Data Science

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. […]

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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

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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

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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,

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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}

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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:

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Understanding Correlation: Simplified Explanation

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

  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

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

  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

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

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