Machine Learning

Classical or Mathematical Probability Examples

Classical or Mathematical Probability Examples Data Science and A.I. Lecture Series   What You Will Learn The definition and basic concepts of probability. Examples of classical probability problems. Application of probability rules such as complements and odds. Step-by-step solutions to real-world probability problems. Introduction Probability is the study of uncertainty. It provides tools to measure […]

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Classical or Mathematical Probability

  Classical or Mathematical Probability Introduction to Probability   Welcome to PostNetwork Academy! This article explains the fundamentals of Classical or Mathematical Probability, including definitions, examples, key characteristics, and limitations. What You Will Learn The definition of Classical Probability and its core formula. Key properties and assumptions of Classical Probability. Examples: Tossing a coin and

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Exhaustive, Favourable, Mutually Exclusive, and Equally Likely Cases

  Master Probability Concepts: Exhaustive, Favourable, Mutually Exclusive, and Equally Likely Cases Welcome to the Data Science and AI Lecture Series brought to you by PostNetwork Academy. What Will We Learn? Exhaustive Cases: Understanding the total number of outcomes in a random experiment. Favourable Cases: Identifying outcomes that lead to the occurrence of an event.

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Deterministic to Random: The Role of Probability in AI and Data Sc.

  Deterministic to Random: The Role of Probability in AI and Data Science Introduction An experiment refers to an operation or activity that can produce some well-defined outcome(s). Types of experiments: Deterministic Experiments Random (or Probabilistic) Experiments Deterministic Experiments These experiments have a fixed outcome or result, no matter how many times they are repeated

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Independence of Origin and Scale in Correlation Coefficient

Karl Pearson’s Correlation −1≤r(X,Y)≤1

  Prove \( -1 \leq r(X, Y) \leq 1 \) for Karl Pearson’s Correlation Coefficient Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Problem Statement Prove that: \[ -1 \leq r(X, Y) \leq 1 \] The correlation coefficient \( r(X, Y) \) is a measure of the linear relationship between

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Karl Pearson’s Correlation Coefficient Numerical Example

  Karl Pearson’s Correlation Coefficient Learn the step-by-step process of finding the correlation coefficient in statistics. Problem Statement Find the Karl Pearson’s coefficient of correlation between \(X\) and \(Y\) for the given data: \[ \begin{aligned} X &: 6, 2, 4, 9, 1, 3, 5, 8 \\ Y &: 13, 8, 12, 15, 9, 10, 11,

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Independence of Origin and Scale in Correlation Coefficient

Independence of Origin and Scale in Correlation Coefficient

Independence of Origin and Scale in Karl Pearson’s Correlation Coefficient Definition of Correlation Coefficient The correlation coefficient \( r(X, Y) \) is defined as: \[ r(X, Y) = \frac{\text{Cov}(X, Y)}{\sqrt{\text{Var}(X) \cdot \text{Var}(Y)}}. \] Covariance: \[ \text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^n (x_i – \bar{X})(y_i – \bar{Y}) \] Variance of \( X \): \[ \text{Var}(X) = \frac{1}{n}

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Definition and Calculation of The Correlation Coefficient Video

The Definition and Calculation of The Correlation Coefficient Data Science and A.I. Lecture Series   1. Definition of Correlation Coefficient The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is denoted by r, and it ranges from -1 to +1: r = +1: Perfect positive correlation. r =

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Covariance

Covariance: A Numerical Example

  Covariance: A Numerical Example Data Science and A.I. Lecture Series   Problem Statement and Table of Deviations Example: Calculate the covariance between the age of husband and wife of the following seven couples. Data: Age of Husband \( X \): 35, 34, 40, 43, 56, 20, 38 Age of Wife \( Y \): 32,

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Covariance

Covariance Made Simple: Unlocking the Secret of Relationships in Data

  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

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