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1. Week
Combinatorial Analysis,
Axioms of Probability
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2. Week
Conditional Probability and Independence,
Random Variables,
Discrete Random Variables,
Cumulative Distributive Function,
Expectation,
Variance
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3. Week
Bernolli and Binomial Random Variables,
Poisson Random Variable,
Geometric Random Variable,
Negative Binomial Random Variable,
Zeta Distrubition,
Properties of CDF
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4. Week
Midterm(July 19, 2019, Friday 10:00)
Continous Random Variables,
Expectation and Variance of Continous Random Variables,
Uniform Random Variable,
Normal Random Variable,
Normal Approxiamation of Binomial Distribution,
Exponential Random Variables,
Distribution of a Function of a Random Variable
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5. Week
Joint Distribution for n Random Variables,
Independent Random Variables,
Sums of Independent Random Variables,
Conditional Distributions,
Order Statistics,
Joint Distribution of Functions of Random Variables
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6. Week
Properties of Expectation,
Covariance, Variance, Sums and Correlations,
Conditional Expectation,
Conditional Variance,
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7. Week
Moment Generating Functions,
Limit Theorems,
Chebyshev's Inequality,
The Weak Law of Large Numbers,
Central Limit Theorem,
The Strong Law of Large Numbers,
One-sided Chebyshev's Inequality,
Markov's Inequality,
Chernoff Bounds
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