Probability Problem: Tossing Three Unbiased Coins Data Science and A.I. Lecture Series Problem Statement Three unbiased coins are tossed simultaneously. Find the probability of: At least two heads At most two heads All heads Exactly one head Exactly one tail Step 1: Sample Space The sample space \(S\) for tossing three unbiased coins is: […]
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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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See Also: How to Compute Quartiles from Given Data Understand Binomial Distribution Poisson Distribution as a Limiting Case of Binomial Distribution Binomial Distribution in Probability and Statistics Binomial Distribution in Statistics
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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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