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! 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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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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Introduction Welcome to the Data Science and A.I. Lecture Series presented by PostNetwork Academy. In this session, we’ll focus on key statistical concepts: moments about the mean, skewness, and kurtosis. These concepts are essential in understanding data distribution characteristics and play a significant role in data science, artificial intelligence, and statistical analysis. In this
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Relation Between Moments About Mean and Arbitrary Point By Bindeshwar Singh Kushwaha Data Science and A.I. Lecture Series – PostNetwork Academy Reach PostNetwork Academy Website: PostNetwork Academy YouTube Channel: PostNetwork Academy Facebook Page: PostNetwork Academy LinkedIn Page: PostNetwork Academy Relation Between Moments About Mean and Arbitrary Point The \(r\)th moment about the mean is given
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Understanding Kurtosis Data Science and AI Lecture Series Introduction Welcome to our Data Science and AI lecture series at PostNetwork Academy! In this post, we’ll break down the concept of kurtosis, a crucial statistical measure that helps us understand the shape of data distributions. Whether you’re a beginner or looking to refresh your
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Understanding Skewness: An Essential Concept in Data Science Welcome to the Data Science and AI Lecture Series by PostNetwork Academy! In this blog post, we’ll dive deep into the concept of skewness, a critical aspect of understanding data distribution in statistics. Whether you’re a beginner or an advanced learner, this post will help clarify the
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Understanding Quartile Deviation: Step-by-Step Calculation & Visualization Quartile deviation, also known as the semi-interquartile range, is a useful measure in statistics that helps to understand the spread or dispersion of the middle 50% of a dataset. This post explains how to calculate quartile deviation using a sample dataset, and how to visualize it on
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Data Science and A.I. Lecture Series: Computing the 70th Percentile Welcome to our Data Science and A.I. lecture series! In this post, we’ll cover a fundamental concept in statistics – percentiles. Specifically, we’ll learn how to compute the 70th percentile, or P70, for a grouped data set. Understanding Percentiles Percentiles divide a data set
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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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