# Fundamentals of Probability

## Learn about the process of modelling count data using probability distributions with this free online course.

Publisher: NPTEL## Description

Probability theory is vital to the study of action and communication as it quantifies uncertainty regarding the occurrence of events. This course begins by describing the basic concepts and the role of axioms in forming the foundations of the probability theory. You will study the procedure for determining all the possible outcomes of a random experiment using probability methods. In addition to this, you will discover how the sample space becomes the universal set in use for a particular probability experiment. Next, you will be taught about the primary rules associated with basic probability. This will include the application of these probability rules to determine the measure of the likelihood of an event occurring. Following this, you will explore the formula that gives the probability function. The process of describing the probability distribution of a discrete random variable using probability functions is explained. The course describes the procedure for estimating the certainty of an event through an illustrative example of the coin toss probability method.

The probabilities come into play whenever there is uncertainty about the outcomes of an event. However, when you have sufficient knowledge of the prior outcome, how will you predict the likelihood of a forthcoming event or outcome? This leads to one of the quintessential concepts in probability theory known as the ‘conditional probability'. You will discover the relationship between Bayes’ theorem and conditional probability in measuring the probability of getting different evidence or patterns based on the occurrence of the prior event. Following this, you will be taught about the process of distinguishing the differences between independent and dependent events. This will include the significance of tree diagrams in portraying the combinations of two or more events by labeling the branch at the end with its outcome and the probability alongside the line. You will comprehend the process of extending almost all the concepts of portability with conditional probability and the application of independence to any number of events.

Finally, you will study the process of describing the outcome of a statistical experiment in numerical terms. This will include the procedure for computing the probabilities of discrete and continuous random variables. Following this, you will be taught about the statistical measure for quantifying the degree of correlation between two or more random variables. In addition to this, you will explore the method of determining the strength of the relationship between independent and dependent variables. Lastly, you will study a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. Lastly, the procedure for finding the mean of the probability distribution and the primary difference between probability and the probability distribution is also described. ‘Fundamentals of Probability’ is is an informative course aimed at highlighting the various combinatorial analysis used in computing probabilities. This course lays the foundation for learners to develop their interests in more advanced probability topics, such as measure-theoretic perspective, convergences of distributions, and conditional expectations. Enroll in this course and learn about the science of how likely events are to happen.

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