Mathematical Statistics
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
San Bernardino, CA
CSU Monterey Bay
San Diego State University
UC Riverside
Name
Year
Major
Fun Fact
Career Goal
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
This course is an introduction to mathematical statistics with an emphasis on statistical estimation and hypothesis testing. The course will be comprised of both theory and applications. We begin with a condensed review of fundamental concepts from Math 352; particularly, we briefly review important discrete and continuous probability distributions. We will then begin our discussion on the main topic of this course, statistical inference, through the study of distributions of functions of random variables using the method of moment-generating functions and order statistics. We then discuss ideas of convergence with sampling distributions and the central limit theorem. Next, we consider the topics of estimation, properties of point estimators, and methods of estimation. Finally, we study the theory of statistical tests and likelihood ratio tests. Depending on time, other topics may be added or removed.
Have a strong math foundation is necessary to be successful in the course. We will be utilizing topics related to:
You can try out these problems to get an idea of the type of math we will be doing in this class here.
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
The use of generative artificial intelligence (AI) to complete any part or all of an assignment/exam is strictly prohibited in this class. This includes, but not limited to, ChatGPT, Claude, Meta AI, and Google Gemini.
You may use AI to enhance you understanding of the material.
You may not use AI to complete assignments.
You may not upload any course material to any AI platforms such as ChatGPT, Claude, Meta AI, and Google Gemini. Exceptions are allowed for DASS-approved services.
There are consequences when you use of AI:
The purpose of this class, and college, is for you to learn about critical thinking skills and perseverance. Using AI will only teach you how to get an answer, which may or may not be correct.
You will not develop the skills needed to problem solve a challenge. Additionally, developing grit is essential to become successful in college and life. There is no easy way out and AI is an illusion to your success in life.
To learn something, it requires hours of work! If not years!
When using AI, you must acknowledge its limitations:
Responses provided may be incorrect
Responses may not be fair
Companies may manipulate responses and/or terms of service for their benefit
Companies may not have your best interst in mind
You should always proceed with caution utilizing these tools!
Additionally, all these individuals are not receiving any royalties for the work to be used in creating generative AI models.
Inside Higher Ed and The New Yorker highlight individual’s concern of their work being used to train AI models.
The use of generative AI raises concerns of what data is being harvested from us, possibly without informed consent or knowledge of impacts.
When you use any large language models, you do not know what information is being harvested from you.
Do you want to upload your thoughts and ideas to a company that can monetize, and possibly exploit you.
Does your Professors consent with you uploading their assignments to large language models?
Stanford provided a report highlighting the risks of our personal data use in large language models.
In order to run these large language models, companies need to use a large amounts of energy. This is because large servers are needed to both train and execute a model.
The LA Times reports the potential impact that running AI models in California.
Additionally, Time reports that a ChatGPT query uses ten times more energy than a Google search query, and global AI demands can consume of 1 trillion gallons of water by 2027.
There are also environmental justice questions about where these data centers are constructed.
The Washington Post and Time (Article 1 and Article 2) reported that AI companies utilize “digital sweatshops” to classify data points for model training.
There is a human cost from the Global South, both financially and mentally, to develop the AI models for users in the United States and Europe.
We must be conscious consumers and demand more from these companies to provide safe working conditions and livable wages.
Yes/No/I don’t know
AI surveillance and data colonialism shape African conflicts
African workers are taking on Meta and the world should pay attention
‘It’s destroyed me completely’: Kenyan moderators decry toll of training of AI models
The AI Industry Is Traumatizing Desperate Contractors in the Developing World for Pennies
ChatGPT advises women to ask for lower salaries, study finds
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
Observational Unit
Variable
Types of Variables
Quantitative
Categorical
Roles of Variables
Predictors
Outcome
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
Categorical Variables
Proportions
p or \(\pi\)
\(\hat p\)
Continuous Variables
Means or Averages
\(\mu\)
\(\hat \mu\) or \(\bar X\)
Variances
\(\sigma^2\)
\(\hat \sigma^2\) or \(s^2\)
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
Simple Random Sampling
Stratified Sampling
Cluster Sampling
Multistage Sampling
Introductions
Class Setup
Generative AI
Extra Credits
Fundamentals of Statistics
Fundamentals of Statistical Inference
Sampling Techniques
Field Trip
m453.inqs.info/lectures/1a