Workshop in Probability and Statistics from Udemy

What's inside

Learning objectives

By the end of this workshop you should be able to pass any introductory statistics course

This workshop will teach you probability, sampling, regression, and decision analysis

By the end of this workshop you should be able to pass any introductory statistics course
This workshop will teach you probability, sampling, regression, and decision analysis

Syllabus

Basic Probability and Terminology

Basic introduction to probability. Examples using the fundamental probability equation.

Comprehension Check 1.1

Continuing the discussion of basic probability we define complements ("not A") and examine how to find the probability of the complement of an event.

More on basic probability. How to find the probability of two or more events occurring when we use the terms "and" and "or." For instance, how to find the probability of events "A and B" / "A or B".

How to find the probability of multiple events all taking place when we know the probability of each event.

Introduction to conditional probability and how to solve using the fundamental probability equation.

Three examples of conditional probability questions solved.

How to calculate the intersection of several events. More examples using decision trees to calculate probabilities.

Bayes' Theorem and how to solve conditional probability questions using decision trees.

Putting it all together with Conditional Probability with a look ahead at Expected Value.

Definition and terms related to random variables and examples of probability distributions, including an explanation of cumulative probability.

Explanation and examples of expected value and its relationship to probability and statistics. Includes a refresher on weighted averages.

How to calculate the Expected Value and Standard Deviation of a function when it contains a Random Variable.

Graphing probability distributions in an X-Y coordinate plane. Calculating probabilities by measuring the area under a curve. Includes explanations of Histograms and the Uniform Distribution.

Introduction to the Normal Distribution and Z Scores. Explanation of how the number of standard deviations from the mean is related to probability.

Popular real estate website Wozill has developed an algorithm for predicting the eventual sales price of any house before it goes on the market. Sometimes the estimate provided by the algorithm is high, and sometimes it is low, but overall the expected difference between the prediction given by the algorithm and the actual sales price of the home is zero--meaning that the averages of all predictions and recorded sales are the same.

Unfortunately, the standard deviation of the difference between the algorithm's predictions and the actual sales prices of the homes is rather large: $100k, normally distributed around $0. Approximately what percentage of estimates provide by the Wozill algorithm will be $200k or more below the actual sales price of the home?

How Z Scores (# of standard deviations from the mean of a normal distribution) can be converted to cumulative probabilities. How to use the Standard Normal (Z) Table.

In this video we solve several problems related to probabilities and the Normal Distribution. Includes solving for observed values, expected values, standard deviations, and cumulative probabilities.

How to calculate confidence intervals using the Normal Distribution and Z Scores.

Definitions, examples, and how to calculate covariances and correlations for two random variables.

Portfolio Analysis has to do with how to calculate the joint variance (and standard deviation) of multiple random variables. This video includes the equation to calculate joint variances when there may be multiple instances of two random variable and the variables may be correlated.

An example illustrating the concepts of Portfolio Analysis as well as correlation and variance of Joint Random Variables.

Introduction to Sampling and the Central Limit Theorem. Also how the size of a sample relates to the accuracy of a prediction for a population parameter.

More on Sampling and the Central Limit Theorem. How to calculate the probability of observing a sample mean using the standard deviation of the sample.

How to apply the principles of Sampling and the Central Limit Theorem to proportions. Includes how to calculate a proportion sample standard deviation.

Definition of the t-distribution an how to perform sampling calculations when the standard deviation of the population is unknown. Also how to use the t-Table.

Several examples demonstrating calculations pertaining to Z values, sampling, confidence intervals, proportion sampling, and t-distributions. All related to the previous four videos: Stats 24-27.

Introduction to Hypothesis Testing and its relationship to Sampling. How to select null and alternative hypotheses and how to determine whether to use a one-tailed or two-tailed test.

Introduction to linear regression. Definitions of independent and dependent variables, scatterplots, best-fit lines, residuals, the least-squares method, and the prediction equation.

More on simple linear regression including how to analyze the output of regression analysis using example data. Definitions of R-squared, coefficients, and standard errors. Also how to test the significance of the relationship between an independent and dependent variable using hypothesis testing.

A grab bag of additional regression concepts including how to calculate confidence intervals for predicted changes to a dependent variable based on a change to an independent variable, degrees of freedom with multiple independent variables, standardized coefficients, and the F-statistic.

How to calculate confidence intervals for point predictions and population averages using regression.

Overview of the four main assumptions of linear regression: linearity, independence of errors, homoscedasticity, and normality of residual distribution.

Overview of multiple regression including the selection of predictor variables, multicollinearity, adjusted R-squared, and dummy variables.

