# 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.

5 Pages

### prob

Course: IS 2000, Fall 2009
School: Pittsburgh
Rating:

Word Count: 648

#### Document Preview

Handout Introductory for Information Science Events and outcomes Let X be an event with N possible mutually exclusive outcomes x1, x2, ..., xN. X {x1, x2, ..., xN} (a discrete distribution) The probability that X = x1 is p1, that X = x2 is p2, that X = xi is p1 for i = 1...N. Equivalent expressions: Pr(X = x1)= P(x1) = p(x1) = p1 . Two important aspects of probability: Every probability value lies between 0 and 1...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Pennsylvania >> Pittsburgh >> IS 2000

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.
Handout Introductory for Information Science Events and outcomes Let X be an event with N possible mutually exclusive outcomes x1, x2, ..., xN. X {x1, x2, ..., xN} (a discrete distribution) The probability that X = x1 is p1, that X = x2 is p2, that X = xi is p1 for i = 1...N. Equivalent expressions: Pr(X = x1)= P(x1) = p(x1) = p1 . Two important aspects of probability: Every probability value lies between 0 and 1 inclusive: , for all i. The sum of probabilities of all possible outcomes is 1: Example: an event M with possible outcomes, gold, silver, bronze, or loser. Pr(M = gold) = 0.05 Pr(M = bronze) = 0.15 Pr(M = silver) = 0.10 Pr(M = loser) = 0.70 Find the probability that M is gold, silver, or bronze. Answer: Pr(M is gold, silver, or bronze ) OR Pr(M is gold, silver, or bronze ) = 1 - Pr(M is loser) = 1 - 0.70 = 0.30 = Pr(M is gold) + Pr(M issilver) + Pr(M isbronze) = 0.05 + 0.10 + 015 = 0.30 Random variables A random variable X takes on a value from a given set. Thus, it is an event where the outcomes x1, x2, ..., xN have numerical values. The expected value of X is . Example: Find the expected value of X if Pr(X = 2) = 0.15 Pr(X = 6) = 0.20 Answer: Pr(X = 5) = 0.45 Pr(X = 8) = 0.20 More than one random variable Two random variables X and Y , with X {x1, x2, ..., xN} and Y {y1, y2, ..., yM} Let X and Y be two simultaneous events with outcomes xi and yj. This joint event has a probability p(xi , yj ). These probabilities can be written in matrix form. Note that the rows sum to the total probability of the corresponding xi , and the columns sum to the total probability of the corresponding yj. The sums of the columns and rows is mathematically expressed as follows: Rows: Columns: The sum of all the joint probabilities is 1: . Example: Given the joint probabilities below, find the probability of each X and each Y: Answer: Using the summation formulas we get p(x1) = 0.3, p(x2) = 0.7 for the X values p(y1) and = 0.2, p(y2) = 0.1, p(y3) = 0.7 for the Y values. Conditional Probabilities (Baye's Theorem) The probability distribution across the X variables may change, depending on whether the Y value is known (and vice-versa). If one variable does not influence the other's probability, the variables are called independent. The probability that X=xi given that we know Y=yj is written p(xi |yj). This is also called the probability of xi conditioned on yj. Baye's theorem expresses the conditional probability as the quotient of the joint probability and the probability of the condition. Equivalently, the joint probability is the product of the conditional probability and the probability of the condition. Note that since p(xi , yj ) = p(yj , xi ), there are two such products (either xi or yj can be the condition): The example below computes conditional probabilities from the joint distribution on the previous page: Example: Given the joint probabilities below, find the conditional probabilities of each X given each Y: Answer: The conditional probabilities are found by dividing each probability by the corresponding p(yj): Note that the columns al...

