Random Variables and Probability Distributions Introduction to Random Variables In many experiments, we are interested in a numerical characteristic associated with outcomes of a random experiment. A random variable (RV) is a function that assigns a numerical value to each outcome of a random experiment. Example: Consider tossing a fair die twice and defining \( […]
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Problems Using Both Addition and Multiplicative Laws Data Science and A.I. Lecture Series PostNetwork Academy Probability Laws The addition law of probability states: \[ P(A \cup B) = P(A) + P(B) – P(A \cap B) \] The multiplicative law of probability for independent events states: \[ P(A \cap B) = P(A) \cdot P(B) \]
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Conditional Probability and Multiplicative Law Data Science and A.I. Lecture Series Conditional Probability Conditional probability represents the likelihood of an event \( A \), given that another event \( B \) has already occurred. It is defined as: \[ P(A|B) = \frac{P(A \cap B)}{P(B)}, \quad \text{if } P(B) > 0. \] Example: Deck
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Addition Law of Probability and Examples Data Science and A.I. Lecture Series Introduction to Addition Law Statement: For any two events \( A \) and \( B \), the probability of their union is given by: \[ P(A \cup B) = P(A) + P(B) – P(A \cap B) \] This formula calculates the probability
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More on Axiomatic Approach to Probability Data Science and AI Lecture Series By Bindeshwar Singh Kushwaha Statement of the First Proof Prove: \( P(A \cap B^c) = P(A) – P(A \cap B) \) This formula expresses the probability of \( A \) occurring without \( B \). It uses the complement rule and properties of
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Venn Diagrams – Data Science and AI Lecture Series Welcome to our Data Science and AI Lecture Series! In this post, we’ll dive into the world of Venn Diagrams, an essential tool in set theory that simplifies understanding the relationships between sets. Whether you’re studying mathematics, data science, or AI, mastering concepts like intersections, unions,
Subjective Approach to Probability Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha What is the Subjective Approach? The subjective approach to probability is based on personal judgment, intuition, wisdom, and expertise. Unlike the classical or frequency-based approaches, it focuses on individual beliefs about the likelihood of an event. When to Use the
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Different Approaches to Probability Theory Data Science and AI Lecture Series Author: Bindeshwar Singh Kushwaha Introduction Classical probability has limitations when outcomes are not equally likely or finite. Alternative approaches are needed in situations where classical definitions fail. This unit introduces methods based on past experiences, observed data, and axioms. Topics discussed include: Relative
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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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