Employing dummy variables and time-lagged variables to come up with a better predictive model for your multiple regression analysis.

This video provides a very brief overview of some ways that you can transform your data so that it takes the form of a linear function and can then be used in a regression. Includes exponential and logarithmic transformations.

An example illustrating the iterative process used to select predictor variables for a multiple regression model.

A quick introduction to ANOVA, including examples of one-way and two-way analysis of variance.

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Suitable for those who need to gain a thorough grounding in probability and statistics

Beginners to statistics will benefit considerably from this course

Those in statistics classes who struggle with textbooks and lectures may find this course invaluable

This course covers a wide range of topics, making it suitable for those seeking a comprehensive understanding of probability and statistics

Reviews summary

Solid introduction to probability and statistics fundamentals

According to learners, this workshop provides a clear and accessible introduction to fundamental probability and statistics concepts, making it a good starting point for beginners or those needing a refresher. Students found the early sections on basic probability and descriptive statistics particularly easy to understand. However, many felt the course lacked sufficient depth for those requiring a more comprehensive understanding, especially in later topics like regression. While the problem sets were seen as helpful for practice, some reviewers noted they could be more challenging or varied.

Problem sets are helpful for practice.

"The problem sets were useful for applying what I learned from the videos."

"Liked that there were walkthroughs provided for the practice problems."

"The problems helped reinforce the concepts taught in each section."

Ideal starting point for learning statistics basics.

"Perfect for someone like me starting from scratch with no prior stats knowledge."

"A great introduction to the subject for absolute beginners."

"If you're struggling with introductory material, this is a helpful place to begin."

Explanations for foundational topics are clear.

"The early modules on basic probability and descriptive statistics were very clear and easy to follow."

"Concepts were explained in an easy-to-understand way, especially the fundamentals."

"Really helped solidify my understanding of the basics before moving on."

Advanced topics coverage could be improved.

"The sections on regression and multiple regression felt rushed and less clear than the beginning."

"Needed outside resources to fully grasp the later concepts presented."

"Wish there was more detailed coverage of the advanced topics covered at the end."

May not be sufficient for full academic courses.

"Good intro, but definitely not enough depth to pass my university statistics class."

"Wish it went into more detail on later topics like hypothesis testing and regression."

"Felt too basic once I got past the initial concepts and needed more advanced content."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Workshop in Probability and Statistics with these activities:

Review Z-Scores and Probability Functions

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Review Z-Scores and Probability Functions to solidify foundational prequisites and refresh comprehension of these key statistical concepts.

Browse courses on Statistics

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Go to Z-Score and Probability Function resource materials from previous statistics course.
Complete practice problems to apply Z-Score / Probability Function concepts.
Take an online quiz or test on Z-Scores / Probability Functions.

Work through Probability Theory Tutorial

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Working through the Probability Theory tutorial will help you gain a deeper understanding of the fundamental principles of probability.

Browse courses on Probability Theory

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Find a reputable Probability Theory tutorial online or in a textbook.
Read through the tutorial and make notes on the key concepts.
Complete any practice problems or exercises that are included in the tutorial.

Solve Probability Practice Problems

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Solving probability practice problems will help you improve your problem-solving skills and reinforce your understanding of the concepts.

Browse courses on Probability

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Find a set of probability practice problems online or in a textbook.
Attempt to solve the problems on your own.
Check your answers and review the solutions to identify any areas where you need to improve your understanding.

Four other activities

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Show all seven activities

Attend a Probability Workshop

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A Probability Workshop can provide you with structured, in-person guidance and allow you to learn from others in a collaborative environment

Browse courses on Probability

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Find a reputable Probability workshop.
Register for the workshop and attend all sessions.
Participate actively in the discussions and exercises.

Write a Blog Post or Article on a Probability Topic

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Creating a blog post or an article on a probability topic will allow you to synthesize your understanding and share your knowledge with others.

Browse courses on Probability

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Choose a topic that you are interested in and that you have a good understanding of.
Research the topic thoroughly and gather credible sources to support your claims.
Write a clear and concise article that explains the topic in a way that is easy to understand.

Tutor Fellow Students in Elementary Probability Concepts

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Mentoring others will help you strengthen your understanding of probability and reinforce your own learning.

Browse courses on Probability

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Identify fellow students who would benefit from your help.
Offer to tutor them and commit to providing them with regular support.
Prepare lessons and activities that will help them understand probability concepts.
Meet with your students regularly to work through problems and answer their questions.

Contribute to the Probability and Statistics Open Source Project

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Contributing to a probability and statistics open source project will allow you to apply your skills in a real-world setting and contribute to the broader community.

