Sheet  Topic 

Sheet 1  Review (sets, sequences, etc.), Counting 
Sheet 2  Basic Probability 
Sheet 3  Conditional Probability and Independence 
Sheet 4  Discrete Random Variables and Distributions 
Sheet 5  Discrete Distributions and Expectation 
Sheet 6  Continuous Random Variables 
Sheet 7  Continuous Random Variables and Distributions 
Sheet 8  Normal Distribution, Central Limit Theorem 
Sheet 9  Hypothesis Testing 
Lab  Topic  Files 

Lab 1  Python, Basic Probability and R 

Lab 2  Bloom Filters 

Lab 3  A Survey of Elementary Distributions through the lens of Bitcoin 

Lab 4  Second Moment Estimation and Load Balancing 

Lab 5  Hypothesis Testing and Linear Regression 
Lecture  Topic  Reading 

Lecture 1  Introduction. 

Lectures 2,3  Sets, set operations. 
Schaum's Ch. 1 
Lecture 4  Functions and counting sequences. Counting rules: bijection rule, product rule, sum rule. 
LLM 15.1.1, 15.2.1, 15.2.3 
Lecture 5  Counting rules continued: generalized product rule, division rule. 
LLM 15.3 beginning, 15.3.2, 15.4 beginning, 15.4.1 
Lecture 6  Counting subsets, permutations. 
LLM 15.3.3, 15.5 beginning, 15.5.1 
Lecture 7  Counting bit sequences. Sequences with repetitions, bookkeeper rule. Inclusionexclusion principle. Pigeonhole principle. 
LLM 15.5.2, 15.6.1, 15.6.2, 15.8 beginning, 15.9 beginning, 15.9.1, 15.9.2, 15.9.4 
Lecture 8  Basic probability: probability spaces, set theory and probability. 
LLM 17.5.1 
Lectures 9, 10  Monty Hall problem, tree diagram method. Probability rules from set theory, uniform probability spaces. 
LLM 17.1, 17.2, 17.5.1, 17.5.2, 17.5.3 
Lecture 11  Conditional probability and independence. 
LLM 18.1, 18.2 
Lecture 12  Tree diagram method for conditional probability. Bestofthree hockey tournament. Why tree diagrams work. Medical testing. 
LLM 18.3, 18.4 
Lecture 13  Medical testing continued. A posteriori probabilities, Bayes rule. 
LLM 18.4.2, 18.4.3, 18.4.4, 18.4.5 
Lecture 14  The law of total probability. 
LLM 18.5 beginning 
Lecture 15  Conditioning on a single event: probability rules from set theory. 
LLM 18.5.1 
Lecture 16  Independence, mutual independence, kwise independence. 
LLM 18.7, 18.8 beginning, 18.8.2 
Lecture 17  Randomized algorithms: testing whether two polynomials are identical. 
Mitzenmacher and Upfal Ch. 1 
Lectures 18, 19  Discrete random variables. Indicator random variables and events. Independence, mutual independence. Distribution functions (PDF, CDF). 
LLM 19.1, 19.2, 19.3 beginning 
Lectures 20, 21  Midterm review. 

Lectures 22, 23  Discrete distributions: Bernoulli, Uniform. Binomial, Geometric. 
LLM 19.3.1, 19.3.2, 19.3.4 
Lecture 24  Expectation of a discrete random variable. Expectation of a Bernoulli and Uniform random variable. Linearity of expectation. 
LLM 19.4 beginning, 19.4.4, 19.5 beginning, 19.5.1 
Lecture 25  Discuss midterm solutions. 
Model midterm solutions posted on Piazza 
Lecture 26  Conditional expectation, law of total expectation. 
LLM 19.4.5 
Lecture 27  Expectation of a Binomial random variable. Expectation of a Geometric random variable. The coupon collector problem. 
LLM 19.4.6, 19.5.2, 19.5.3, 19.5.4 
Lecture 28  Continuous random variables: PDF and CDF. Continuous random variable that is uniform over an interval. Discrete vs. continuous vs. mixed random variables. 
Class notes 
Lecture 29  Playing darts: more examples of discrete, continuous, mixed random variables. 
Class notes 
Lecture 30 
Independence. Expectation. Conditional probability and conditional expectation. Continuous distributions: Uniform and Exponential. 
Class notes 
Lecture 31  Exponential distribution: connection to Geometric, expectation, memoryless property. Normal distribution. 
Class notes 
Lecture 32 
Normal distribution: sending bits across noisy channels, standardization. Variance and standard deviation. 
Class notes LLM 20.2 beginning, 20.2.1, 20.2.2. 
Lecture 33 
Properties of variance. Variance of Bernoulli, Geometric, and Binomial random variables. Variance of a sum of independent random variables. 
LLM 20.3.1, 20.3.2, 20.3.3, 20.3.4. 
Lecture 34, 35 
Parameter estimation. Markov Inequality, Chebyshev Inequality. Central limit theorem. 
Parameter estimation section in the class notes LLM 20.1 beginning, 20.1.1, 20.2 beginning, 20.4 
Lectures 36, 37  Hypothesis testing. 
Hypothesis testing section in the class notes 
Lecture 38  Chernoff Inequality and applications. 
LLM 20.6.2, 20.6.3, 20.6.5, 20.6.7 
Lectures 39, 40  Final exam review. 