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Exam 1 : Study Guide MATH 166:503 Fall 2015 Administrative details • The exam is on Friday (September 25th ) in class. Students will sit in their assigned seats. • The exam will consist of three parts. Part I will have 5 questions (5 points each) with multiple-choice answers. Each question will have only one correct answer and students will clearly mark their choice by encircling the letter signifying that option. Any ambiguous answer will be considered incorrect. No work will be graded and no partial credit will be given for this part. • Part II will have 1 question with 5 sub-parts (2 points each). Each of them will be True/False questions. Again, ambiguous answers will be considered incorrect and no partial credit will be awarded for any of these sub-parts. • Part III will have 7 short answer type questions (total worth of 65 points). All necessary work will have to be shown for full credit i.e. answers with no supporting work will not receive full credit. Partial credit may be awarded for correct work shown. Final answers will need to be clearly put in a box. • Use of calculators is permitted for arithmetic calculations. • Answers to problems on probability will have to be rounded up, wherever necessary. If it is a question involving percentages then answers will have to be rounded up to 4 decimal places. If the question does not involve percentages, then answers will have to be rounded up to 2 decimal places. • You will be allowed to enter the room beginning at 12:25pm. Have your ID and a cleared calculator ready to show us when you enter the room and before you take your seat. • Bring: Writing Utensils, Picture ID, Calculator. All other materials should be left at the sides or front of the room during the exam. Electronic devices must be off or silent and out of sight during the exam. • Students without a picture ID will have to bring a picture ID to my office and sign a document allowing them to pick up their exam and have the grade recorded! 1 Suggestions for studying • Read lecture notes with all worked out examples. • Read examples from the textbook. (Online copy available in Webassign) • Review Online Homework problems. • Practice from the suggested homework problems. http://www.math.tamu.edu/~sdutta/math166/Math166_PracticeProblems.pdf • Review problems from the Week-in-review. http://www.math.tamu.edu/~dmanuel/math166/wir/index.html • Office Hours (week of exam): Wednesday 2:30 - 4:00 PM and Thursday 1:30 - 3:30 PM Summary of topics (* denotes important topics) 1. Section L.1 • Simple and compound statements. • Use of connectives — conjunction (∧), disjunction (∨), exclusive disjunction (∨), negation (∼). • Conversion of symbolic expressions to English statements and vice versa. * 2. Section L.2 • Construction of truth tables for symbolic expressions of upto three simple statements. * • Tautology and contradiction. 3. Section 1.1 • Understanding set operations — union, intersection, complement, disjoint, subsets. Be aware of the difference between ⊆ and ∈. • Reading and shading Venn diagrams. * • A set with n elements will have 2n subsets and 2n−1 proper subsets. * • Use of De Morgan’s laws. 4. Section 1.2 • Counting elements with two and three sets using Venn diagrams. * • Union of disjoint sets : n(A ∪ B) = n(A) + n(B). • Union rule for two sets : n(A ∪ B) = n(A) + n(B) − n(A ∩ B). * • Union rule for three sets : n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C). * 2 5. Section 1.3 • Determining the sample space of an experiment and listing outcomes of events.* • Mutually exclusive events : E ∩ F = ∅ and n(E ∪ F ) = n(E) + n(F ). • Determining union, intersection and complement of events. 6. Section 1.4 • Probability of an event : P (E) = n(E) . n(S) • Reading and writing probability distribution tables. * Events must be mutually exclusive. 7. Section 1.5 • Elementary rules : 0 ≤ P (E) ≤ 1, P (S) = 1 and P (∅) = 0. • Union rule : P (E ∪ F ) = P (E) + P (F ) − P (E ∩ F ). * For mutually exclusive events : P (E ∪ F ) = P (E) + P (F ). • Complement rule : P (E C ) = 1 − P (E). * P (E) P (E) = . C P (E ) 1 − P (E) Probability of an event with odds a : b or a/b is • Odds in favor of an event : a . a+b 8. Section 1.6 • Conditional probability that E occurs given that F has occurred is P (E ∩ F ) P (E|F ) = . * P (F ) • Product rule : P (E ∩ F ) = P (F )P (E|F ) = P (E)P (F |E). * • Drawing and using probability trees. * • Independent events : P (E|F ) = P (E) and P (E ∩ F ) = P (E)P (F ). * True for more than just two events and also for complements. 9. Section 1.7 • Bayes’ Theorem : If E1 , E2 , E3 are mutually exclusive events and F is any event in S then, P (E1 ∩ F ) P (E1 )P (F |E1 ) P (E1 |F ) = = P (F ) P (E1 )P (F |E1 ) + P (E2 )P (F |E2 ) + P (E3 )P (F |E3 ) Note: This is just an application of the conditional probability law. 3