An Invitation to Probability Theory

Dive into the fundamentals of probability with practical insights

Probability theory underpins critical decisions in data science, finance, actuarial science, and beyond.

On this eight-week course from the University of Padova, you’ll explore key probability concepts, distributions, and theorems, equipping you with the skills to tackle uncertainty confidently.

Explore foundational concepts of probability

You’ll begin with the fundamentals of probability spaces, covering sample spaces, events, and probability measures.

Next, you’ll learn combinatorial calculus, conditional probability, and Bayes’ Theorem, applying these concepts to real-world scenarios, such as medical decision-making.

Master discrete and continuous random variables

You’ll dive into discrete and continuous random variables, unpacking their key properties, like distributions, expectations, and variances.

Through hands-on exercises, you’ll also apply key probability distributions such as Binomial, Poisson, and Gaussian.

Uncover advanced theorems and applications

Finally, you’ll move on to more advanced probability topics. You’ll break down joint densities, the Law of Large Numbers, and the Central Limit Theorem. Discover Monte Carlo methods for problem-solving and use limit theorems to make accurate predictions.

By the end of this course, you’ll walk away with some of the basic tools to apply probability theory to real-world challenges with confidence.

This course is designed for professionals and learners eager to deepen their understanding of probability theory. Ideal for those in finance, actuarial science, data science, research, and academia, it also provides valuable preparation for advanced studies in related fields.

This course is designed for professionals and learners eager to deepen their understanding of probability theory. Ideal for those in finance, actuarial science, data science, research, and academia, it also provides valuable preparation for advanced studies in related fields.

• Explain key concepts in probability theory such as probability spaces, sample spaces and probability density functions.
• Explain the principles of conditional probability and event independence.
• Calculate probabilities using combinatorial calculus the law of total probability
• Calculate expected values, variances, and covariances for discrete and continuous random variables.
• Apply the central limit theorem and the law of large numbers to approximate sums of independent random variables