Mathematical Theory of Probability
Rutgers MATH 477, Spring 2019.
daniel.krashen+prob@gmail.com
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Lecture 1
: Combinatorial analysis, part 1.
lecture notes
in class worksheet
Lecture 2
: Combinatorial analysis, part 2. Introduction to probability.
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Lecture 3
: Inclusion-exclusion, equally likely outcomes.
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Lecture 4
: Conditional probability, part 1.
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in class worksheet
Lecture 5
: Conditional probability, part 2.
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Lecture 6 (substitute, no notes)
: Independence.
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Lecture 7 (substitute, no notes)
: Conditional probability as probability.
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in class worksheet
Lecture 8
: Conditional probability wrap up, introduction to random variables.
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Lecture 9 (no in-class worksheet)
: Expected values, variance, Bernoulli and Poisson variables.
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Lecture 10
: A bestiary of random variables.
lecture notes
in class worksheet
Lecture 11
: Binomial expectation and variance.
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Lecture 12
: Introduction to continuous random variables.
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Lecture 13
: Introduction to continuous random variables, part 2.
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Lecture 14
: Joint probability distributions.
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in class worksheet
Lecture 15
: Dropping the ball: the normal distribution.
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Lecture 16
: Mostly sums of random variables.
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Lecture 17
: More sums of random variables and the gamma distribution.
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in class worksheet
Lecture 18
: Expected value of functions of random variables, linearity of expectation.
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Lecture 19
: More linearity of expectation.
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Lecture 20
: Conditional expectation.
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Lecture 21
: Probability generating functions.
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in class worksheet
Lecture 22
: Review.
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Lecture 23
: Variance, covariance and moments.
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Lecture 24
: Moment generating functions and the central limit theorem.
lecture notes
in class worksheet