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# Probability: Basic Concepts & Discrete Random Variables

### Overview

Our capacity to collect and store data has exponentially increased, but deriving information from data from a scientific perspective requires a foundational knowledge of probability.

Are you interested in a career in the emerging data science field, or as an actuarial scientist? Or want better to understand statistical theory and mathematical modeling?

In this statistics and data analysis course, we will provide an introduction to mathematical probability to help meet your career goals in the exciting new areas becoming known as information science.

In this course, we will first introduce basic probability concepts and rules, including Bayes theorem, probability mass functions and CDFs, joint distributions and expected values.

Then we will discuss a few important probability distribution models with discrete random variables, including Bernoulli and Binomial distributions, Geometric distribution, Negative Binomial distribution, Poisson distribution, Hypergeometric distribution and discrete uniform distribution.

To continue learning about probability, enroll in Probability: Distribution Models & Continuous Random Variables, which covers continuous distribution models, central limit theorem and more.

The Center for Science of Information, a National Science Foundation Center, supports learners by offering free educational resources in information science.

### Syllabus

Unit 1: Sample Space and Probability
Introduction to basic concepts, such as outcomes, events, sample spaces, and probability.

Unit 2: Independent Events, Conditional Probability and Bayes’ Theorem
Introduction to independent events, conditional probability and Bayes’ Theorem with examples.

Unit 3: Random Variables
Random variables, probability mass functions and CDFs, joint distributions.

Unit 4: Expected Values
In this unit, we will discuss expected values of discrete random variables, sum of random variables and functions of random variables with lots of examples.

Unit 5: Models of Discrete Random Variables I
Bernoulli and Binomial random variables; Geometric random variables; Negative Binomial random variables.

Unit 6: Models of Discrete Random Variables II
Poisson random variables; Hypergeometric random variables; discrete uniform random variables and counting.

Mark D. Ward

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