Essential Definitions in Probability Theory that You Need to Know
In this post, we are going to walk through the Essential Definitions in Probability Theory. Understanding these concepts is critical to comprehend further advanced concepts in probability theory. Here, you will learn:
- The key concepts such as random variables and conditional probabilities.
- You gain knowledge about how these notions are related.
Random Variables
The random variable is one of the essential definitions in probability theory. In probability theory, the outcomes of a random phenomenon determine the random variable values. In other words, a random variable is a variable that its values are determined with a random event. We should be able to measure a random variable that provides the capability to assign probabilities to its possible values. The domain of a random variable is the sample space. For example, in the case of having a dice, only six possible outcomes are considered, as {1,2,3,4,5,6}.
Conditional probability
One of the essential definitions in probability theory is the conditional probability. This is because a lot of events depends on other precedent events or available partial information. Recognizing and calculating this dependency can lead to a more precise probability estimation. As below figure, how many layers should you wear, depends on the weather!!
The mathematical formulation of the conditional probability of two events is as below:
Bayes’ Rule
The above special case can be extended to the below more general rule called the Bayes’ rule.
The concept of independence
Conclusion
In a previous post, you learned about what is probability and some mathematical background. In this post, you acquire knowledge about the fundamentals of probability theory and its key concepts. What you learned so far, aimed to prepare you to utilize probability notions and further strengthen your background for more advanced probabilistic concepts in Machine Learning. Do you have any questions or suggestions? Feel free to comment and share your point of view.
Originally published at https://www.machinelearningmindset.com on February 9, 2020.
