8/21/2017

About the Instrcutor

Syllabus

Course Info

Grading

Grades

  • There will be NO curving of individual exam grades
  • A student must earn a minimum of 60% on AT LEAST ONE of the 3 exams in order to pass this class.
letter_grade percent
A 90-100
B 80-89
C 70-79
D 60-69
F below 60

Quiz

  • 8 are scheduled
  • Close book and close notes
  • The lowest quiz will be dropped
  • Make-up quiz
    • Official documented University business or a documented illness
    • Contact your instructor at least TWO DAYS in advance

Homework

  • 5 assignments
  • Due at the begining of class
  • Late homework will NOT be accepted
  • Must be handwritten or typed using mathematical notation.
  • Each homework is worth 25 points, NO homeworks are dropped.

Exams

  • Two evening exams from 8:00 – 9:30 pm
    • Tueday 9/26/17
    • Thursday 11/2/17
  • A final exam, during the day during final exam week
  • Close book and close notes
  • Items allowed
    • pencils
    • erasers
    • a scientific calculator (must not have capability to do integration),
    • one-page cheat sheet for mid-terms and two-page for the final,
  • Show a photo ID to your instructor

Cheat sheet

  • 8 1⁄2 \(\times\) 11
  • Handwritten in your own writing
  • Both sides
  • Handing in your cheat sheet at the end of the exam is required
  • Use of printed or photocopied material on a cheat sheet is prohibited and considered cheating in this course

Emergency

  • If you hear a fire alarm inside, proceed outside
  • If you hear a siren outside, proceed inside
  • Fire emergency:
    • immediately suspend class, evacuate the building, and proceed outdoors
    • do not use the elevator
    • meet outside by fountain near John Purdue’s grave
  • Tornado warning/servere weather event
    • suspend class and shelter in interior hallway on \(1_{st}\) floor
  • SHELTER IN PLACE
    • suspend class and shelter in the classroom
    • shutting the door and turning off the lights

Introduction to Probability and Set Theory

Probability Theory

  • Probability theory is the study of randomness and all things associated with randomness

Key concepts

  • Random Experiment: an action whose outcome cannot be predicted with certainty beforehand - drawing a card
    • rolling a die
    • flipping a coin
  • Potential Outcome: One specific result from a random experiment

  • Event: a collection of some outcomes
    • empty set \(\Phi\): no outcomes
    • sample space \(S\): consists of all outcomes

Examples

  • flipping a coin
    • potential outcomes
    • sample space
    • events
      • head
  • roll a regular dice
    • potential outcomes
    • sample space
    • events
      • greater than 3
      • get an odd number
      • greater than 7

Subset

  • Event A is a subset of event B, written \(A \subset B\), if every outcome in A is also an outcome in B

  • roll a dice:
    • A: the roll is 2
    • B: the roll is event number

Probability of Events

  • Probability: the proportion of times the event occurs in independent repetitions of the random experiment in the long run
  • \(P(E) = \frac{|E|}{n}\)
  • The probability of event E is the number of times an outcome in E occurs divided by the number of experiment repetitions

Equally likely framework

  • Any individual outcome in \(S\) is equally likely to occur
  • \(P(E) = \frac{|E|}{|S|}\)
  • If all outcomes are equally likely, then then probability of event E is the number of outcomes in E divided by the number of outcomes in the sample space

Roll two 6-sided dice

  1. \(P\)(the sum is 5)
  2. \(P\)(the rolls are the same)
  3. \(P\)(the sum is even)