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1 General Info Lecture 1: Classroom: Physics 259 Time: Mondays, Wednesdays 2:50 pm - 4:05 pm Statistics 10 Colin Rundel January 11, 2012 Professor: Office: Teaching Assistants: Course Website: Colin Rundel Old Chemistry 211E colin.rundel@stat.duke.edu Yun Yang - yy84@stat.duke.edu stat.duke.edu/ courses/ Spring12/ sta104.1 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Required materials Webpage stat.duke.edu/ courses/ Spring12/ sta104.1 All announcements and assignments will be posted on the website. Lecture slides will be posted by noon the day of the lecture. Textbook: Software: Probability, Pitman Springer, 1 st Edition 7 th Printing, 1993 ISBN: RStudio Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17

2 Office Hours Grading Professor: Tuesdays 3:00 pm - 5:00 pm Also after class or by appointment. TAs: Sunday - Thursday 4pm - 9pm starting next week at the SECC (Old Chemistry 211A) You are highly encouraged to stop by with any questions or comments about the class. Note that most homework assignments will be due on Wednesday. I recommend that you attempt all homework problems over the weekend so that you can come to office hours with questions. Homework 30% Midterm 1 20% Midterm 2 20% Final 30% Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Homework Exams Questions from the book and the occasional computational question. Due at the beginning of class on the due date. Graded out of 100 Late work policy: Late but during class: -10 points After class on due date: -20 points Next day: no credit Show all your work to receive full credit. Encouraged to work with others, but you must turn in your own work. Lowest homework score will be dropped. Midterm 1: Wednesday, February 15th Midterm 2: Wednesday, March 21st Final: Wednesday, May 2nd, 7:00-10:00 pm (Cumulative) No make-up exams will be given. Calculators will not be allowed. cheat sheet - you can bring one sheet ( ) of notes prepared by you (no photocopies) to the exam. You may use both sides of the sheet. You cannot pass the class if you do not take the final. Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17

3 Policies I will regularly send announcements by , so make sure to check your daily. While is the quickest way to reach me outside of class, note that it is much more efficient to answer most statistical questions in person. There will not be make-ups for any of the homework or exams. All regrade requests on homework assignments and exams should be discussed with the professor within one week of receiving your grade. There will be no grade changes after the final exam. Academic Integrity & Duke Community Standard Excused absences Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 What does it MEAN to say that: The probability of Point Up for a thumbtack is P(U) = 1/2? The probability of Heads for a coin is P(H) = 1/2? The probability that Apple stock rises $1 today is P(+) = 1/2? Interpretations: Symmetry: If there are k equally-likely outcomes, each has P(E) = 1/k Frequency: If you can repeat an experiment indefinitely, [#E] P(E) = lim n n Belief: If you are indifferent between winning $1 if E occurs or winning $1 if you draw a blue chip from a box with 100 p blue chips, rest red, P(E) = p Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Terminology Outcome space (Ω) - set of all possible outcomes (ω). Examples: 3 coin tosses {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} 3 coin tosses (binary) {0,1,2,3,4,5,6,7} One die roll {1,2,3,4,5,6} Sum of two rolls {2,3,...,11,12} Concat two rolls {11,12,...,16,21,22,...,66} Seconds waiting for bus [0, ) Event (E) - subset of Ω (E Ω) that might happen, or might not Examples: 2 heads {HHT, HTH, THH} Even number {2,4,6} < 2 minutes [0, 120) Impossible event ( ) - empty set Random Variable (X ) - a value that depends somehow on chance Examples: # of heads {3, 2, 2, 1, 2, 1, 1, 0} # flips until heads {3, 2, 1, 1, 0, 0, 0, 0} 2ˆdie {2, 4, 8, 16, 32, 64} Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17

4 Set Operations Rules of Probability (1) Non-negative: P(E) >= 0 Intersection E and F, EF, E F Union E or F, E F Complement not E, E c Disjoint EF = Difference E\F = E F c Symmetric Difference E F = (E F c ) (E c F ) (2) Addition: (2) Countable Addition: (3) Total one: P(E F ) = P(E) + P(F ) if EF = ( ) P E i = i=1 P(E i ) if E i E j = for i j i=1 P(Ω) = 1 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Events Examples For each of the following examples describe Ω and a rule for computing P(E) for every event E in Ω If there are n possible outcomes in Ω then how many possible events are there? 1 Toss a thumbtack that falls Up with probability 52% 2 Sum of the roll of two fair dice 3 Toss a coin until first Head What if E = Even # of tails precede 1st head Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17

5 Useful Identities Useful Identities, cont. Commutativity & Associativity: A B = B A (A B) C = A (B C) (A B) C = (A C) (B C) A B = B A (A B) C = A (B C) *Think of union as addition and intersection as multiplication: (A + B)C = AC + BC DeMorgan s Rules: not (A and B) = (not A) or (not B) not (A or B) = (not A) and (not B) Complement Rule: P(not A) = P(A c ) = 1 P(A) Difference Rule: P(B and not A) = P(BA c ) = P(B) P(A) if A B Inclusion-Exclusion: P(A B) = P(A) + P(B) P(AB) Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17 Statistics 10 (Colin Rundel) Lecture 1: January 11, / 17