Gravner, Janko - Department of Mathematics, University of California, Davis

• Patterns in coin tosses Assume that you repeatedly toss a coin, with heads outcome represented by 1 and
• Replication in one-dimensional cellular automata Janko Gravner
• RANDOM GROWTH MODELS WITH POLYGONAL SHAPES Janko Gravner
• 13 MARKOV CHAINS: CLASSIFICATION OF STATES 151 13 Markov Chains: Classification of States
• 7 JOINT DISTRIBUTIONS AND INDEPENDENCE 81 Interlude: Practice Midterm 2
• 18 POISSON PROCESS 208 Interlude: Practice Final
• 9 CONVERGENCE IN PROBABILITY 111 9 Convergence in probability
• 12 MARKOV CHAINS: INTRODUCTION 143 12 Markov Chains: Introduction
• Replication in one-dimensional cellular automata Janko Gravner
• 8 MORE ON EXPECTATION AND LIMIT THEOREMS 103 Interlude: Practice Final
• 6 CONTINUOUS RANDOM VARIABLES 58 6 Continuous Random Variables
• 15 MARKOV CHAINS: LIMITING PROBABILITIES 176 Interlude: Practice Midterm 2
• 7 JOINT DISTRIBUTIONS AND INDEPENDENCE 70 7 Joint Distributions and Independence
• RANDOM GROWTH MODELS WITH POLYGONAL SHAPES Janko Gravner
• MODELING SNOW CRYSTAL GROWTH I: Rigorous Results for Packard's Digital Snowflakes
• 11 COMPUTING PROBABILITIES AND EXPECTATIONS BY CONDITIONING 126 11 Computing probabilities and expectations by conditioning
• 18 POISSON PROCESS 196 18 Poisson Process
• Example. Here is a question asked on Wall Street job interviews. (This is the original formu-lation; the macabre tone is not unusual for such interviews.)
• 4 CONDITIONAL PROBABILITY AND INDEPENDENCE 24 4 Conditional Probability and Independence
• 8 MORE ON EXPECTATION AND LIMIT THEOREMS 87 8 More on Expectation and Limit Theorems
• 17 THREE APPLICATIONS 188 17 Three Applications
• MODELING SNOW CRYSTAL GROWTH I: Rigorous Results for Packard's Digital Snowflakes
• Lecture Notes for Introductory Probability Janko Gravner
• 3 AXIOMS OF PROBABILITY 11 3 Axioms of Probability
• 4 CONDITIONAL PROBABILITY AND INDEPENDENCE 38 Interlude: Practice Midterm 1
• 5 DISCRETE RANDOM VARIABLES 45 5 Discrete Random Variables
• Lecture Notes for Introductory Probability Janko Gravner
• 10 MOMENT GENERATING FUNCTIONS 119 10 Moment generating functions
• 11 COMPUTING PROBABILITIES AND EXPECTATIONS BY CONDITIONING 138 Interlude: Practice Midterm 1
• 14 BRANCHING PROCESSES 161 14 Branching processes
• 16 MARKOV CHAINS: REVERSIBILITY 182 16 Markov Chains: Reversibility
• Parrondo's Paradox This famous paradox was constructed by Spanish physicist J. Parrondo. We will
• Erdos-Feller-Pollard renewal theorem Example 1. Roll a fair die forever and let Sm be the sum of outcomes of first m rolls.
• Math 17C, Spring 2011. Linear Systems, Complex Eigenvalues
• 15 MARKOV CHAINS: LIMITING PROBABILITIES 167 15 Markov Chains: Limiting Probabilities
• Twenty problems in probability This section is a selection of famous probability puzzles, job interview questions (most high-
• Robust periodic solutions and evolution from seeds in one-dimensional edge cellular automata