Statistics

Exhaustive, Favourable, Mutually Exclusive, and Equally Likely Cases

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

  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. […]

Exhaustive, Favourable, Mutually Exclusive, and Equally Likely Cases Read More »

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

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

  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

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

Spearman’s Rank Correlation Coefficient

Artificial Intelligence, Data Handling, Probability and Statistics, Research and Development, Statistics /

Spearman’s Rank Correlation Coefficient Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Need for Spearman’s Rank Correlation Coefficient In many cases, the relationship between variables is not linear, making Pearson’s correlation coefficient unsuitable. Spearman’s Rank Correlation measures the strength and direction of a monotonic relationship between two variables. It is

Spearman’s Rank Correlation Coefficient Read More »

Derivation of Correlation Coefficient Property

Artificial Intelligence, Data Handling, Probability and Statistics, Research and Development, Spreadsheet, Statistics /

  Derivation of the Correlation Coefficient Data Science and A.I. Lecture Series   Problem Statement Objective: Derive the formula for the correlation coefficient \( r(X, Y) \): \[ r(X, Y) = \frac{\sigma_X^2 + \sigma_Y^2 – \sigma_{X-Y}^2}{2 \sigma_X \sigma_Y}. \] Definitions: \( \sigma_X^2 \): Variance of \( X \). \( \sigma_Y^2 \): Variance of \( Y

Derivation of Correlation Coefficient Property Read More »

Independence of Origin and Scale in Correlation Coefficient

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

Artificial Intelligence, Data Handling, Machine Learning, Research and Development, Spreadsheet, Statistics /

  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

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

Karl Pearson’s Correlation Coefficient Numerical Example

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

  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,

Karl Pearson’s Correlation Coefficient Numerical Example Read More »

Independence of Origin and Scale in Correlation Coefficient

Independence of Origin and Scale in Correlation Coefficient

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

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}

Independence of Origin and Scale in Correlation Coefficient Read More »

Definition and Calculation of The Correlation Coefficient Video

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

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 =

Definition and Calculation of The Correlation Coefficient Video Read More »

Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality Data Science and A.I.

Artificial Intelligence, Data Handling, Research and Development, Statistics /

Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality   Covariance and Standard Deviation Definitions: Sample Covariance: \[ \text{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^n (X_i – \bar{X})(Y_i – \bar{Y}) \] Sample Standard Deviations: \[ \sigma_X = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (X_i – \bar{X})^2}, \quad \sigma_Y = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (Y_i – \bar{Y})^2} \] Cauchy-Schwarz Inequality The Cauchy-Schwarz inequality states:

Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality Data Science and A.I. Read More »

©Postnetwork-All rights reserved.