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Sister site of KDnuggets, Statisticshas a wide range of statistics-related content available, written by experts, content that has been accumulating over a few brief years. We decided to lend a hand our readers become aware of this great source of statistics, math, data science, and programming content by organizing and sharing some of its fantastic tutorials with the KDnuggets community.
Learning statistics can be hard. It can be frustrating. And most of all, it can be confusing. That’s why Statistics is here to lend a hand.
Theoretical Probability: Definition + Examples
Probability is a topic in statistics that describes the likelihood of certain events occurring. When we talk about probability, we often refer to one of two types.
You can remember the difference between theoretical probability and experimental probability by using the following trick:
- The theoretical probability of an event occurring can be calculated theoretically using mathematics.
- The probability of an experimental event occurring can be calculated by directly observing the results of the experiment.
Posterior Probability: Definition + Example
Posterior probability is the updated probability of an event occurring after taking into account up-to-date information.
For example, we may be interested in finding the probability of some event “A” occurring given some event “B” that has just occurred. We can calculate this posterior probability using the following formula:
P(A|B) = P(A) * P(B|A) / P(B)
How to interpret odds ratios
In statistics, probability refers to the chance of an event occurring. It is calculated as follows:
PROBABILITY:
P(event) = (number of desired outcomes) / (number of possible outcomes)
For example, suppose we have four red balls and one green ball in a bag. If you close your eyes and randomly select a ball, the probability that you will select a green ball is calculated as follows:
P(green) = 1 / 5 = 0.2.
The Law of Large Numbers: Definition + Examples
The law of immense numbers states that as the sample size increases, the sample mean approaches its expected value.
The most basic example of this involves flipping a coin. Each time we flip a coin, the probability that it will come up heads is 1/2. So the expected percentage of heads that will come up in an infinite number of flips is 1/2, or 0.5.
Set operations: union, product, complement and difference
A set is a collection of items.
We denote a set with a capital letter, and define the elements in the set with curly braces. For example, suppose we have a set called “A” with elements 1, 2, 3. We would write this as:
A = {1, 2, 3}
This tutorial explains the most popular set operations used in probability theory and statistics.
General Multiplication Rule (Explanation and Examples)
The general rule of multiplication states that the probability of two events A and B occurring can be calculated as follows:
P(A and B) = P(A) * P(B|A)
The vertical bar | denotes “given”. So P(B|A) can be read as “the probability that B occurs, given that A occurs”.
If events A and B are independent, then P(B|A) is simply equal to P(B) and the rule can be simplified to:
P(A and B) = P(A) * P(B)
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Matthew Mayo (@mattmayo13) holds a Master’s degree in Computer Science and a postgraduate diploma in Data Mining. As Managing Editor of KDnuggets & Statisticsand contributing editor at Mastering Machine LearningMatthew aims to make elaborate data science concepts accessible. His professional interests include natural language processing, language models, machine learning algorithms, and exploration of emerging artificial intelligence. He is driven by a mission to democratize knowledge within the data science community. Matthew has been coding since he was 6 years venerable.