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:

Pittsburgh - MCS - 2
#!/usr/bin/perl -w# Restriction digestionuse strict;use warnings;use lib '/Users/mcs2/sacc/lib'; #&lt; your path to your library of modulesuse BeginPerlBioinfo; # see Chapter 6 about this modulemy \$dna;if(@ARGV){ \$dna = get_dna_from_f
Pittsburgh - MCS - 2
#!/usr/bin/perl -w\$file = 'mouse_bmp4.gb';open(FH, &quot;\$file&quot;)|die&quot;Cannot open \$file: \$!&quot;;\$position = tell(FH);print &quot;Position = \$position\n&quot;;\$i=0;while(&lt;FH&gt;){ \$i+; \$position = tell(FH); push(@positions, \$position); print &quot;Line
Pittsburgh - MCS - 2
#!/usr/bin/perl -wuse strict;use warnings;use lib '/Users/mcs2/sacc/lib'; #&lt; your path to your libraryuse BeginPerlBioinfo; print &quot;#&quot;x40, &quot;\nParsing a GenBank file using an ARRAY\n&quot;, &quot;#&quot;x40, &quot;\n\n&quot;;my \$file = &quot;mouse_bmp4.gb&quot;;my @an
Pittsburgh - MCS - 2
#/usr/bin/perl -wuse strict;my \$seq;if(@ARGV){ \$seq = shift(@ARGV);}else{ die &quot;No input\n&quot;;}print &quot;\n\$seq\nPercent GC = &quot;, calc_gc(\$seq), &quot;\n&quot;; my \$polyA = find_polyA(\$seq);print &quot;Longest stretch of A's = \$polyA\n&quot;;exit;##sub c
Pittsburgh - MCS - 2
#!/usr/bin/perl -wuse strict;use warnings;my \$time1 = time;# Write a program that creates a HASH of ARRAYS# HASH keys are the integers from 1.100# HASH values are anonymous arrays containing the prime# factors of the hash key## For examp
Pittsburgh - WOL - 1
Wooyoung Lim 4518 W.W. Posvar Hall Department of Economics University of Pittsburgh Pittsburgh, PA 15260, USA. DATE OF BIRTH EDUCATION December 14th 1978 20062010 (expected ) 20052006 20042005 19992004 University of Pittsburgh Ph.D. in Economics Univ
Pittsburgh - SUPER - 7
Measuring Epidemiologic OutcomesEpidemiological OutcomesRatio: Relationship between two numbersExample: males/femalesProportion: A ratio where the numerator is included in the denominatorExample: males/total birthsRate: A proportio
Pittsburgh - SUPER - 7
Using verbal autopsy to assess to pass to death Infant Mortality in Talas oblast, Kyrgyzstan, Years 1997-2001A. Napoletano, D. Coclite, R. Ferrelli, . zzaccaraIstituto Supepriore di Sanita, ISS, Rome - Italy. shiraliev, . inbaevCenter for Socia
Pittsburgh - SUPER - 7
How to do Meta AnalysisAssociate Director, Fogarty International Training Program Kolkata, India February, 2005 arin.basu@gmail.com phone: 919830153666Arindam BasuWhat is meta analysis?Quantitative approach for systematically combining results
Pittsburgh - SUPER - 7
Identification of needs in needs a high risk populationHamda Qotba, B.Med.Sc, M.D, ABCMBy What is need? Capacity to benefit from intervention The ability to benefit from health care (DoH)Dr.Hamda Qotba 2Health Is a state of complete phys
Pittsburgh - MCS - 2
Curr Genet (2005) 47: 335344 DOI 10.1007/s00294-005-0576-2R ES E AR C H A RT I C L ERhonda R. McCartney Eric M. Rubenstein Martin C. SchmidtSnf1 kinase complexes with different beta subunits display stress-dependent preferences for the three S
Pittsburgh - SOC - 0150
