Probability and Statistics 1: The Complete Guide from Udemy

I know, Probability and Statistics is difficult. But is there a way to make it easy? Of course. I for one managed that.

I know a lot of people struggle with it; a very small group of people are good at it. Back in university, I was in that bigger group, the group that struggled through Probability and Statistics lecture. I needed help; I couldn't understand a thing, but I finally found help and turned my exam result around. I guess since you're looking at this, you need help too.

This 6-hour It's packed with videos that have been categorised into different topics, hence easy for you to learn.

I've included lots of definitions, theorems, quizzes, examples, concise notes for EVERY single section, exercises, and a walkthrough of all the exercise sheets. Most importantly, I've done a BONUS section for you. It includes some additional questions that will strengthen your skill even more.

With this basic Probability and Statistics course, you will have a good core understanding to pursue many more difficult Mathematics topic. In this course, everything has been broken down into a simple structure to make learning and understanding easy for you.

This COMPLETE guide is for those of you are looking to get a full understanding of the basics; the important parts. You've already shown half of your determination by looking at the course, so if this course sounds right for you, boost your eagerness to learn and join me on this journey.

Tips:

1) It will be very useful if you also take notes of your own as you're watching the lectures, it will help you understand everything better and quicker. Just pause if I move on to other topics too fast or if you haven't fully understood the previous sub-topic before you move on to the next parts.

2) Please ask any questions you may have in the Q&A section if you don't understand. It's one thing to not understand it, but it's a whole new experience and a very important thing to do when learning Maths to be able to discuss it with fellow students who are going through the same thing.

3) Use headphones for better sound. (I suggest you turn the volume up)

4) Don't forget you can always slow down or speed up the video.

What's inside

Learning objectives

Representation and characterisation of data
Elementary probability theory
Combinatorics
Rules for computing probabilities
Conditional probability and independence of events
Discrete random variables and their probability distributions
Expectation value of a discrete random variable
Examples of discrete random variables
Moment generating functions
Continuous random variables and their probability distributions
Expectation value of a continuous random variable

Examples of continuous random variables
Chebyshev's theorem
Bivariate probability distributions
Expectations of functions of random variables
Covariance
Independent random variables
Sums of independent random variables
Hypothesis testing
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Representation and characterisation of data
Elementary probability theory
Combinatorics
Rules for computing probabilities
Conditional probability and independence of events
Discrete random variables and their probability distributions
Expectation value of a discrete random variable
Examples of discrete random variables
Moment generating functions
Continuous random variables and their probability distributions
Expectation value of a continuous random variable
Examples of continuous random variables
Chebyshev's theorem
Bivariate probability distributions
Expectations of functions of random variables
Covariance
Independent random variables
Sums of independent random variables
Hypothesis testing
Show more
Show less

Syllabus

Introduction

Representation and Characterisation of Data

Quiz 2

Elementary Probability Theory

Questions 1, 2, and 3

Questions 4, 5, 6, and 7

Questions 1 and 2

Questions 3, 4, and 5

Questions 6, 7, and 8

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Covers representation and characterization of data, which are essential first steps in understanding and applying statistical methods to real-world problems

Includes combinatorics, which is a fundamental tool for counting and analyzing the number of possible outcomes in various scenarios

Explores discrete and continuous random variables, which are core concepts for modeling and understanding random phenomena in various fields

Features hypothesis testing, which is a crucial skill for making informed decisions based on data and drawing conclusions about populations

Requires learners to take notes and engage in Q&A, which may be challenging for students who prefer a more passive learning style

Includes a bonus section with extra questions, which provides additional practice and strengthens skills for those seeking a deeper understanding

Reviews summary

Clear and comprehensive probability and statistics basics

According to learners, this course provides a clear and accessible introduction to Probability and Statistics, making a typically difficult subject feel understandable and manageable. Students particularly appreciate the instructor's ability to break down complex topics and the inclusion of useful exercises and solutions that help solidify understanding. It is widely considered a great starting point for beginners looking to build a solid foundation. However, some learners note that the pace might feel slow if they have some prior knowledge, suggesting it is best suited for those with little to no background in the subject.

Pace varies, best for absolute beginners.

"For someone with zero background, the pace is just right."

"I found the pace a bit slow at times because I had some prior exposure."

"It caters very well to those starting fresh, maybe less so for intermediate."

"The course moves deliberately to ensure foundational concepts are solid."

Ideal starting point for new learners.

"If you're completely new to stats, this is the course to start with."

"It built up my understanding from the ground up, exactly what I needed as a beginner."

"This course is perfect for someone who has struggled with P&S before."

"It gave me a strong basic understanding to build upon."

