Statistics

Bayes’ Theorem and Examples | Data Science & AI

  Bayes’ Theorem and Examples Formula The formula for Bayes’ Theorem is given by: $$ P(E_i | A) = \frac{P(E_i) P(A | E_i)}{\sum_{j=1}^{n} P(E_j) P(A | E_j)} $$ Key Terminology \(E_i\) are hypotheses or possible causes. \(P(E_i)\) is the prior probability of \(E_i\). \(P(E_i | A)\) is the posterior probability of \(E_i\). The denominator ensures […]

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Addition and Multiplicative Laws Probability Explained

  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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Probability

Probability of Happening at Least One Independent Event

  Probability of Happening at Least One Independent Event Data Science and A.I. Lecture Series By: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy 1. Probability of Happening at Least One Independent Event If \( A \) and \( B \) are independent events, the probability of happening at least one of the events is: \[ P(A

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Conditional Probability and Multiplicative Law, Independent Events

  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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More on Axiomatic Approach to Probability

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

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,

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