Recorded by Meghan Dyson Social Theory Lecture Notes February 23, 2006 Erik Olin Wright on Weber: Attributes Intrinsic to Categories: Sphere of Interaction Economic Communal Political Category Class Status Group Party Objective Properties Yes Yes Yes
Pittsburgh - SOC - 0150
Notes for Soc 0150 4.11.06 Recorded by Erin Davis with some comments or clarifications from Dr. Brush Dubois and the self -wrote Philadelphia Negro (1899), which is highly descriptive and devoid of what isusually thought of as theory (Ritzer &amp; Good
Pittsburgh - WOL - 1
Advanced Microeconomic Theory II, 2008 Spring TA : Wooyoung Lim1Discussion on 2nd Homework(HW1) 8. Read Osborn and Runinstein, A Course on Game Theory, Chapter 11 (p.215) and Chapter 6. (HW2) 1. How to nd a symmetric Nash equilibrium without a
Pittsburgh - KIS - 23
Nicomachean EthicsAristotle Adapted from the translation by W. D. RossBook I, Chapter 7 (excerpt) Let us again return to the good we are seeking, and ask what it can be. It seems different in different actions and crafts; it is different in medici
Pittsburgh - NAK - 54
What the Cerebellum computesT Ohyama, WL Nores, M Murphy and MD Mauk A review by Narayanan Krishnamurthy February 16, 2007What Cerebellum (CB) computes? Crux - To understand the input to output transformation i.e, how and what does CB compute? T
Pittsburgh - SUPER - 7
How Adults LearnPeter J. Fabri, M.D.Professor of Surgery Associate Dean of Graduate Medical Education University of South Florida Health Sciences CenterOrganic Chemistry 1966 I couldn't understand it So I memorized it Every night I would rewri
Pittsburgh - SUPER - 7
Methods Whole Sweden 1990-94; children 0-19 years National Hospital Discharge and Causes of Death registers Boys and girls in 4 age groups 4 socio-economic groups 4 diagnosis groups within traffic Relative Risks (compared with high and middle l
Pittsburgh - SUPER - 7
CLASSIFICATIONPETER H. RUSSELL, BVSc, PhD, FRCPath, MRCVS Department of Pathology and Infectious Diseases, The Royal Veterinary College, Royal College Street, London NW1 OTU.E-mailWeb siteObjectives Students should be able to: describe in out
Pittsburgh - SUPER - 7
New Approaches to Epidemiological Risk Assessment ManagementKonstantyn Atoyev Cybernetics Center of National Academy of Sciences. Kiev. Ukraine.One of the most important tasks of modern epidemiology is the effective monitoring, forecasting and man
Pittsburgh - SUPER - 7
PAPOVAVIRIDAEPETER H. RUSSELL, BVSc, PhD, FRCPath, MRCVS Department of Pathology and Infectious Diseases, The Royal Veterinary College, Royal College Street, London NW1 OTU.E-mailWeb siteLEARNING OBJECTIVES Students should be able to: Underst
Pittsburgh - SUPER - 7
REHABILITATION SCIENCE AND DISABILITY STUDIES: ARE THEY COMPLEMENTARY?Katherine D. Seelman, Ph.D. Associate Dean and Professor School of Health and Rehabilitation Science University of Pittsburgh and Visiting Prince Fellow Rehabilitation Institute o
Pittsburgh - ECON - 2200
ECON 2200: Problem Set 1 Due September 8th 2008, 11:00 a.m. 1. Consider the following games, in which player 1 chooses the row and player 2 chooses the column: L 1, 1 0, 0 R 0, 0 0, 0 L 1, 1 1, 0 R 0, 1 -1, -1 L 1, 1 1, 1 1, 1 l 1, 2 1, 1 -10, -10 r
Pittsburgh - ECON - 2100
