In this module, you will be introduced to the basics of set theory and probability. You will learn about the axioms of probability and conditional probability. You will understand the difference between dependent and independent events. You will also explore one of the important concepts in data science (machine learning), i.e., Bayes’ formula.

In this module, you will learn how to generalize the events and their outcomes by a variable, that is, a random variable. You will explore types of random variables. You will gain an understanding of a mathematical expectation. You will further learn about the procedure to find the mean and variance using mathematical expectation. This module also covers the probability distribution function.

In this module, you will learn about various discrete probability distributions. You will be able to understand Binomial and probability distributions with their corresponding probability distribution functions. You will also learn about the mean and variance of Binomial and Poisson distributions.

In this module, you will learn continuous probability distributions in general and normal/Gaussian distribution in particular. You will gain an understanding of the mean and variance of normal distribution. You will also explore the standard normal distribution with the help of normal distribution tables. Furthermore, you will be introduced to other continuous distributions like uniform distribution and Gamma distribution.

In this module, you will learn the importance of sampling and various sampling techniques. You will be introduced to sampling distribution, which plays an important role in understanding data. You will learn about the central limit theorem that will help you understand the use of normal distribution in many situations. Then, you will be introduced to the next step in sampling, that is, estimation. You will also gain an understanding of the t- and chi-square distribution.

In this module, you will learn to identify and validate hypotheses using various statistical techniques, including sampling. You'll cover forming hypotheses, type I and type II errors, and their impact on test significance and power. The module also explores hypothesis testing with proportions, handling both large and small samples, and validating multiple proportions using the chi-square test.

In this module, you will learn how to understand the relation between two variables in the given data and the types of correlation that exists between two variables. You will be able to find coefficient correlation to establish this. The module answers why it is important to use the given data for future prediction for which regression is helpful. This module will also help you understand simple linear regression with the help of normal equations and their matrix form.

In this module, you will learn how to predict when nonlinearity exists in the data. With the learnings from simple linear regression, you will understand the regression for prediction when nonlinearity exists in the data. Furthermore, in nonlinear regression, you will focus on polynomial regression.