Johns Hopkins University
Foundations of Probability and Random Variables
Johns Hopkins University

Foundations of Probability and Random Variables

Ian McCulloh

Instructor: Ian McCulloh

Gain insight into a topic and learn the fundamentals.
Intermediate level

Recommended experience

49 hours to complete
3 weeks at 16 hours a week
Flexible schedule
Learn at your own pace
Gain insight into a topic and learn the fundamentals.
Intermediate level

Recommended experience

49 hours to complete
3 weeks at 16 hours a week
Flexible schedule
Learn at your own pace

What you'll learn

  • Master combinatorial techniques, including permutations, combinations, and multinomial coefficients, to solve counting and probability problems.

  • Apply probability axioms, construct Venn diagrams, and calculate sample space sizes to evaluate probabilities in various scenarios.

  • Utilize Bayes' formula, the multiplication rule, and conditional probability to assess event relationships and solve real-world problems.

  • Analyze discrete and continuous random variables using probability density functions, cumulative distribution functions, and expected values.

Details to know

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Recently updated!

October 2024

Assessments

21 assignments

Taught in English

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This course is part of the Statistical Methods for Computer Science Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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There are 6 modules in this course

This course provides a comprehensive introduction to fundamental concepts in probability and statistics, focusing on counting principles, permutations, combinations, and multinomial coefficients. Students will explore probability axioms, conditional probabilities, and Bayes’s Formula while using Venn diagrams to visualize events. The course covers random variables, including discrete and continuous types, expected values, and various probability distributions. Practical applications in R programming and data analysis tools will enhance understanding through simulations and real-world problem-solving. By the end, students will be equipped to analyze and interpret statistical data effectively.

What's included

2 readings1 plugin

This module covers the usefulness of an effective method for counting the number of ways that things can occur. Many problems in probability theory can be solved simply by counting the number of different ways that a certain event can occur.

What's included

9 videos2 readings3 assignments1 ungraded lab

This module introduces the concept of the probability of an event and then shows how probabilities can be computed in certain situations.

What's included

9 videos3 readings4 assignments1 ungraded lab

This module explores one of the most important concepts in probability theory, that of conditional probability. The importance of this concept is twofold. First, we are often interested in calculating probabilities when some partial information concerning the result of an experiment is available; in such a situation, the desired probabilities are conditional. Second, even when no partial information is available, conditional probabilities can often be used to compute the desired probabilities more easily.

What's included

9 videos3 readings4 assignments1 ungraded lab

This module discusses the function of outcomes rather than the actual outcomes themselves. In particular, we examine random variables that can take on at most a countable number of possible values. We call these types of variables, discrete random variables.

What's included

9 videos4 readings5 assignments1 ungraded lab

This module extends the concept of random variables where the outcomes cannot be counted. We explore probability density functions, cumulative distribution functions, the normal distribution and other common distributions.

What's included

10 videos4 readings5 assignments1 ungraded lab

Instructor

Ian McCulloh
Johns Hopkins University
8 Courses186 learners

Offered by

Recommended if you're interested in Probability and Statistics

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