Examples from Permutations Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha, PostNetwork Academy Example 1 How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed? Solution: Total digits: 9 Required 4-digit numbers: \[ P(9, 4) = \frac{9!}{(9-4)!} = 9 \times 8 […]
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Permutations and Their Theorems Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Theorem 1: Permutations of Distinct Objects The number of permutations of n different objects taken r at a time is: \[ P(n, r) = \frac{n!}{(n-r)!} \] Explanation: First position: n choices. Second position: n-1 choices. Continue until the
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Understanding Permutations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha PostNetwork Academy Introduction to Permutations A permutation is an arrangement of objects in a specific order. The order of arrangement is crucial in permutations. Example: Arranging the letters of the word “ABC”. Total permutations = $3! = 6$. Key Formula for Permutations The
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Concept of Odds in Favor and Against Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Concept of Odds Odds in Favor and Against Odds in Favor: Ratio of favorable cases to unfavorable cases:\[ \text{Odds in favor of } A = m : (n – m) \] Odds Against: Ratio of
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Probability Problems Based on Classical Definition of Probability Data Science and A.I. Lecture Series Questions What is the total number of outcomes (sample space)? How do we determine favorable cases? How do probability rules apply to the problem? Example: Throwing Two Dice Find the probability of: A doublet (same number on both dice) Sum
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Probability Problem: Throwing a Fair Die Data Science and A.I. Lecture Series Problem Statement A fair die is thrown. Find the probability of: A prime number An even number A number multiple of 2 or 3 A number multiple of 2 and 3 A number greater than 4 Step 1: Sample Space Sample Space:
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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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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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Covariance Explained: Change of Origin vs. Scale Made Simple! Welcome to PostNetwork Academy’s Data Science and AI Lecture Series! In this post, we’ll explore the mathematical concept of covariance and how it behaves under changes of origin and scale. Let’s break it down step by step. Theorem: Covariance Independence We aim to prove that: Covariance
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Introduction Welcome to the Data Science and A.I. Lecture Series presented by PostNetwork Academy. In this session, we’ll focus on key statistical concepts: moments about the mean, skewness, and kurtosis. These concepts are essential in understanding data distribution characteristics and play a significant role in data science, artificial intelligence, and statistical analysis. In this
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