Exercises help practice and reinforce learning.

"The exercises with solutions are really helpful for putting the theory into practice."

"Working through the examples provided helped me confirm my understanding."

"I appreciated the plenty of practice problems included in the course."

"The exercise walkthroughs were great for clarifying any doubts."

Instructor makes complex topics easy to grasp.

"The instructor explains concepts very clearly, which is crucial for a subject like this."

"I finally understand probability thanks to the way he broke it down step by step."

"Complex ideas were made simple and easy to follow throughout the lectures."

"The lectures are easy to digest, making difficult concepts seem straightforward."

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 Probability and Statistics 1: The Complete Guide with these activities:

Review Basic Set Theory

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Strengthen your understanding of set theory, which is foundational for probability and combinatorics.

Browse courses on Set Theory

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Review definitions of sets, subsets, and power sets.
Practice set operations like union, intersection, and complement.
Work through examples involving Venn diagrams.

Review 'Naked Statistics: Stripping the Dread from the Data' by Charles Wheelan

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Gain a more intuitive understanding of statistics through real-world examples and engaging explanations.

View Naked Statistics: Stripping the Dread from the... on Amazon

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Read the chapters relevant to the course topics.
Reflect on the real-world examples provided.
Consider how these concepts apply to your own life.

Review 'Probability and Statistics' by Schaum's Outlines

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Reinforce your understanding of probability and statistics concepts with a comprehensive study guide.

View Schaum's Outline of Probability and Statistics,... on Amazon

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Read the chapters corresponding to the course syllabus.
Work through the solved problems in each chapter.
Attempt the practice exercises and check your answers.

Four other activities

Expand to see all activities and additional details

Show all seven activities

Solve Combinatorics Problems

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Improve your combinatorics skills by solving a variety of problems involving permutations and combinations.

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Find online resources with combinatorics problems.
Solve problems involving permutations and combinations.
Check your solutions and review the concepts.

Create a Probability Cheat Sheet

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Consolidate your knowledge by creating a concise cheat sheet of key probability formulas and concepts.

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Review the key probability formulas and definitions.
Organize the information into a cheat sheet format.
Include examples and explanations for each formula.

Analyze a Real-World Dataset

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Apply your probability and statistics knowledge to analyze a real-world dataset and draw meaningful conclusions.

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Find a publicly available dataset of interest.
Apply statistical techniques to analyze the data.
Interpret the results and draw conclusions.
Write a report summarizing your findings.

Help Others in Online Forums

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Solidify your understanding by helping other students with their probability and statistics questions in online forums.

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Find online forums related to probability and statistics.
Answer questions from other students.
Explain concepts in a clear and concise manner.

Career center

Learners who complete Probability and Statistics 1: The Complete Guide will develop knowledge and skills that may be useful to these careers:

Statistician

Statisticians collect, analyze, and interpret numerical data and quantitative information. They apply statistical theories and methods to provide useful information on a variety of subjects. This introductory Probability and Statistics course provides the groundwork in elementary probability theory, discrete and continuous random variables, probability distributions, and hypothesis testing. These topics are crucial as a statistician examines data. Furthermore, the inclusion of exercises and solutions in the course may help one master the fundamental concepts and methods required to excel as a statistician.

See salaries and explore the career path for Statistician

Data Analyst

A Data Analyst interprets data and turns it into information which can offer ways to improve a business, thus affecting business decisions. The role includes gathering data from various sources, analyzing it, and identifying patterns and trends. This course helps build a foundation in the essential probability and statistics concepts used when making sense of the data and drawing sound conclusions. With the course's coverage of data representation, probability distributions, hypothesis testing, and more, one can obtain the key skills of data analysis.

See salaries and explore the career path for Data Analyst

Business Intelligence Analyst

A Business Intelligence Analyst examines data trends to help companies make better business decisions. The role involves identifying, collecting, and analyzing data to create reports and dashboards that visualize trends and insights. This Probability and Statistics course helps build a foundation in data analysis, as it covers data representation, probability theory, and statistical distributions. Further, the course's section on hypothesis testing may be applicable to A/B testing.

See salaries and explore the career path for Business Intelligence Analyst

Actuary

Actuaries assess and manage financial risks. This role requires strong analytical skills and knowledge of mathematics, statistics, and finance. This Probability and Statistics course provides the tools to excel as an actuary. The course's coverage of probability distributions, expectation value of a random variable, and hypothesis testing may be particularly helpful. With the inclusion of numerous examples and solved exercises, one may be able to master the concepts required for actuarial work.