ECON 2100: Problem Set 2 Due 9/24/08 in class 1. A consumer of two goods faces positive prices and has positive income. His utility function is u (x1 , x2 ) = max {ax1 , ax2 } + min {x1 , x2 } , Compute the Walrasian demand functions. 2. Consider a t
Pittsburgh - ECON - 2100
ECON 2100: Problem Set 1Due September 8th in class1. Suppose there is some nite set of alternatives X. An individuals weak preference relation on X is denoted by R and her strict preference relation (derived from R) by P . R is reexive and comple
Pittsburgh - ECON - 2200
ECON 2200: Problem Set 4 Due 10/27/08 1. Find the set of rationalizable strategies in the guess the average game in which n players simultaneously choose a number in the set {1, 2, . . . , K} (K 3), and a prize of \$1 is split evenly among the one or
Pittsburgh - ECON - 2100
ECON 2100: Problem Set 3 Due 10/14/08 in class 1. Calculate the supply function y (p) and the prot function (p) for each of the following production functions: (a) f (a) = a , where 0 &lt; 1. 1 (b) g (a) = a1 + a2 , where , &gt; 0. (c) h (a) = min {a1
Pittsburgh - ECON - 2100
ECON 2100: Problem Set 4 Due 11/3/08 in class 1. Technology for producing q gives rise to a cost function c (q) = aq + bq 2 . The market demand for q is p = q. (a) If a &gt; 0, if b &lt; 0, and if there are J rms in the industry what are the short-run eq
Pittsburgh - ECON - 2100
ECON 2100: Problem Set 6 Due 12/5/08 1. In an economy with two types of consumer, each type has the respective utility function and endowment: u1 (x11 , x21 ) = x11 x21 u2 (x12 , y22 ) = x12 x22 and and 1 = (8, 2) , 2 = (2, 8) .(a) Draw an Edgewort
Pittsburgh - ECON - 2100
ECON 2100: Problem Set 5 Due 11/19/08 in class 1. Consider an Edgeworth-box economy in which the two consumers have locally nonsatiated preferences. Let xli (p) be consumer is demand for good l at prices (p1 , p2 ) . (a) Show that p1 (ix1i (p) 1
Pittsburgh - ECON - 1905
ECON 1905: Problem Set 3 Due 4/17/08 in class 1. Suppose a group of citizens are faced with the following public goods contribution problem: the benet to each citizen if the good is provided is 1; the cost of contributing to the good is 3 ; 8 and the
Pittsburgh - ECON - 1905
ECON 1905: Problem Set 2 Due 2/19/08 in class 1. Suppose there are two voters, 1 and 2, trying to choose between three alternatives, x, y, and z. If we assume preferences are strict, we can represent a voting rule in a 66 grid, describing the outcome
Pittsburgh - SUPER - 7
Prof. Suad M. Sulaiman, Tropical Medicine Research Institute P.O.Box 1304, Khartoum 11111, SUDAN ( tropmed@sudanmail.net)EL RAHAD FIELD RESEARCH CENTRE - CHALLENGING HEALTH PROBLEMS WESTERN SUDANSULAIMAN, S. M.M.Sc. (LSHTM), Ph.D. ( U. of Khartou
Pittsburgh - SUPER - 7
PROBLEM-BASED LEARNINGPresented by: Dr. Soha Rashed Aref Mostafa Prof. of Community Medicine Member of Medical Education Department Faculty of Medicine Alexandria University Egypt Traditional NewSPICES Medical Innovative Continuum Curricula C
Pittsburgh - SUPER - 7
Corrective &amp; Preventive Action ProgrammeqCorrective and preventive action managed by one programme Closely linked to the internal auditqprogramme q Managed by the Quality Manager q Process managed using corrective action form1.CAR Raised 2.C
