Leonard -- MATH/IENG 381 Probability & Statistics I
Fall 2022 -- SD Mines
Sections
Section M02: MWF 1000-1050, CB 109
Section M05: MWF 1300-1350, CB 118
Section M06: MWF 1500-1550, CB 206W
Syllabus & Calendar
The calendar is on the last page.
R Installation
The most recent version (4.2.1) can be found here.
Base R is fine (it's all we'll need for our course), but if you are familiar with other R interfaces (such as RStudio and RCommander), you are welcome to use them if you prefer.
Quest Revision Deadlines
Quest 1: 28 September (by 5pm)
Quest 2: 17 October (by 5:15pm)
Quest 3: 31 October (by 5pm)
Quest 4: 30 November (by 5pm)
Quest 5: 30 November (by 5pm)
Quest 6: 9 December (by 12:00pm)
Grading Guidelines
Please refer to the syllabus.
Academic Integrity
South Dakota Mines is committed to academic honesty and scholarly integrity. The South Dakota Board of Regents Policy 2:33 provides a comprehensive definition of "Academic Dishonesty", which includes cheating and plagiarism. All instructors at South Dakota Mines are required to report allegations of academic misconduct to the Student Conduct Officer. The South Dakota Board of Regents Policy 3:4 provides detailed information regarding key definitions, policy information, prohibited conduct, and the Student Conduct process adhered to at South Dakota Mines. Any student suspected of violating academic integrity standards will be reported in accordance with the process outlined on the South Dakota Mines website.
Course Handouts & Suggested Practice Problems
UNIT 1
Capitals vs Lower Case
In this course, distinctions between capital and lower case letters, in many cases, will impact the meaning of what you write, and therefore we must be very careful to distinguish our capital and lower case letters in those cases where they are not necessarily distinct in casual writing.
Click here to see an image of how I distinguish my capital and lower case letters.
You are welcome to make your distinctions as I have done in the example above, but you are also welcome to come up with your own system. In a questing situation, you are welcome to provide a key on your paper which shows how you plan to distinguish your capital and lower case letters.
Section 1.1: Probability in Finite Sample Spaces
Section 1.2: Some Formalities & Additional Results
Section 1.3: Bayes' Theorem
Section 1.4: Sample Statistics & Population Parameters
Solutions to Additional Practice Problems
Beware of three mistakes in the solution to question three!
The sample mean is actually 7203.191.
The sample variance is actually 295435.702.
The sample standard deviation is actually 543.54.
Good catch by Sage!
I will update the solutions PDF file on Friday when I return to campus.
Other Practice Problems
From Probability & Statistics For Engineering and the Sciences (8th or 9th edition) by Jay L. Devore...
For the problems listed below in sections 1.3 and 1.4: ignore the directions, and use the given data sets to compute the mean, median, variance, and standard deviation of each sample. If the population names are not specified (as a capital letter), then give the population(s) a capital letter name of your choice, and be sure to label the calculated sample statistics accordingly.
Section 1.3: 33-39
Section 1.4: 44-47, 49-51, 54
Section 2.1: 1-8
Section 2.2: 10-23
Section 2.4: 45, 46, 48-52, 59, 60, 61a, 62, 64-66
UNIT 2
Section 2.1: Discrete Random Variables
Section 2.2: Binomial Distributions
Section 2.3: Hypergeometric Distributions
Section 2.4: Poisson Distributions
UNIT 3
Section 3.1: Continuous Random Variables
Section 3.2: Exponential Distributions
Section 3.3: Normal Distributions
Section 3.4: Q-Q Plots for Normality Testing
Section 3.5: t-Distributions
A link to an article discussing degrees of freedom.
A link to Gosset's article which appeared in Biometrika in 1908.
UNIT 4
Section 4.1: Sampling Distributions of Sample Means & The Central Limit Theorem
NOTE: Most of the videos for Units 4, 5, and 6 were made when we flipped online in Spring 2020. At the time of these recordings, my 381 classes were still using a textbook; as a result, most of the following videos refer to section numbers of a textbook that we aren't using. Additionally, the quality of some of these videos may be poorer than those you've seen previously -- please stop by office hours if you'd like some clarification on anything that might be hard to read or hear.
Section 4.2: Hypothesis Testing for One Population Mean
Section 4.3: Confidence Intervals for One Population Mean
UNIT 5
Section 5.1: Hypothesis Testing for Two Independent Population Means
An article by Michael Allwood which discusses how we arrive at the Satterthwaite Formula for degrees of freedom we see in sections 5.1 and 5.2.
Section 5.2: Confidence Intervals for Two Independent Population Means
Section 5.3: Hypothesis Testing for Paired Means
Section 5.4: Confidence Intervals for Paired Means
UNIT 6
Section 6.1: Hypothesis Testing for One Population Proportion
Section 6.2: Hypothesis Testing for Two Independent Population Proportions
Section 6.3: Confidence Intervals for One & Two (Independent) Population Proportions
A paper by Newcombe which compares several types of confidence intervals for a single proportion.
A paper by Brown/Cai/DasGupta regarding interval estimation for a single proportion.
A paper by Agresti & Coull regarding interval estimation for a single proportion.
A paper by Newcombe which compares several types of confidence intervals for the difference of two independent proportions.