Maths

Different Approaches to Probability Theory

Artificial Intelligence, Mathematics, Maths, Probability and Statistics, Research and Development, Statistics /

Different Approaches to Probability Theory Data Science and AI Lecture Series Author: Bindeshwar Singh Kushwaha   Introduction Classical probability has limitations when outcomes are not equally likely or finite. Alternative approaches are needed in situations where classical definitions fail. This unit introduces methods based on past experiences, observed data, and axioms. Topics discussed include: Relative […]

Different Approaches to Probability Theory Read More »

Probability-Examples-Related-to-Combinations

Probability Examples Related to Combinations

Artificial Intelligence, Counting Principle, Machine Learning, Mathematics, Maths, Permutations and Combinations, Probability and Statistics, Statistics /

Probability Examples Related to Combinations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Example: Drawing Two Cards from a Well-Shuffled Pack of Cards Find the probability of the following scenarios: One red and one black card. Both cards of the same suit. One jack and one king. One red card and one card

Probability Examples Related to Combinations Read More »

Combinations

Theorem Related to Combinations

Artificial Intelligence, Counting Principle, Machine Learning, Mathematics, Maths, Permutations and Combinations, Probability and Statistics, Statistics /

Examples and Theorem Related to Combinations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Theorem: Relationship Between Permutations and Combinations Theorem: The number of permutations of \(n\) different objects taken \(r\) at a time is related to the number of combinations by: \[ P^n_r = C^n_r \cdot r! \] where \(0 < r

Theorem Related to Combinations Read More »

Understand Combinations

Artificial Intelligence, Counting Principle, Machine Learning, Mathematics, Maths, Permutations and Combinations, Probability and Statistics, Statistics /

  Understand Combinations Data Science and A.I. Lecture Series Introduction to Combinations A combination is a selection of items where the order does not matter. Example: Selecting 2 players from a group of 3 players (X, Y, Z). Possible combinations: XY, XZ, YZ. Formula for combinations: \[ \binom{n}{r} = \frac{n!}{r!(n-r)!}, \quad 0 \leq r \leq

Understand Combinations Read More »

Examples of Permutations

Artificial Intelligence, Data Handling, Machine Learning, Mathematics, Maths, Statistics /

  Examples from Permutations Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha, PostNetwork Academy Example 1 How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed? Solution: Total digits: 9 Required 4-digit numbers: \[ P(9, 4) = \frac{9!}{(9-4)!} = 9 \times 8

Examples of Permutations Read More »

Probability

Concept of Odds in Favor and Against

Artificial Intelligence, Data Handling, Machine Learning, Mathematics, Maths, Probability and Statistics, Statistics /

Concept of Odds in Favor and Against Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Concept of Odds Odds in Favor and Against Odds in Favor: Ratio of favorable cases to unfavorable cases:\[ \text{Odds in favor of } A = m : (n – m) \] Odds Against: Ratio of

Concept of Odds in Favor and Against Read More »

probability

Probability Problems based on the Classical Definition of Probability

Artificial Intelligence, Data Handling, Machine Learning, Mathematics, Maths, Probability and Statistics, Statistics /

Probability Problems Based on Classical Definition of Probability Data Science and A.I. Lecture Series   Questions What is the total number of outcomes (sample space)? How do we determine favorable cases? How do probability rules apply to the problem? Example: Throwing Two Dice Find the probability of: A doublet (same number on both dice) Sum

Probability Problems based on the Classical Definition of Probability Read More »

Covariance

Covariance Made Simple: Unlocking the Secret of Relationships in Data

Artificial Intelligence, Data Handling, Machine Learning, Maths, Probability and Statistics, Statistics /

  Covariance Made Simple: Unlocking the Secret of Relationships in Data Welcome to Postnetwork Academy! In this post, Bindeshwar explains the concept of covariance, a fundamental tool in statistics and data science. Covariance helps us understand how two variables move together—whether they increase, decrease, or show no relationship at all. What You’ll Learn in This

Covariance Made Simple: Unlocking the Secret of Relationships in Data Read More »

Covariance Explained: Change of Origin vs. Scale Made Simple!

Artificial Intelligence, Data Handling, Machine Learning, Mathematics, Maths, Probability and Statistics, Research and Development, Statistics /

Covariance Explained: Change of Origin vs. Scale Made Simple! Welcome to PostNetwork Academy’s Data Science and AI Lecture Series! In this post, we’ll explore the mathematical concept of covariance and how it behaves under changes of origin and scale. Let’s break it down step by step. Theorem: Covariance Independence We aim to prove that: Covariance

Covariance Explained: Change of Origin vs. Scale Made Simple! Read More »

Binomial Distribution

Understand Binomial Distribution

Mathematics, Maths, Probability and Statistics, Statistics /

Before understanding Binomial distribution you have to understand Bernoulli trial. What is Bernoulli trial? A Bernoulli trial is a random experiment in which  there are two possible outcomes failure and success getting head when tossing a coin is success and getting tail is failure getting 4 is success when rolling a dice and failure when

Understand Binomial Distribution Read More »

©Postnetwork-All rights reserved.