Stats 116: Introduction to Probability
As noted on the course information page,
we will cover the following topics (time permitting):
Counting (.5 weeks)
Axioms of probability (1 week)
Independence and conditional probability (1 week)
Random variables (2 weeks)
Continuous random variables and distributions (2 weeks)
Laws of large numbers and the central limit theorem (2 weeks)
Concentration inequalities (1 week)
Lectures and course schedule (at least as planned)
We strongly recommend completing the readings (and will assume you
have completed all readings in the Ross textbook). We will list
chapters in Ross's First Course in Probability by the name Ross,
chapters in Blitzstein and Hwang's Introduction to Probability by
BH. These are not required, but often give excellent alternative
perspective.
| Topics | Reading | Notes |
| Mon, 28 March | Overview and introduction | Ross Chs. 1–2, BH Ch. 1 | 01 |
| Tue, 29 March | Combinatorics and discrete spaces | Ross Chs. 1–2, BH Ch. 1 | 02 |
| Wed, 30 March | Basics of probability | Ross Chs. 1–2, BH Ch. 1 | 02 |
| Thu, 31 March | Axioms of probability | Ross Ch. 2, BH Ch. 1 | 03 |
| Mon, 4 April | Axioms, begin conditional probability | Ross Ch. 2–3, BH Ch. 2.1–2.2 | 03 |
| Tue, 5 April | Conditional probability | Ross Ch. 3, BH Ch. 2.1–2.3 | 04 and 06 |
| Wed, 6 April | Bayes’ Rule and conditioning | Ross Ch. 3, BH Ch. 2.3–2.8 | 06 and 07 |
| Thu, 7 April | Independence | Ross Ch. 3, BH Ch. 2.5 | 08 |
| Mon, 11 April | Independence and Random Variables | Ross Ch. 4, BH 2.5–2.8 | 09 |
| Tue, 12 April | Probability mass functions | Ross Ch. 4, BH 3.1–3.4 | 10 |
| Wed, 13 April | Means and expectations | Ross Ch. 4, BH 4.1–4.2 | 11 |
| Thu, 14 April | Expectations, independence of random variables | Ross Ch. 4, BH 4.1–4.4 | 12 |
| Mon, 18 April | Independence and variance | Ross Ch. 4, BH 4.1–4.6 | 13 |
| Tue, 19 April | Variance and examples of random variables | Ross Ch. 4, BH 4.6–4.8 | 14 |
| Wed, 20 April | Poisson and geometric random variables | Ross Ch. 4, BH 4 | 15 |
| Thu, 21 April | Continuous random variables | Ross Ch. 5, BH 5.1–5.2 | 16 |
| Mon, 25 April | Exponential, Gaussian distributions | Ross Ch. 5, BH 5.4–5.6 | 17 |
| Tue, 26 April | Means and variances of continuous distributions | Ross Ch. 5,BH 5.4–5.6, 6.1–6.3 | 18 |
| Wed, 27 April | Joint distributions (discrete) | Ross 6, BH 7.1 | 19 |
| Thu, 28 April | Joint distributions | Ross 6.1–6.2, BH 7.1 | 20 |
| Mon, 2 May | Joint distributions of continuous RVs | Ross 6.3–6.5 | 21 |
| Tue, 3 May | Midterm Exam | Ross Ch. 1–5 | |
| Wed, 4 May | More continuous RVs | Ross 5.6, 6.6, BH 8.2–8.6 | 23 |
| Thu, 5 May | Beta distributions and order statistics | Ross 5.6, 6.6,BH 8.2–8.6 | 24 |
| Mon, 9 May | Linear algebra review | BH A.3, A.6 | 25 |
| Tue, 10 May | Linear algebra review | BH A.3, A.6 | 26 |
| Wed, 11 May | Change of variables | Ross 6.7, BH 8.1, 8.5, A.7 | 27 |
| Thu, 12 May | Examples of change of variables | Ross 6.7, BH 8.1, 8.5, A.7 | 28 |
| Mon, 16 May | Multivariate normal distributions | Ross 7.8.1, BH 7.5 | 29 |
| Tue, 17 May | Covariance | Ross 7.4, BH 7.1–7.4 | 30 |
| Wed, 18 May | Conditional expectation | Ross 7.5–7.6, BH 9.1–9.2 | 31 |
| Thu, 19 May | Inequalities and concentration | Ross 8.1, 8.2, BH 10.1 | 32 |
| Mon, 23 May | Moment generating functions | Ross 7.7, BH 6.4–6.5 | 33 |
| Tue, 24 May | Moment generating functions and Chernoff bounds | Ross 7.7, 8.1, 8.5, BH 10.1 | 34 |
| Wed, 25 May | Laws of large numbers | BH 10.2 | 35 |
| Thu, 26 May | Central limit theorem | BH 10.3–10.4 | 36 |
| Mon, 30 May | No class | Memorial Day | |
| Tue, 31 May | Central limit theorem | BH 10.3–10.4 | 37 |
| Wed, 1 June | Review | | 38
|
|