Probability and Statistics 10 | The Cheatsheet for Distributions, the Statistical Inference, and…

Series: Probability and Statistics

Probability and Statistics 10 | The Cheatsheet for Distributions, the Statistical Inference, and the Confidence Interval

  1. 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
  • PDF
  • Mean
  • Variance
  • Graph

(2) Normal Distribution

  • Notation
  • PDF
  • Mean
  • Variance
  • Graph

(3) Student’s t Distribution

  • Notation
  • PDF
  • Mean
  • Variance
  • Graph

(4) Chi-Square Distribution

  • Notation
  • PDF
  • 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