Probability and Statistics 10 | The Cheatsheet for Distributions, the Statistical Inference, and…
Probability and Statistics 10 | The Cheatsheet for Distributions, the Statistical Inference, and the Confidence Interval
- Discrete Distribution
(1) Binomial Distribution
- Notation
- PMF
- Mean
- Variance
- Graph
(2) Geometric Distribution I
- Concept
Random variable X is the number of failures before the 1st success
- Notation
- PMF
- Mean
- Variance
- Graph
(3) Geometric Distribution II
- Concept
Random variable X is the trial on which the 1st success occurs.
- Notation
- PMF
- Mean
- Variance
- Graph
(4) Hypergeometric Distribution
- Concept
Random variable X is the number of successes in the sample.
- Notation
- PMF
- Mean
- Variance
- Graph
(5) Poisson Distribution
- Notation
- PMF
- Mean
- Variance
- Graph
2. Continuous Distributions
(1) Exponential Distribution
- Notation
- Mean
- Variance
- Graph
(2) Normal Distribution
- Notation
- Mean
- Variance
- Graph
(3) Student’s t Distribution
- Notation
- Mean
- Variance
- Graph
(4) Chi-Square Distribution
- Notation
- Mean
- Variance
- Graph
(5) F Distribution
Note: F distribution is very dirty and ugly, so we are not going to state it here, just leave it for future discussions (if possible).
3. Statistical Inference
(1) One-Sample Mean with σ known: Z-Test
(2) One-Sample Mean with σ unknown: T-Test
(3) Two-Sample Difference of Means with σ1 = σ2: Paired T-Test with Pooled Variance
(4) Two-Sample Difference of Means with σ1 ≠ σ2: Paired T-Test with Satterthwaite Degree of Freedom
(5) One-Sample Proportion: Z-Test (De Moivre-La Place Theorem)
(6) Two-Sample Difference of Proportions: Z-Test (De Moivre-La Place Theorem)
(7) One-Sample Correlation Coefficient: Z-Test with the Fisher Transformation
(8) Two-Sample Difference of Correlation Coefficient: Z-Test with the Fisher Transformation
(9) One-Sample Variance: χ² Test
(10) Two-Sample Variances Ratio: F-Test
4. Confidence Interval
(1) One-Sample Mean with σ known
(2) One-Sample Mean with σ unknown
(3) Two-Sample Difference of Means with σ1 = σ2
(4) Two-Sample Difference of Means with σ1 ≠ σ2
(5) One-Sample Proportion
(6) Two-Sample Difference of Proportions (Note this is different from the hypothesis test)
(7) One-Sample Correlation Coefficient
(8) Two-Sample Difference of Correlation Coefficient
(9) One-Sample Variance
(10) Two-Sample Variances Ratio
5. Statistical Distribution Table
(1) Standard Normal Distribution Table
(2) Student’s t Distribution Table
(3) Chi-Square Distribution Table
(4) F Distribution Table