ECON 221 • Midterm • Introduction to Probability and Statistics I

Introduction

Frequency Distribution

Example 1

Relative Frequency Distribution

Example 2

Cumulative Frequency Distribution

Example 3

Frequency Histogram

Definition of O-give

Example 4

Example 5

Example 6

Measures of Central Tendancy

Example 7

Measures of Dispersion

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Chebyshev's Inequality

Example 14

Understanding Data 1

Understanding Data 2

Understanding Data 3

Understanding Data 4

Sample Space and Events

Probability

Axioms of Probability

Some Rules

Coin Example

Dice Example

Card Example 1

Card Example 2

Ball Example

Set Example

Birthday Example

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

Counting 1 - Product Rule

Counting 2 - Product Rule

Counting 3 - Product Rule

Counting 4 - Product Rule

Counting 5 - Permutations

Counting 6 - Permutations

Counting 7 - Permutations

Counting 8 - Permutations

Counting 9 - Permutations

Counting 10 - Permutations

Counting 11 - Circular Permutation

Counting 12 - Repeated Permutation

Counting 13 - Combinations

Conditioning Events

Total Probability Rule

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Bayes' Rule

Bayes' Rule Example 1

Bayes' Rule Example 2

Independence

Independence Example 1

Independence Example 2

Conditional Probability and Independence 1

Conditional Probability and Independence 2

Conditional Probability and Independence 3

Conditional Probability and Independence 4

Conditional Probability and Independence 5

Conditional Probability and Independence 6

Conditional Probability and Independence 7

Conditional Probability and Independence 8

Conditional Probability and Independence 9

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

Bayes' Rule 6

Bayes' Rule 7

Bayes' Rule 8

Bayes' Rule 9

Random Variables

Probability Mass Function

PMF Example 1

PMF Example 2

Cumulative Distribution Function

CDF Example 1

Expected Value

Expected Value Example 1

Expected Value Example 2

Variance

Variance Example 1

Variance Example 2

Discrete Random Variable 1

Discrete Random Variable 2

Discrete Random Variable 3

Discrete Random Variable 4

Discrete Random Variable 5

Discrete Random Variable 6 - Expected Value

Discrete Random Variable 7 - Expected Value

Discrete Random Variable 8 - Variance

Discrete Random Variable 9 - Expected Value

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Understanding Data 1

Understanding Data 2

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

Counting, Combination and Permutations 1

Counting, Combination and Permutations 2

Counting, Combination and Permutations 3

Counting, Combination and Permutations 4

Conditional Probability 1

Conditional Probability 2

Conditional Probability 3

Conditional Probability 4

Conditional Probability 5

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Independence 1

Independence 2

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Discrete Random Variables 5