See salaries and explore the career path for Actuary

Quantitative Analyst

Quantitative Analysts apply mathematical and statistical methods to financial and risk management problems. Typically, this role requires a degree in a quantitative field, sometimes at the graduate level. With its focus on probability, random variables, distributions, expectations, and hypothesis testing, this Probability and Statistics course helps prepare one for the rigors of quantitative analysis. The course's coverage of covariance may be useful in the quantitative analysis of portfolios and risk.

See salaries and explore the career path for Quantitative Analyst

Research Scientist

Research Scientists design and conduct experiments, analyze data, and write reports on their findings. They work in a variety of fields, including medicine, environmental science, and engineering and often hold a graduate degree. With its focus on probability, distributions, and hypothesis testing, this Probability and Statistics course helps build a foundation for scientific research. The course's coverage of bivariate probability distributions may be applicable to the research scientist's work with multivariate data.

See salaries and explore the career path for Research Scientist

Risk Manager

Risk Managers identify and evaluate risks that threaten a company's assets, earning capacity or success. The role involves developing strategies to mitigate these risks and ensure compliance with regulations. This Probability and Statistics course's coverage of probability theory, distributions, and covariance may be useful, as it gives one tools to model and assess risks. The course's section on hypothesis testing may be applicable to evaluating the effectiveness of risk mitigation strategies.

See salaries and explore the career path for Risk Manager

Market Research Analyst

Market Research Analysts study market conditions to examine potential sales of a product or service. This role interprets data on competitor performance and consumer spending habits, and typically requires a bachelor's degree. This introductory Probability and Statistics course helps one understand statistical data. The course's coverage of hypothesis testing may be applicable to A/B testing. The material on representation and characterization of data may be helpful for understanding market research information.

See salaries and explore the career path for Market Research Analyst

Biostatistician

Biostatisticians develop and apply statistical methods to address problems in biology, medicine, and public health. This role typically requires a graduate degree. With its focus on probability and statistical concepts, the Probability and Statistics course may be useful in pursuing biostatistics. The course's material on bivariate probability distributions may be applicable to the modeling of biomedical data. Furthermore, the course includes content on hypothesis testing.

See salaries and explore the career path for Biostatistician

Data Scientist

Data Scientists analyze large datasets to extract knowledge and insights that may help guide decision-making. This role requires a strong foundation in statistics, machine learning, and programming. This course may be useful in pursuing data science, as it provides coverage of statistical topics. The course's material on bivariate probability distributions, covariance, and hypothesis testing may be applicable to the data scientist's work with data.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers design, research and create self-running artificial intelligence systems. This role develops algorithms and programming to enable machines to act without being specifically directed. This Probability and Statistics course may be useful, as it covers foundational statistical concepts such as probability theory, random variables, and distributions. The course's inclusion of combinatorics and moment generating functions may help in understanding machine learning models. The material on hypothesis testing may be valuable for evaluating model performance.

See salaries and explore the career path for Machine Learning Engineer

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to improve efficiency and effectiveness in organizations. This role involves analyzing data, developing models, and providing recommendations. With its focus on probability and statistical concepts, this Probability and Statistics course provides some of the tools required for operations research. The course's material on independent random variables may be applicable to the modeling of operational systems.

See salaries and explore the career path for Operations Research Analyst

Economist

Economists study the production and distribution of resources, goods, and services by collecting and analyzing data, researching trends, and evaluating economic issues. This role often requires a graduate degree. This Probability and Statistics course may be useful for economists, as it covers statistical distributions, expectations, covariance, and hypothesis testing. These techniques may allow an economist to analyze economic data and build econometric models.

See salaries and explore the career path for Economist

Financial Analyst

Financial Analysts provide guidance to businesses and individuals making investment decisions. This role assesses the performance of stocks, bonds, and other investments, and typically requires a bachelor's degree in a related field. This Probability and Statistics course may be useful, as it helps one understand financial data. The course's coverage of expectations and covariance may be applicable to analyzing investment portfolios. Furthermore, the inclusion of hypothesis testing may help in the making of informed financial decisions.

See salaries and explore the career path for Financial Analyst

Consultant

Consultants are hired by companies to provide expert advice and help solve problems. This role requires strong analytical and communication skills. This Probability and Statistics course may be applicable. The course's coverage of data representation, probability theory, and hypothesis testing may be useful for consultants who work with data-driven projects. The course's material on representation and characterization of data may be helpful when a consultant makes business strategy recommendations at the highest level.

See salaries and explore the career path for Consultant

Probability and Statistics 1

The Complete Guide

What's inside

Learning objectives

Syllabus

Traffic lights

Save this course

Reviews summary

Clear and comprehensive probability and statistics basics

Activities

Career center

Reading list

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