Stat310
Probability and Statistics


      Hadley Wickham
1. Two important facts

2. Syllabus

3. Introduction to probability

4. Definitions & properties

5. Probability as a set f...
HE LLO
 my name is




Hadley
had.co.nz/stat310
Introduction to
  probability
What is probability?

• Mathematical machinery to deal with
  uncertain events


• What does uncertain mean?
• What is an ...
Random experiment

An observation that is uncertain:
we don’t know ahead of time what the
answer will be (pretty common!)
...
Sample space

A set containing all possible outcomes
from an experiment. Often called S.
An event is a subset of the sampl...
Random experiments
• The sequence of dice • The length of time until
  rolls until you get a six your next sneeze
• The we...
Your turn
• How could you classify these different
  experiments based on the sample
  space?
• Think (2 min)
• Pair (3 mi...
Contents

• Numeric (quantitative)
• Non-numeric (qualitative)


• Will need to put both on a common
  framework (next wee...
Cardinality
• Small (< 10)
• Large, but finite
• Countably infinite
• Uncountably infinite
• We will follow this order as we ...
Events
• An event is a subset of the sample
  space
• Set of all possible events is the
  power set of S


• Examples
Set algebra
• Intersection and union are:
  • Commutative (order from left to right doesn’t matter)
  • Associative (order...
Terminology

• Mutually exclusive
• Exhaustive
• Mutually exclude + exhaustive =
  partition
How do we define
      uncertainty?
• Associate a probability with each
  element of the sample space.
• Defined by the func...
Properties of pmf
• What are some properties that the pmf
  must have? (Use your common sense)
• For example, take the ran...
Properties of pmf

• Basic (as defined by book)
• Important derived properties
  (T 1.2-1 - T1.2-6)
• Strategies of T1.2-3 ...
Upcoming SlideShare
Loading in...5
×

Introduction

555

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
555
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Introduction

  1. 1. Stat310 Probability and Statistics Hadley Wickham
  2. 2. 1. Two important facts 2. Syllabus 3. Introduction to probability 4. Definitions & properties 5. Probability as a set function
  3. 3. HE LLO my name is Hadley
  4. 4. had.co.nz/stat310
  5. 5. Introduction to probability
  6. 6. What is probability? • Mathematical machinery to deal with uncertain events • What does uncertain mean? • What is an event?
  7. 7. Random experiment An observation that is uncertain: we don’t know ahead of time what the answer will be (pretty common!) Ideally we want the experiment to be repeatable under exactly the same initial conditions (pretty rare!)
  8. 8. Sample space A set containing all possible outcomes from an experiment. Often called S. An event is a subset of the sample space
  9. 9. Random experiments • The sequence of dice • The length of time until rolls until you get a six your next sneeze • The weather tomorrow • My age • The next hand in a • The result of a coin flip poker game • The weight of a bag of • Your final grade in this m&m’s class • The sex of a randomly • The next President of selected member of the United States class
  10. 10. Your turn • How could you classify these different experiments based on the sample space? • Think (2 min) • Pair (3 min) • Square (3 min) • Share (2 min)
  11. 11. Contents • Numeric (quantitative) • Non-numeric (qualitative) • Will need to put both on a common framework (next week)
  12. 12. Cardinality • Small (< 10) • Large, but finite • Countably infinite • Uncountably infinite • We will follow this order as we develop increasingly complex mathematical tools
  13. 13. Events • An event is a subset of the sample space • Set of all possible events is the power set of S • Examples
  14. 14. Set algebra • Intersection and union are: • Commutative (order from left to right doesn’t matter) • Associative (order of operation doesn’t matter) • Distributive (can expand brackets) • You should be familiar with everything on: http://en.wikipedia.org/wiki/Algebra_of_sets
  15. 15. Terminology • Mutually exclusive • Exhaustive • Mutually exclude + exhaustive = partition
  16. 16. How do we define uncertainty? • Associate a probability with each element of the sample space. • Defined by the function probability mass function (pmf). • The probability is the long run relative frequency
  17. 17. Properties of pmf • What are some properties that the pmf must have? (Use your common sense) • For example, take the random experiment of flipping two coins and observing whether they come up heads or tails. How are the probabilities of the different events related?
  18. 18. Properties of pmf • Basic (as defined by book) • Important derived properties (T 1.2-1 - T1.2-6) • Strategies of T1.2-3 and T1.2-5 particularly important
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×