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 Wednesday March 6th. Midterm exam topics: everthing up to and not including the intro to continuous random variables! [Scheduled make-up midterm exams will take place Monday after spring break, in my office RE-208, at 11:25am.] The midterm will be graded within one week, and so you will be able to see your grades by 3/13. But the physical exams may not be returned until 3/20.
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Final exam will take place on Monday, April 29th, 10:30am-12:30pm at PH108. 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 1/17]. Homework 2 is due week 3, day 2 [Wed 1/24]. |
| Week 3 | ||
| 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, 2.4. | Homework 3 is due week 4, day 2 [Wed 1/31]. |
| Week 4 | ||
| 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. | Homework 4 is due week 5, day 2 [Wed 2/7]. |
| Week 5 | ||
| Conditional probability and independence; the general multiplication rule; probability trees. The law of total probabilty and Bayes’ rule. | 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 5 is due week 6, day 2 [Wed 2/14]. |
| 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 2/21]. |
| Week 7 | ||
| During the week, at some point, we discuss counting (see section 2.3!). Random variables: Binomial, multinomial, hypergeometric. |
Section 5.2, 3.4, and 5.3. | Homework 7 is due week 8, day 2 [Wed 2/28]. |
| Week 8 | ||
| Poisson process and the Poisson random variable. Intro to continuous random variables: normal, standard normal, and applications. Other recommended reading: section 3.4 in the book - this puts into context notions such as ‘probability density function’. |
Section 6.2, 6.3, 6.4. | Homework 8 - SHORT! is due week 9, day 1 [Mon 3/4]. |
| Week 9 | ||
| MONDAY: wrapping up from week 8. WEDNESDAY: midterm exam! |
Sections tbd. | Homework 9 will be due week 10, day 2 [Wed 3/20]. moved |
| Spring break | ||
| If you have not taken the time to go outside, do it now. See you next week :) :) | Review confusing concepts, that’s it. | |
| Week 10 | ||
| Applications of normal distribution; the uniform distribution; review of mean and variance of random variables/ Cool stuff: starting statistical inference soon! :) Introduction to inference & random sampling. |
6.1, 6.5; revisit 4.1, 4.2. Z table for your use | Homework 9 is due week 11, day 2 [Wed 3/27]. Z table for your use |
| Week 11 | ||
| Sampling, statistics, and sampling distributions. Properties of sample mean and proportion. | 8.1, 8.2, 8.3, 8.4. Free reading: section 8.5. | Homework 10 is due week 12, day 2 [Wed 4/3]. |
| Week 12 | ||
| Confidence intervals for mean and proportion. Meaning of confidence interval and interpretation. What to do when population variance is unknown. The common form of normal confidence interval: estimator plus/minus margin of error, computed using the estimator’s variance! | 9.1-9.5, 9.10, 9.12. (and 9.14 for overview.) | Homework 11 is due week 13, day 2 [Wed 4/10]. |
| Week 13 | ||
| Hypothesis tests: overview and the z-test for population proportion. | 10.1, part of 10.2 (ignore the “testing errors” part for this week!!), and 10.3. | Homework 12 is due week 14, day 2 [Wed 4/17]. |
| Week 14 | ||
| Hypothesis tests: The z-test and t-test for population mean. | 10.4. | Homework 13 is due week 15, day 1 [Monday! But Wednesday will not be considered late.]. Data in excel format and Data for R |
| Week 15 | ||
| Testing errors etc. | Rest of 10.2. | No more hw! |
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: holiday [no class].
- wk2, day2: 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).
- wk3, day1: How do you summarize “data spread”? Think about the histograms we saw in week 2. How you do detect an outlier?
- Also included: a pop-up ‘quiz’ on boxplots! [low stakes - participation credit for any answer!]
- wk3, day2: Wrapping up standard deviations as a measure of variability in the data. Formal introduction to probability: meaning, notation, likelihood, and computation using relative frequency of an event in a sample space. Empirical computation of probability & the Law of Large Numbers.
- wk4, day1: Beginning of theoretical computations of probability: equally likely outcomes, sample spaces and events, and basic probability rules (complement rule, general addition rule, disjoint events).
- wk4, day2: 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.
- wk5, day1: conditional probability: definition and computation. Independence events and 4 equivalent ways to testing independence.
- wk5, day2: probability trees, the rule of total probability, and the Bayes rule.
- wk6, day1: the concept of random variables, discrete vs. continuous. Probability distribution, rules and how to compute it. Means of random variables: meaning and use.
- wk6, day2: Rules for means and variances of random variables. Standard deviation and meaning. Relating back to the law of large numbers and outliers discussion from week 3.
- wk7, day1: Binomial random variables: how do they arise? what is the ‘binomial experiment’? How to compute the probability distribution of a binomial random variable? mean and variance formula.
- wk7, day2: Multinomial random variables (generalizing binomial) and the corresponding experiment, example to recognize in application. Hypergeometric distribution and acceptance sampling, with example.
- wk8, day1: Poisson random variables and the Poisson process. Approximation to Binomial for $n\to\infty$ and $p\to0$. Intro to continuous random variables: what is a probability density function? (relate to histogram of a discrete r.v.) Example of shoe size vs. foot length. The normal random variable, and the standard deviation rules for the normal. Why density, not just “a probability distribution”? Probability of being in an interval using the density curve leads to integrals.
- wk8, day2: But what is the integrand above? Normal density formula. Standard normal: why? (“how many stdevs away from the mean?”) Applications and examples using the normal calculations and standard normal $z$-scores.
- wk9, day1: wrap up any remaining examples from above.
- wk9, day2: midterm exam.
- wk10, day1: after spring break we continue with applications of the normal distribution: approximation and binomial. Our first real large-sample theorems. Statistical inference, here we come! :) Also we will introduce the uniform distribution which we skipped before the break.
- wk10, day2: wrapping up probability and intro to statistical inference. Returning the midterm exam (graded) for those students who did not pick it up on Monday from my office.
- wk11, day1: sampling distribution of the sample mean. The Central Limit Theorem. Application / example.
- wk11, day2: summary of probability (all we have learned!); intro to inference. Three types of statistical inference. Point estimation and unbiased estimators.
- wk11, day1: Confidence intervals for population mean. Meaning of confidence interval and interpretation. What to do when population variance is unknown. The common form of normal confidence interval: estimator plus/minus margin of error, computed using the estimator’s variance!
- wk11, day2: confidence interval for population proportion. what’s that estimator in the center of the confidence interval? – brief overview of MLE!
HW formatting
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