• Explain the key concepts and principles of probability theory and its relationship to statistics and data science
• Use basic rules of probability, such as addition, multiplication, conditional, Bayes’, and independence to calculate probabilities
• Use probability distributions, such as binomial, normal, Poisson, exponential, uniform, etc., to model uncertain events and outcomes
• Use expected value, variance, standard deviation, coefficient of variation, etc., to measure risk and uncertainty
• Use Monte Carlo simulations to generate and analyze random data
• Apply probability theory to real-world problems and case studies from various domains, such as finance, engineering, health, etc.

This course is designed for professionals who want to learn how to use probability theory to understand and model uncertainty. It is suitable for professionals from any industry, function, or region who are interested in or responsible for data analysis in their organization or personally. It is also suitable for those who are currently taking a basic data science course or have already finished a data science course and are searching for a practical probability theory project course.

Day One:

Introduction to Probability Theory

• What is probability theory and why does it matter for data analysis?
• Probability spaces, events, and axioms
• Basic rules of probability
• Conditional probability and Bayes’ theorem
• Independence and dependence

Day Two:

Probability Distributions

• What are probability distributions and how to use them for modeling uncertainty?
• Discrete and continuous random variables
• Common discrete distributions: binomial, geometric, Poisson, etc.
• Common continuous distributions: normal, exponential, uniform, etc.
• Joint, marginal, and conditional distributions

Day Three:

Risk and Uncertainty Measures

• What are risk and uncertainty measures and how to use them for evaluating uncertainty?
• Expected value and variance
• Standard deviation and coefficient of variation
• Moments and moment generating functions
• Skewness and kurtosis

Day Four:

Monte Carlo Simulations

• What are Monte Carlo simulations and how to use them for generating and analyzing random data?
• Random number generation
• Sampling methods
• Simulation techniques
• Simulation examples

Day Five:

Probability Theory Applications

• How to apply probability theory to real-world problems and case studies from various domains?
• Probability theory in finance: portfolio optimization, option pricing, risk management, etc.
• Probability theory in engineering: reliability analysis, quality control, system design, etc.
• Probability theory in health: epidemiology, diagnosis, testing, treatment, etc.

To enhance learning and practical application of concepts, the training course will use a combination of interactive lectures, case studies, group discussions, practical exercises, and real-world examples. Participants will also get the chance to collaborate on group projects and create action plans adapted to the needs of their respective organizations.