1
Preface
2
Set Theory and Probabilities
2.1
Terminologies
2.2
Types of Events
2.3
Relationships between Events
2.4
Algebra of Events
2.5
Axioms of Probabilities
2.6
Properties of Probabilities
2.7
A Simple Example
2.8
Determining Probabilities Systematically
2.9
Permutation and Combination
2.10
Conditional probability
2.11
Independence
3
Random Variable
3.1
Random variable and events
3.2
Probability mass function (pmf)
3.3
Cumulative distribution function (cdf)
3.4
Steps to obtain cdf for discrete distributions
3.5
Steps to obtain pmf from cdf
3.6
Expected value and Variance
4
Discrete Distributions
4.1
Bernoulli distribution
4.2
Binomial distribution
4.3
Geometric distribution
4.4
Negative Binomial Distribution
4.5
Hypergeometric Distribution
4.6
Poisson distribution
5
Continuous Distributions
5.1
Probability Density Function (pdf)
5.2
Cumulative Distribution Function (cdf)
5.3
Expected Values and Variance
5.4
Uniform Distribution
5.5
Normal Distribution
5.6
Exponential Distribution
5.7
Gamma Distribution
5.8
Chi-squared Distribution
5.9
Relationship between Poisson, Exponential and Gamma Distributions
5.9.1
Postulates of Poisson Process
5.10
Beta Distribution
6
Joint Distributions and Correlation
6.1
Two Discrete rv
6.2
Marginal Distribution
6.3
Two Continuous rv
6.4
Independence
6.5
Conditional Distributions
6.6
Expected Values
6.7
Covariance
6.8
Correlation
7
Point Estimation and Sampling Distribution
7.1
Parameter
7.2
Statistic
7.3
Sampling Distributions
7.4
Sampling Distributions of Normal Populations
7.5
Other Sampling Distributions
8
Interval Estimation
8.1
Review
8.2
Assumptions
8.3
CI for Population Mean
8.4
CIs of Other Confidence Level
8.5
One-sided CIs
8.6
CI for Population Mean with unknown
\(\sigma\)
8.7
CIs for Large
\(n\)
8.8
Interpretation of CI
8.9
Summary
8.10
CIs for other Parameters
8.10.1
CI for Population Proportion
8.10.2
CIs for Population Variance
9
Hypothesis Testing on One Sample
9.1
Basic Framework
9.1.1
Formulation of Hypotheses
9.1.2
Test Procedure and P-values
9.1.3
Significance Level
9.1.4
Rejection Region
9.1.5
P-values
9.1.6
Type I and Type II errors
9.2
Tests on Population Mean
9.2.1
Z-tests
9.2.2
T-tests
9.3
One-sided Tests
9.3.1
One-sided z-tests
9.3.2
One-sided t-tests
9.4
Type II Error and Power
9.4.1
Type II Error
9.4.2
Power
9.5
Summary of Tests on Population mean
9.5.1
Z-test
9.5.2
T-test
9.5.3
Large sample-test
10
Hypothesis Testing on Two Samples
10.1
Z-test of two population means (two-sided)
10.2
Z-test of two population means (right-sided)
10.3
Z-test of two population means (left-sided)
10.4
Generalization to
\(H_0: \mu_1-\mu_2=\Delta\)
10.5
Summary of z-test for two population means
10.6
T-tests between two population means
10.7
Summary of t-test for two population means
10.8
Hypothesis Testing and Confidence Intervals
11
Appendix
11.1
Common discrete distributions
11.2
Common continuous distributions
11.3
Table of standard normal distribution
11.3.1
Confidence Interval Critical Values,
\(z_{α/2}\)
11.3.2
Hypothesis Testing Critical Values
11.4
Table of
\(t\)
-critical values
References
Handbook of Probability and Statistics for Science and Engineering
References
Devore, Jay L. 2016.
Probability and Statistics for Engineering and the Sciences
. 9th ed. Cengage.
Ross, Sheldon M. 1987.
Introduction to Probability and Statistics for Engineers and the Scientists
. John Wiley & Sons.