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Probability Foundations for Data Science

Probability Foundations for Data Science

4h 52mIntermediate2024-08-26

Authors

Megan Silvey

Megan Silvey

Course details

A solid understanding of mathematics, especially probability, is crucial for successful data science endeavors. This course covers the essentials of probability with clear explanations, common equations, simple examples, and real-life applications. First, a review of the basics, like random variables, are covered along with the core distribution types: discrete, continuous, cumulative, and joint. Then, expectation and variance are explored, including conditional expectation, standard deviation, covariance, and correlation. Next, several standard discrete distributions and continuous distributions are detailed, followed by popular limit theorems and approximations. After that, Bayesian probability is explored, including how it differs from frequentist probability. Finally, a few common estimation methods are covered. Join Megan Silvey as she takes you through each section, imparting her expertise to you.

Skills covered

StatisticsData EngineeringData AnalysisData ScienceBusiness Analysis and StrategyBusiness Software and ToolsOne-Off

Concepts

0. Introduction

  • 01 - Introduction to probability
  • 02 - What you should know
  • 03 - Calculus review - Limits and derivatives
  • 04 - Calculus review - Integrals

1. Probability Fundamentals

  • 05 - Basic probability
  • 06 - Random variables
  • 07 - Discrete distributions
  • 08 - Continuous distributions
  • 09 - Cumulative distributions
  • 10 - Joint distributions

2. Expectation and Variance

  • 11 - Expectation
  • 12 - Expectation of discrete random variables
  • 13 - Expectation of continuous random variables
  • 14 - Conditional expectation
  • 15 - Variance and standard deviation
  • 16 - Discrete vs. continuous dispersion
  • 17 - Covariance
  • 18 - Correlation

3. Discrete Distributions

  • 19 - Discrete distributions - Introduction
  • 20 - Discrete uniform distribution
  • 21 - Bernoulli distribution
  • 22 - Binomial distribution
  • 23 - Negative binomial distribution
  • 24 - Geometric distribution
  • 25 - Hypergeometric distribution
  • 26 - Poisson distribution

4. Continuous Distributions

  • 27 - Continuous distributions - Introduction
  • 28 - Uniform distribution
  • 29 - Exponential distribution
  • 30 - Gamma distribution
  • 31 - Pareto distribution
  • 32 - Standard normal distribution
  • 33 - Normal distribution
  • 34 - Chi-squared distribution
  • 35 - t distribution
  • 36 - F distribution

5. Limit Theorems and Approximations

  • 37 - Chebyshev's inequality
  • 38 - Weak Law of Large Numbers
  • 39 - Strong Law of Large Numbers
  • 40 - Monte Carlo Approximation
  • 41 - Central Limit theorem
  • 42 - Normal approximation of the binomial distribution

6. Bayesian Probability

  • 43 - Bayesian probability - History
  • 44 - Bayes' theorem
  • 45 - Bayesian inference
  • 46 - Frequentist vs. Bayesian probability
  • 47 - Bayesian applications

7. Estimation

  • 48 - Maximum likelihood estimation (MLE)
  • 49 - MLE for binomial distribution
  • 50 - MLE for exponential distribution
  • 51 - MLE for normal distribution
  • 52 - Maximum a posteriori estimation (MAP)
  • 53 - MAP applications

Conclusion

  • 54 - Next steps

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