Browse courses on Probability

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Find a reputable open source project that is related to probability or statistics.
Join the project and familiarize yourself with its codebase.
Identify areas where you can contribute your skills and make a meaningful contribution.

Career center

Learners who complete Workshop in Probability and Statistics will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

A Quantitative Analyst is a financial professional who uses mathematics and statistics to analyze financial data. They develop and use models to predict the performance of stocks, bonds, and other financial instruments. This course can help you develop the skills you need to be a successful Quantitative Analyst by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Quantitative Analyst

Machine Learning Engineer

A Machine Learning Engineer is a professional who develops and deploys machine learning models. They work with data scientists to identify business problems that can be solved using machine learning, and then develop and implement models that can solve those problems. This course can help you develop the skills you need to be a successful Machine Learning Engineer by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Machine Learning Engineer

Data Scientist

A Data Scientist is a professional who uses data to solve business problems. They use a variety of techniques, including machine learning and artificial intelligence, to analyze data and identify patterns. This course can help you develop the skills you need to be a successful Data Scientist by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

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Risk Analyst

A Risk Analyst is a professional who identifies, assesses, and manages risks. They work in a variety of industries, including finance, insurance, and healthcare. This course can help you develop the skills you need to be a successful Risk Analyst by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Risk Analyst

Actuary

An Actuary is a financial professional who uses mathematics and statistics to assess the financial risks of insurance companies. They develop and use models to calculate the probability of events such as death, disability, and property damage. This course can help you develop the skills you need to be a successful Actuary by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Actuary

Market Researcher

A Market Researcher is a professional who conducts research to gather information about consumer behavior and market trends. They use a variety of research methods, including surveys, interviews, and experiments, to collect data that can help businesses make informed decisions. This course can help you develop the skills you need to be a successful Market Researcher by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

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Statistician

A Statistician is a scientist who uses mathematics to collect, analyze, interpret, and present data. They work in a variety of industries, including healthcare, finance, and government. This course can help you develop the skills you need to be a successful Statistician by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Statistician

Operations Research Analyst

An Operations Research Analyst is a professional who uses mathematics and statistics to improve the efficiency of business operations. They develop and use models to optimize processes, reduce costs, and improve customer satisfaction. This course can help you develop the skills you need to be a successful Operations Research Analyst by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Operations Research Analyst

Data Engineer

A Data Engineer is a professional who builds and maintains the infrastructure that is used to store and process data. They work with a variety of technologies to ensure that data is available to users when and where they need it. This course can help you develop the skills you need to be a successful Data Engineer by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis. This knowledge can be helpful for developing data pipelines that are efficient, reliable, and scalable.

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Database Administrator

A Database Administrator is a professional who manages and maintains databases. They work with a variety of database technologies to ensure that data is stored and processed efficiently and securely. This course can help you develop the skills you need to be a successful Database Administrator by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis. This knowledge can be helpful for developing databases that are efficient, reliable, and scalable.

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Financial Analyst

A Financial Analyst is a professional who provides financial advice to individuals and businesses. They use a variety of analytical techniques to evaluate financial data and make recommendations for investment decisions. This course can help you develop the skills you need to be a successful Financial Analyst by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

See salaries and explore the career path for Financial Analyst

Data Analyst

A Data Analyst is a business professional who uses data to help businesses make informed decisions. They collect, clean, and analyze data to identify trends and patterns. This course can help you develop the skills you need to be a successful Data Analyst by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis. This course may also be useful for Data Analysts who want to learn more about advanced statistical techniques.

See salaries and explore the career path for Data Analyst

Business Analyst

A Business Analyst is a professional who uses data to help businesses make better decisions. They work with stakeholders to identify business needs, collect and analyze data, and develop recommendations for improvement. This course can help you develop the skills you need to be a successful Business Analyst by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis.

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Software Engineer

A Software Engineer is a professional who designs, develops, and maintains software applications. They work with a variety of programming languages and technologies to create software that meets the needs of users. This course can help you develop the skills you need to be a successful Software Engineer by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis. This knowledge can be helpful for developing software that is efficient, reliable, and user-friendly.

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Web Developer

A Web Developer is a professional who designs and develops websites. They work with a variety of programming languages and technologies to create websites that are visually appealing, functional, and user-friendly. This course can help you develop the skills you need to be a successful Web Developer by providing you with a strong foundation in probability and statistics. You will learn how to collect, clean, and analyze data, as well as how to interpret the results of your analysis. This knowledge can be helpful for developing websites that are efficient, reliable, and user-friendly.

See salaries and explore the career path for Web Developer