CE 303 • Midterm I • Introduction to Probability & Statistics for Civil Engineers

Introduction

Frequency Distribution

Example 1

Relative Frequency Distribution

Example 2

Cumulative Frequency Distribution

Example 3

Frequency Histogram

Measures of Central Tendancy

Example 4

Measures of Dispersion

Example 5

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

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

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

Counting 1

Counting 2

Counting 3

Counting 4

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

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

Probability Density Function - PDF

Example 1

Cumulative Distribution Function - CDF

Example 2

Expected Value

Expected Value - Example 1

Expected Value - Example 2

Variance

Variance - Example 1

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Discrete Random Variables 5

Discrete Random Variables 6

Discrete Random Variables 7

Discrete Random Variables 8

Discrete Random Variables 9

Discrete Random Variables 10

Discrete Random Variables 11

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

Discrete Joint Random Variables

Discrete Joint RV Example

Marginal PMF and CDF for Discrete Joint RV

Conditional PMF and CDF for Discrete Joint RV

Expected Value for Discrete Joint RV

Variance for Discrete Joint RV

Example 8

Conditional Expectation for Discrete Joint RV

Example 9

Example 10

Continuous Joint Random Variables

Marginal PDF and CDF for Continuous Joint RV

Conditional PDF and CDF for Continuous Joint RV

Expected Value and Variance for Continuous Joint RV

Conditional Expectation for Continuous Joint RV

Example 11

Example 12

Example 13

Covariance

Example 1 (Discrete)

Example 2 (Continuous)

Example 3 (Continuous)

Exam Like Question 1

Exam Like Question 2

Variance of Sums

Example 4

Chebyshev's Theorem

Example 5

Discrete Joint Distribution 1

Discrete Joint Distribution 2

Discrete Joint Distribution 3

Discrete Joint Distribution 4

Continuous Joint Distribution 1

Continuous Joint Distribution 2

Continuous Joint Distribution 3

Continuous Joint Distribution 4

Continuous Joint Distribution 5

Continuous Joint Distribution 6

Covariance 1

Covariance 2

Covariance 3

Covariance 4

Chebyshev's Theorem 1

Chebyshev's Theorem 2