Pittsburgh - SUPER - 7
Introduction to Environmental HealthAllison Robinson University of Pittsburgh Pittsburgh, Pennsylvania November 2001Learning Objectives Define fundamental terms Explain the basic relationship between the environment and health Explain impact of
FIU - GLY - 5835
Surface Adhesion (Adsorption) in LBMKey Papers Martys, N. and H. Chen, 1996, PRE 53, 743750 Raiskinmki, P., A. Koponen, J. Merikoski, and J. Timonen, 2000, Comp. Materials Sci. 18, 7 12Key Books Adamson, A. W., and A.P. Gast, Physical Chemist
Pittsburgh - CALC - 3
Math 0240 - Midterm Review Questions The midterm will cover the following sections of the text: Chapter 8: 8.1, 8.2, 8.3, 8.6 Chapter 9: 9.2, 9.3, 9.4, 9.5, 9.6, 9.7 Chapter 10: 10.1, 10.2, 10.3, 10.5, 10.6, 10.7 1. Find an equation for the tangent p
Pittsburgh - CHEM - 1460
The following links provide descriptions of the following three problems: the predatorprey problem, the pendulum problem, and the Van der Pol equation.http:/dmpeli.math.mcmaster.ca/Matlab/CLLsoftware/predator/predator.html http:/dmpeli.math.mcmaste
Pittsburgh - MATH - 230
Practice Problems on Differentiation Differentiate the following functions. 1) x2 + (2x + 3)7 3) x cos(2x) 5) ln x cos(3x) 7) ex sin(4x) 9) x4 sec(x2 + 1)2x+ln x x2 -72) 52x - 14) x2 cos(2x) 6) log5 x cos(4x) 8) 32x-3 tan(4x) 10)sin(2x)
Pittsburgh - CHEM - 1410
CHEM 1410Homework Set #1(Chapters 11,12)1. Normalize the following wavefunctions a) = sin 2x on (0,L) Lb) = C on (-a, a), C = constant c) = e x on (-, )2d) = e r in 3-dimensional space2. Consider the wavefunction =x 2 sin for a
Pittsburgh - CALC - 3
Math 240 Summer 2006 Homework 3 1. Convert the following: (a) (5, 5 3, 0) from Cartesian coordinates into cylindrical and spherical coordinates. (b) (8, 3/4, 6) from cylindrical coordinates into Cartesian and spherical coordinates. (c) (2, 7/4, 2/3)
Pittsburgh - BIOSC - 1820
Blose 1820 Metabolic Pathways and Regulation Spring, 2008 Prof. Jeffrey L. Brodsky Final Exam April 23, 2008NAME:Each answer is worth 2 points. GOOD LUCK!SHORT ANSWER:1. What two attributes of the reaction catalyzed by fatty acid synthase make
Pittsburgh - BIOSC - 1820
BIOSC 1820 :Metabolic Pathways and Regulation Spring, 2006 Prof. Jeffrey L. Brodsky Final Exam April 28, 2006NAME:Unless indicated otherwise, each answer is worth 2 points. GOOD LUCK! 1. RECITATIONA. Under starvation conditions, the transcriptio
Pittsburgh - BIOSC - 1820
Blose 1820Metabolic Pathways and Regulation Spring, 2007 Prof. Jeffrey L. Brodsky Mid-Term Exam March 4, 2008 NAME:1. MATCHINGChoose the letter below or on right that BEST matches a choice below:NADsterk acidE.carnitine@j\.~&quot; .&quot;.
Pittsburgh - BIOSC - 1820
,43a tJI03CVl8'eJOOcf'Z4=17Blose 1820 Metabolic Pathways and Regulation Spring, 2007 Prof. Jeffrey L. Brodsky Quiz #1 January 24,2007NAME:1. Even though the standard free energy for a biochemical reaction (AG'O) may bepositive, several
Pittsburgh - BIOSC - 1820
Blose 1820 Metabolic Pathways and Regulation Spring, 2007 Prof. Jeffrey L. Brodsky Quiz #4 March 19, 2008NAME:1. The following structure depicts an intermediate in the reaction catalyzed bywhichenzyme'~o II00 -IINH3 I-O-P-O-C-CHz-CH?
