Drawing Balls from a Bag Data Science and AI Lecture Series Problem Statement A bag contains: 4 red balls 5 black balls 2 green balls One ball is drawn at random. Find the probability that: It is a red ball. It is not black. It is green or black. Step 1: Total Balls […]
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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 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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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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Understanding Probability: Sample Space, Sample Points, and Events Sample Space The set of all possible outcomes of a random experiment is called the Sample Space, denoted by \( S \). \( S \) is a set containing all possible outcomes of a random experiment. Examples: Tossing a single coin: \( S = \{H, T\}
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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 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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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
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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 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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