Stats & Probability

Introduction to Statistics and Probability

Much of the material that is currently on this blog is going to be moved to https://mathsatstatslab.wordpress.com/ very soon.

1. Introduction to Statistics

  1. Types of data
  2. Variables (Notes)

2. Introduction to Probability

  1. Sample Spaces
  2. Basic Probability Distribution
  3. Rules of Probability
  4. Independent Events
  5. Conditional Probability [6:45]
  6. The Addition Rule for Probability
  7. Probability Trees (Example 1)
  8. Probability Trees (Example 2)

3. Techniques for Counting

  1. Venn Diagrams
  2. Sampling with/out Replacement
  3. Choose Operator (Binomial Coefficients)
  4. Choose Operator Exercises  [9:16]
  5. Permutations

4. Descriptive Statistics

  1. Measures of Centrality
  2. Computing the Median of a Data Set.
  3. Introduction to Dispersion
  4. Measures of Dispersion
  5. Box plots (Box and Whisker Plots)
  6. Five Number summary, IQR, Fences, Midhinge and Trimean [6:51]

5. Random Variables

  1. Introduction to Probability Distributions
  2. Expected Values and Probability
  3. Joint and Marginal Distributions
  4. Probability Mass functions

6. Discrete Probability Distributions

  1. The binomial distribution
  2. The geometric distribution
  3. The Poisson distribution

7. Continuous Probability Distributions

  1. Interval Probabilities for Continuous Random Variables.
  2. The Uniform distribution
  3. Exponential Distribution [15:00]
  4. Other important Continous probability distributions (Notes)

8. Normal Distribution

  1. Standardization and Z-scores
  2. Using Statistical Tables
  3. The Complement and Symmetry Rules
  4. Interval Probability (example)
  5. Asssumption of Normality (Notes)

9. Introduction to Statistical Inference

  1. Sampling (Notes)
  2. Sampling Distributions and the Central Limit Theorem
  3. Standard Error for the Mean
  4. Introduction to Confidence Intervals (Notes)
  5. Hypothesis testing
  6. Type I and II Error (Notes)

9A. Commonly used Hypothesis Tests

  •    Hypothesis test for the mean of a single sample
  •    Hypothesis test for the mean of two independent samples
  •    Hypothesis test for the proportion of a single group
  •    Hypothesis test for the proportions of two independent samples
  •    Other Inference Procedures
10. Statistical Procedures for simple samples
  1. One-tailed tests for means
  2. Confidence Intervals for Proportions
11. Statistical Procedures for two indepedent samples
  1. Assumption of Equal Variance (The F-test)
12. Non-Parametric Statistics
  1. Introduction to Non-Parametric Statistics (Notes)
  2. Non-Parametric Statistical Measures
13. Goodness of Fit tests
  1. Chi-Square Univariate Test
  2. Chi-Square Goodness of Test
14 Bivariate Data
  1. Correlation
  2. Spearman’s Correlation (notes)
  3. Simple Linear Regression

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