Pittsburgh - BIOSC - 1820
Blose 1820 Metabolic Pathways and Regulation Spring, 2007 Prof. Jeffrey L. Brodsky Quiz #3 February 21, 2007 NAME:1. Some bacteria can grow on acetic acid as their sole carbon source. and specificcomplex sugars (derived from glucose) are essentia
Pittsburgh - BIOSC - 1820
4AtMSLY/J/~5t ~ ~o3-'; #'-1Blose 1820 Metabolic Pathways and Regulation Spring, 2006 Prof. Jeffrey L. Brodsky Quiz #2 February 8, 2006 NAME:1. There is a difference in kinetics between insulin and the synthetic insulin anaiogue (SIA) with resp
Pittsburgh - BIOSC - 1820
BIOSC 1820 Metabolic Pathways and Regulation Spring, 2006 Prof. Jeffrey L. Brodsky Quiz #4 March 22, 2006NAME:/jJ!~ SJ;:.Y .6'1t?~ /,f02tJ 01-.: It: /01. Match the term or structure on the right with the best choice on the leftJi stimula
Pittsburgh - BIOSC - 1820
BIOSC 1820 Metabolic Pathways and Regulation Spring, 2007 Prof. Jeffrey L. Brodsky Quiz #5 April 2, 2008NAME:1. Multiple Choice and Short Answer:A. Each of the following statements about Complex III are TRUE except:t. Electrons are delivered
Pittsburgh - BIOSC - 1820
BIOSC 1820 Metabolic Pathways and Regulation Spring, 2006 Prof. Jeffre:r L. Brodsky Final Exam April 28, 2006NAME:KEYUnless indicated otherwise, each answer is worth 2 points. GOOD LUCK!1. RECITATIONA. Under starvation conditions, the transcr
Pittsburgh - BIOSC - 1820
oBlose 1820 Metabolic Pathways and Regulation Spring, 2007 Prof. Jeffrey L. Brodsky Quiz #2 February 7, 2007 NAME!( E&quot;(/1. The pentose phosphate pathway is critical for the production of NADPH which-in turn-reduces another molecule that de-toxif
Pittsburgh - SUPER - 7
ISLAMIC TEACHINGS ON REPRODUCTIVE HEALTH AND FERTILITY TRANSITION IN MUSLIMMAJORITY COUNTRIESMehtab S. Karim, Ph.D. Head, Reproductive Health Program Professor of Demography Department of Community Health Sciences Aga Khan University mehtab.kari
Pittsburgh - SUPER - 7
The Economics of Clinical Governancewww.bradfordvts.co.ukBrian Ferguson, Professor of HealthEconomics, Nuffield Institute for Health, University of Leeds; and Head of Clinical Governance, North Yorkshire Health AuthorityProfessors&quot;a professor
FIU - WP - 2008
Incomplete Information In a Long Run Risks Model of Asset PricingPrasad V. BidarkotaDepartment of Economics, Florida International UniversityAbstract We study the effects of incorporating incomplete information in the recently developed long run
FIU - WP - 2004
EFFICIENT TESTS OF LONG-RUN CAUSATION IN TRIVARIATE VAR PROCESSES WITH A ROLLING WINDOW STUDY OF THE MONEY-INCOME RELATIONSHIPJONATHAN B. HILL Abstract. This paper develops a simple sequential multiple horizon noncausation test strategy for trivaria
FIU - MACRO - 2
Expectations and the Nonneutrality of LucasLong before rational expectations, macroeconomists interpreted time series of aggregate quantities, monetary and scal variables, and nominal price levels in ways designed to inform macroeconomic policy dec
Pittsburgh - SUPER - 7
The role of journals in promoting prevention (beyond the publication of original research)Richard SmithEditor, BMJ Marbella, April 2003 www.bmj.com/talksOr, &quot;Can journals change the world?&quot;NoWhat I want to talk about What can journals do and
Pittsburgh - SUPER - 7
THE DECLINE OF MORTALITY IN THE SECOND HALF OFTHTHE 20CENTURYVictor R. FuchsHenry J. Kaiser Jr. Professor Emeritus Stanford UniversityDepartment of Health London 8 May 2003Country Austria Canada Denmark England &amp; Wales Finland France Italy
Pittsburgh - SUPER - 7
Epidemiologic Transition: Changes of fertility and mortality with modernizationAbdel Omran. The Epidemiologic Transition: A Theory of the epidemiology of population change. Milbank Quarterly. 1971;49:509-538Imhotep,the &quot;father of medicine&quot;. The w