Research and Development

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

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: […]

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Understanding Correlation: Simplified Explanation

  Understanding Correlation: A Simplified Explanation Welcome to this post in the Data Science and A.I. Lecture Series by Bindeshwar Singh Kushwaha from PostNetwork Academy! Today, we’ll dive into correlation—a crucial concept in data science and statistics. — What is Correlation? In simple terms, correlation measures the strength and direction of the relationship between two

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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 Explained: Change of Origin vs. Scale Made Simple!

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

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Covariance Simplified: Learn It Once, Understand It Forever! Video #|109 Data Science and A.I.

Covariance Simplified: Learn It Once, Understand It Forever

Covariance Simplified: Learn It Once, Understand It Forever! Covariance measures the relationship between two random variables \(X\) and \(Y\). The formula for covariance is: \[ \text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^n (x_i – \bar{X})(y_i – \bar{Y}) \] Expanding the terms: \[ \text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^n \textcolor{red}{x_i y_i} – \textcolor{green}{x_i \bar{Y}} – \textcolor{blue}{\bar{X} y_i} + \textcolor{red}{\bar{X}

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Bivariate Distribution

Bivariate Distribution Made Simple: From Definition to Covariance Calculation

  Introduction Welcome to the Data Science and AI Lecture Series! In this post, we will simplify the concept of Bivariate Distribution and demonstrate how to calculate Covariance. These are fundamental concepts in statistics for understanding the relationship between two variables. Let’s dive into it! Bivariate Distribution Made Simple: From Definition to Covariance Calculation Author:

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Pearson's Beta and Gamma Coefficients Karl Pearson defined the following coefficients based on the first four central moments:

Calculation of Skewness and Kurtosis using Pearson’s Beta and Gamma Coefficients

  Calculation of Skewness and Kurtosis using Pearson’s Beta and Gamma Coefficients Subtitle: Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Date: December 4, 2024 Contact PostNetwork Academy Website: www.postnetwork.co YouTube Channel: www.youtube.com/@postnetworkacademy Facebook Page: www.facebook.com/postnetworkacademy LinkedIn Page: www.linkedin.com/company/postnetworkacademy Pearson’s Beta and Gamma Coefficients Karl Pearson defined the following coefficients

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Skewness

Measures of Skewness – Data Science and AI Lecture Series

   Measures of Skewness – Data Science and AI Lecture Series In this post, Bindeshwar Singh Kushwaha from PostNetwork Academy explains the concept of  Measures of Skewness. Skewness refers to the lack of symmetry in a data distribution. Understanding skewness is essential in data science and AI, as it helps to interpret the distribution of

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Data Science and A.I. : How to Calculate Percentiles Step-by-Step Guide

  From the Following Data, Compute the Value of P27 Given Data xi 0 1 2 3 4 5 6 7 8 fi 1 9 26 59 72 52 29 7 1 Solution Percentile divides the dataset into 100 equal parts. To compute P27, we use the following formula: Formula: P27 = 27N/100 Given N

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Data Science and A.I. : How to Calculate Percentiles Step-by-Step Guide

Numerical Example to Compute Percentile Given the data set: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, calculate the 30th and 60th percentiles. Percentile Percentiles are those values of the variate which divide the distribution into 100 equal parts, therefore the number of

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