawaiian IslandsThis document contains two exercises involving volcanism, plate tectonics, and the Hawaiian Islands. Please type your answers on a separate sheet of paper, and hand them in together with your charts, graphs and draw
Penn State - GEOSC - 001
Minerals and their Socio-Economic ConsequencesIn class and in the laboratory we discuss the physical and chemical properties of minerals, with the goal of enabling you to identify them in hand sample as key indicators of rock evolution. For thousand
Penn State - GEOSC - 001
Sedimentary Stratigraphy of the Western United StatesSedimentary rocks provide geologists with insight into the changing environments of the past. In the laboratory you have learned to identify several key sedimentary rock types, and have gained som
Penn State - CMPSC - 101
Programming in C+Dale/Weems/Headington Chapter 12 Applied Arrays: Lists and Strings1String in C+A string is an array of characters which contains a non-printing null character `\0' ( with ASCII value 0 ) marking its end. A string can be initial
Penn State - CMPSC - 12
Programming in C+Dale/Weems/Headington Chapter 12 Applied Arrays: Lists and Strings1String in C+A string is an array of characters which contains a non-printing null character `\0' ( with ASCII value 0 ) marking its end. A string can be initial
Penn State - NUTR - 119
BakingMethods of Mixing Conventional Cream fat + sugar Stir in egg Stir flour:liquid (3:2) Quick Mix Mix all Beat with mixerBakingMethods of mixing continued. Muffin Mix dry only Blend liquids Make well in dry Biscuit/Pastry Mix
Penn State - ASTRO - 001
MOON &amp; ECLIPSESDrawn to scale: scaleEarthMoonMoon's orbit viewed from above Earth's north poleNear side Orbit period = 27.3 days (Sidereal Period) Far sideNear SideFar SideMOTION OF THE MOON (Viewed from Earth) Diurnal (Daily) Mot
Penn State - ASTRO - 001
A Sense of Where We Are Outline 1. Sizes of Some Astronomical Things A. B. C. D. E. F. G. H. I. J. K. L. 2. Models A. Modelers Equation Real Size/Distance of Object 1 Model Size/Distance of Object 1 = Real Size/Distance of Object 2 Model Size/Distanc
Penn State - ASTRO - 001
Moon &amp; Eclipses Outline 1. Lunar Facts * Distance/diameter relative to Earth * Orbit: period = 27.3 days * Far side, near side 2. Motion of the Moon * Daily: east to west * Monthly: eastward relative to stars * Orbit plane tipped relative to Earth's
Penn State - ASTRO - 001
Additional Problem on Gravitation Consider Newton's form of Kepler's 3rd law: a3 M + m = 2 P Here, the Sun's mass is M, and a planet's mass is m. In the system of units used in this equation, the Sun has a mass of 1. In the solar system, we know that
Penn State - MKTG - 471
Sample Questions Mrkt 471 Exam I 1. The Grand Ole Opry began December 1927. In 1953, Opry annual attendance reached 243,000 per year. Patrons had to order tickets months in advance. Today most Grand Ole Opry shows are played in an auditorium that is
Penn State - EXK - 106
SMEAL College of Businesslaboratory for economic management and auctionseBay Auctions: Bidding and InformationIn recent years, the use of auctions and dynamic pricing for procurement and sales has been steadily increasing.1 Much of the emphasis o
Penn State - AXR - 15
Pennsylvania State University The Smeal College of Business Spring, 2006 Marketing 521 Scientific Marketing Analysis &amp; ImplementationInstructor: Office: Phone: e-mail: Arvind Rangaswamy 481 Business Building 814 865-1907 arvindr@psu.edu Class Hours:
Penn State - MEF - 11
amily oundations: A Strong StartPROGRAM OVERVIEW&quot;I think these classes are perfect for first-time parents.&quot; &quot;This class is great.&quot; &quot;Its real and not textbook.&quot; - First-Time Parents&quot;I am thankful I am included in these classes. I feel that this
Washington University in St. Louis - CSE - 260
CSE 260 Digital Computers: Organization and Logical DesignFinal Exam SolutionsJon Turner5/3/20071. (10 points) Draw a transistor-level diagram (using n-FETs and p-FETs) of a NOR gate with 3 inputs, A, B and C.A B C (A+B+C)'Suppose all thre
Penn State - KAH - 1020
Penn State - KAH - 1020
Washington University in St. Louis - CS - 577
CS/EE 577 - Exam 212/8/001. (15 points) Fill in the following table. x 4,5 (x) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19What is (2,95) in D125,5 ?What is (3,520) in Y1024,4 ?12. (15 points) For each of the networks shown below, giv
Penn State - LA - 483
From: &quot;Terry D. Mathias&quot; &lt;GE0515@SIUCVMB.BITNET&gt;Subject: Why God Never Received Tenure at a University! &quot;1. Because He had only one major publication. 2. And it was in Hebrew. 3. And it had no references. 4. And it wasn't publi