EconBasicProbability

EconBasicProbability - Introductory Statistics Stats 210...

Info iconThis preview shows pages 1–19. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Introductory Statistics Stats 210 Spring 2007
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 So what is this all about??? Let’s assume we want to investigate the following relationships What is the relationship between student performance and class size? What is the relationship between education and wages? Do I earn more if I drink a lot? No really !
Background image of page 2
3 600 620 640 660 680 700 15 20 25 Test Scores and Student-Teacher Ratio Student-Teacher Ratio Test Scores
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 0 10 20 30 40 50 5 10 16 20 Highest Grade Attended Hourly Earning and Education Earnings per hour 12
Background image of page 4
5 The next slide is VERY, VERY, VERY, VERY, VERY, VERY, ……, VERY IMPORTANT!
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Population vs. Sample Population (random) Samples
Background image of page 6
7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 In a Nutshell…… Probability Theory Describe the whole population in probabilistic terms Finding Population Probabilities Describing Probability Distributions, i.e. Normal Distribution Statistics Use a sample of the population to learn about the population Use a sample of wages to learn about the average wage in the population Use a sample of the population to investigate the relationship between schooling and education
Background image of page 8
9 Set Theory: Experiment & Outcome Assume we are performing an experiment Experiment = An action or process whose outcome is subject to uncertainty i.e tossing a coin taking a random persons wage (height) Every experiment will have a number (set) of different outcomes Heads or Tails Virtually any positive number for wage
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 Set Theory: Sample Space We define the SAMPLE SPACE of an experiment as the set of all possible outcomes Sample space for coin toss S=[Head, Tail] The number of outcomes is finite Outcomes are discrete Sample space for wage S=[0,infinity] Infinite number of outcomes Outcomes are continuous
Background image of page 10
11 Set Theory: Event Event = is an outcome OR a set of outcomes of an experiment = subset of the sample space Let’s look at tossing a coin two times Sample Space S = [HH, TH, HT, TT] Event: AT LEAST ONE HEAD Other event: EXACTLY ONE HEAD
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
12 S Events and Outcomes = OUTCOMES = EVENTS
Background image of page 12
13 The Venn Diagram The rectangle represents the sample space and the forms two events A and B B A S
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
14 Relationships between Events Union The union of two events A and B is an event itself It is the event that either A or B or both occur Denoted by: A U B = B A S Note: Can overlap
Background image of page 14
15 Relationships between Events Intersection The intersection of two events A and B is an event itself It is the event that both A and B occur Denoted by: A B = B A S
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
16 Relationships between Events Complement The complement of an event A is also an event itself It is the event that A does not occur Denoted by: A C = Note: This can be extended to a complement of any event, i.e. (A U B) C A S A C B (A U B) C
Background image of page 16
17 Relationships between Events Disjoint Two events that are disjoint have no outcomes in common If A and B are disjoint: A B = Ø where Ø is the empty set B A S
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
18 Relationships between Events Exhaustive
Background image of page 18
Image of page 19
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 45

EconBasicProbability - Introductory Statistics Stats 210...

This preview shows document pages 1 - 19. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online