MathStat474
Welcome to Math 474 @ IIT by Sonja Petrović. The section numbers in the tables below refer to the following course textbook: Walpole, Meyers, Meyers, Ye: Probability and Statistics for Engineers and Scientists, 9th edition.
Important dates
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Midterm will take place in class on date tbd. Midterm exam topics: everything up to and not including the intro to continuous random variables! The midterm will be graded within one week, and so you will be able to see your grades by x/xx. But the physical exams may not be returned until x/xx.
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Final exam will take place on date and location tbd. The exam will be comprehensive, with 2/3 of the topics from after the midterm, and 1/3 before the midterm!
Weekly schedule
| Topics | Reading | Homework |
|---|---|---|
| Weeks 1 & 2 | ||
| Introduction to basics Research questions Populations, samples, and data collection Sample spaces and types of data Summarizing quantitative data graphically |
Sections 1.1, 1.2, 1.5, parts of 1.6, 1.7. Section 2.1. | Homework 1 is due week 2, day 2 [Wed 8/27]. Homework 2 is due week 3, day 2 [Wed 9/3]. |
| Week 2 | ||
| Wrapping up the basics of EDA: measures of spread in the data: range, quartiles, IQR, standard deviation, and what they all mean for data summaries and statistics. Also we will go over the construction and interpretation of boxplots. Introduction to probability. |
Sections 1.3, 1.4, and 2.1, 2.2, 2.3, 2.4. | Homework 2 is due week 3 [Wed 9/3]. |
| Week 3 | ||
| Introduction to probability: sample spaces and events, equally likely outcomes, and basic rules of probability. | Sections 2.4, 2.5. Read through 2.3 as extra. Due to Labor Day week, we have an additional reading assignment. Completing it counts for participation credit! | Homework 3 is due week 4, day 2 [Wed 9/10 at 11:30pm]. |
| Week 4 | ||
| Basic rules of probability. Conditional probability and independence. | Please read section 2.3 carefully, and study the formulas in there, as you will likely need to use them for homework! Sections 2.6 and 2.7. |
Homework 4 is due week 5, day 2 [Wed 9/17 at 11:30pm]. |
| Week 5 | ||
| The general multiplication rule; probability trees. The law of total probabilty and Bayes’ rule. Introduction to Randoom variables (time permitting). |
Sections 2.6 and 2.7. | Homework 5 is due week 6, day 2 [Wed 9/24]. |
| Week 6 | ||
| Random variables: discrete random variables. | Section 3.1, 3.2; 4.1, 4.2, and 4.3. | Homework 6 is due week 7, day 2 [Wed 10/1]. |
Main concepts / ideas:
- wk1, day1: Research questions, population, sample, sample space with notation, data, data collection mechanisms, types of data. Where does randomness come from (I am not random!)? How data are generated.
- wk1, day2: “the big picture” relating probability to inference; examples of studies and conclusions. Why is it important to quantify the uncertainty (e.g., “with 95% confidence we conclude that 65% of the US adult population favors X…”) Sent (on Slack) a data set to try to see a pie chart or a bar chart. Begin to think about how data are usually summarized graphically: visualization of a categorical variable.
- wk2, day1: Histograms - visualizing distributions for quantitative variables. (Remember, we talked about boxplots for discrete variables in week 1.) Interpreting histograms. Measures of center and beginning to think about measures of spread (e.g. range). How do you summarize “data spread”? Think about the histograms we saw in week 2. How you do detect an outlier?
- wk2, day2: Wrapping up standard deviations as a measure of variability in the data. Introduction to probability: sample spaces and events, equally likely outcomes, and basic rules of probability. Formal introduction to probability: meaning, notation, likelihood, and computation using relative frequency of an event in a sample space. Empirical computation of probability - quick overview.
- wk3, day1: Labor Day holiday [no class].
- wk3, day1&2: Beginning of theoretical computations of probability: equally likely outcomes, sample spaces and events, and basic probability rules (complement rule, general addition rule, disjoint events). Finish multiplication rule, discussed independent events, and talked about using given probabilities for two categorical variables to construct a two-way probability table, including the marginal totals.
- wk4, day1: finished up multiplication rule, discussed independent events, and talked about using given probabilities for two categorical variables to construct a two-way probability table, including the marginal totals.
- wk4, day2: Finish second example of probability table. (relevant for HW!) Conditional probability: definition and computation. Independence events and 4 equivalent ways to testing independence.
HW formatting
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Weekly
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