Introduction to probability

摘要: Introduction to Probability - Lecture 8: Basic Inequalities and Law of Large Numbers Page 1 Introduction to Probability Lecture 8: Basic Inequalities and Law of Large Numbers Mateja Jamnik, Thomas Sauerwald University of Cambridge, Department of Computer Science and Technology email: {mateja.jamnik,thomas.sauerwald}@cl.cam.ac.uk Easter 2023 Page 2 Outline Introduction Markov’s Inequality and Chebyshev’s Inequality Weak Law of Large Numbers Intro to Probability Introduction 2 Page 3 Intro: Sum of Independent (Uniform) Random Variables Let X1 and X2 be two independent random variables, both uniformly distributed on [0, 1]. How does the probability density of X1 + X2 look like? What happens for X1 + X2 + X3 etc.? Answer Example 1 Intro to Probability Introduction 3 Page 4 Intro: Sum of Independent (Uniform) Random Variables Let X1 and X2 be two independent random variables, both uniformly …