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

• 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.

• Final exam will take place on Thursday, December 11, 2-4pm at our regular classroom HH005. 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. During the week, at some point, we will return to counting (see section 2.3!). Important discrete random variables: Binomial, multinomial, hypergeometric. Please note, we are covering discrete parts of chapters 3&4 before doing continuous. The HW reflects this.	Section 3.1, 3.2; (the discrete parts of the following): 4.1, 4.2, and 4.3. Sections 5.1, 5.2. Additional examples for reading here.	Homework 6 is due week 7, day 2 [Wed 10/1].
Week 7
Poisson process and the Poisson random variable. Intro to continuous random variables: normal, standard normal, and applications. The concept of mathematical expectations, which is tied to functions of random variables.	Section 5.5. Also Section 3.3.(That is, wrapping up sections in chapters 3&4 that we didn’t cover for continuous distributions yet.)	NOTE: I did not assign homework due on the day of the midterm! Homework 7 is due week 9, day 2 [Wed 10/15].
Week 8
WEDNESDAY: midterm exam! Applications of normal distribution; the uniform distribution; review of mean and variance of random variables	Section 6.2, 6.3, 6.4, 6.5; revisit 4.1, 4.2.	Homework 7 is due week 9, day 2 [Wed 10/15].
Week 9
Remaining fundamental concepts on random variables: joint distributions, marginals, conditionals. Note: MONDAY is the fall break day.	Sections 3.4, 5.2, 5.3.	Homework 8 due week 10, day 2 [Wed 10/22]. Z table for your use
Fall break day assignment
	If you have not taken the time to go outside, do it now. See you on Wednesday :) :)
Week 10
Finishing last lecture: statistical mathematical independence. Multinomial and hypergeometric distributions. Cool stuff: starting statistical inference! Introduction to inference & random sampling. Sampling, statistics, and sampling distributions.	Section 8.1, 8.2, 8.3, 8.4. Free reading: section 8.5.	Homework 9 is due week 11, day 2 [Wed 10/29]. Z table for your use
Week 11
Sampling, statistics, and sampling distributions applied to statistical inference: sample mean, sample proportion, sample variance as estimators for the corresponding population parameters. What does it mean for an estimator to be unbiased. Properties of sample mean and proportion.	9.1, 9.2, 9.3, 9.4.	Homework 10 is due week 12, day 2 [Wed 11/5].
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, 9.8. (and 9.14 for overview.)	Homework 11 is due week 13, day 2 [Wed 11/12].
Week 13
tbd	tbd	Homework 12 is due week 14, day 2 [Wed 11/19].
Week 14
tbd	tbd	Homework 13 is due week 15, day 1 [Mon 12/1] but Wed 12/3 will not be considered late! Here is the data in excel format and data for R
Week 15
tbd	tbd	hw: just review, final the following week.

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.
• wk5, day1: discussed more on computation of conditional probabilities and started talking about the Bayes rule.
• wk5, day2: derived the Bayes rule and talked more about the example of the lie detector (lies vs. spies in a company example!). Started introduction to discrete random variables and their mean.
• wk6, day1: meaning and formula of mean, same for variance/standard deviation. Comparing two distributions. Linear transformations of random variables. Definitions of PMF and CDF for a discrete random variable.
• wk6, day2: we will continue with discrete r.v. and two particular examples!
• wk7, day1: Poisson. Recalling defn. of mean, interpretation of mathematical expectations, both for discrete and continuous random variables, and general functions of r.v.s.

• wk7, day2: Continuous distributions, pdf, cdf, means, variance. Formal functions of random variables, expectations. Introduction to the normal distribution, and the standard deviation rule (and why it holds).
• wk8, day1: Wrapping up the normal distribution, standard normal values and computation, normal approximation to the binomial. Uniform distribution.
• wk8, day1: midterm exam. TOPICS: everything up to but not including the continuous distributions!
• wk9, day1: fall break day.
• wk9, day2: Wrapping up the main concepts behind random variables that we didn’t cover yet: joint distributions, marginals, conditionals. We did one continuous and one discrete example, all from the book. read the rest of this secton!
• wk10, day1: mathematical independence. Also, two more special r.v.s: multinomial and hypergeometric distributions. Then, onto stats… Regarding random samples in section 8.1: note that we already covered ideas behind these concepts during the first few weeks.
• wk11, day1: Recall that the sampling distribution of the sample mean is given by the Central Limit Theorem. Application / example. Summary of probability (what have we learned) and intro to inference. Three types of statistical inference. Point estimation and unbiased estimators. What does it mean to estimate a parameter for a population? Connecting the dots: estimators, statistics, parameters, means, and variances.
• wk11, day2: Wrapping up last lecture’s discussion with more examples. Intro to interval estimation. Confidence intervals for population mean.
• wk12, day1: “Guessing” confidence intervals for proportions. Why is sample size typically around 1100 in popular media polls? (The minimum sample size necessary to achieve a 3% margin of error for population proportion confidence intervals!)
• wk12, day2: One-sided confidence bounds for population mean. Two samples: estimating the difference between two means. (Confidence intervals, still.)

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Weekly

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