F71DX - Probability and Statistics for Data Science

Aims

This course provides a comprehensive introduction to probability and statistics, tailored for students with no prior training in these areas. The focus is on understanding fundamental concepts and applying them to real-world data science problems.

Syllabus

1. Introduction to Probability (1.1 Importance of probability in data science. , 1.2 Basic definitions: experiment, outcome, event, sample space. , 1.3 Classical probability, empirical probability, and subjective probability., 1.4 Conditional probability and its properties. , 1.5 Independence of events. , 1.6 Bayes' Theorem and its applications.)

2. Introduction to Statistics and Data Summary tools (2.1 Importance of statistics in data science. , 2.2 Descriptive statistics: measures of central tendency and dispersion. , 2.3 Graphical representation of data: histograms, box plots, scatter plots. , 2.4 Concepts of population and sample. , 2.5 Sampling methods and techniques. , 2.6 Point estimation and properties of estimators.)

3. Random Variables and Probability Distributions (3.1 Introduction to random variables discrete and continuous. , 3.2 Probability mass functions PMF and probability density functions PDF. , 3.3 Cumulative distribution functions CDF. , 3.4 Discrete distributions: Binomial, Poisson, Geometric. , 3.5 Continuous distributions: Uniform, Normal, Exponential. , 3.6 Properties and applications of these distributions.)

4. Mathematical Methods (4.1 Expected value mean of a random variable. , 4.2 Variance and standard deviation. , 4.3 Properties and applications of expectation and variance. , 4.4 Basics of hypothesis testing. , 4.5 Null and alternative hypotheses. , 4.6 Type I and Type II errors, significance level, p-value.)

5. Core methods for Data Science (5.1 Constructing and interpreting confidence intervals. , 5.2 Introduction to simple linear regression. , 5.3 Least squares estimation and correlation. , 5.4 Multiple linear regression. , 5.5 Analysis of variance ANOVA. , 5.6 Introduction to logistic regression and classification.)