Introduction Fuzzy set theory generalizes classical set theory by allowing degrees of membership. The following fundamental properties hold in fuzzy set theory, just like in classical set theory. These include commutativity, associativity, distributivity, and DeMorgan’s laws. (i) Commutativity Statement: A ∪ B = B ∪ A A ∩ B = B ∩ A Proof: Let […]
Introduction In the field of Artificial Intelligence (AI), especially in rule-based expert systems, inference engines use two major strategies to derive conclusions: Forward Chaining and Backward Chaining. Both methods are applied to derive facts from rules but in opposite directions of reasoning. Forward Chaining Forward chaining is a data-driven inference technique. It starts with the
Introduction First-Order Predicate Logic (FOPL) is a formal system in which statements are expressed using quantifiers, variables, and logical connectives. One of the crucial transformations in FOPL is converting a formula into Prenex Normal Form (PNF), followed by Skolemization when preparing for automated reasoning or theorem proving. Prenex Normal Form (PNF) Prenex Normal Form is
Problem Statement Use the A* (A-Star) algorithm to find the most cost-effective path from Node A to Node J in the given graph. Edge weights represent the cost (distance), and node values represent the heuristic (h(n)) to the goal node (J). Given Graph Structure: Nodes and their heuristics (h): A (10), B (3), C (2),
Q5: Find the most cost-effective path to reach from Node A to Node J using A* Algorithm Read More »
Problem Statement We are given an 8-puzzle problem with a defined start state and goal state. The task is to find the minimum cost path from the start state to the goal state. Start State: 1 2 3 4 8 – 7 6 5 Goal State: 1 4 7 – 8 6 2 3 5
Introduction Artificial Intelligence (AI), Machine Learning (ML), and Deep Learning (DL) are closely related terms but they are not the same. Each concept builds upon the previous one, with AI being the broadest, ML being a subset of AI, and DL being a further subset of ML. Understanding the differences and relationships among these terms
Compare Artificial Intelligence, Machine Learning, and Deep Learning Read More »
Introduction Machine Learning (ML) is a subset of Artificial Intelligence (AI) that enables machines to learn from data and improve their performance without being explicitly programmed. ML techniques can be classified into three main types: Supervised Learning, Unsupervised Learning, and Reinforcement Learning. Each type of learning solves different types of problems and uses distinct methods
Introduction Artificial Intelligence (AI) is a multidisciplinary field that aims to create machines capable of performing tasks that typically require human intelligence. These tasks include reasoning, learning, problem-solving, understanding natural language, perception, and even physical movement. AI is rapidly evolving and is classified based on its functionalities and capabilities. In this answer, we will focus
MECE-102: ADVANCED ECONOMETRIC METHODS Tutor Marked Assignment Course Code: MECE-102 Asst. Code: MECE-102/AST/2024-25 Maximum Marks: 100 Note: Answer all the questions. While questions in Section A carry 20 marks each, those in Section B carry 12 marks each. Section A a) What is simultaneity bias? Explain the conditions required for identification of parameters in a
MECE-102: Advanced Econometric Methods – Assignment Answer Key 2024-25 Read More »
a) ARCH Model (Autoregressive Conditional Heteroskedasticity) The ARCH model, introduced by Robert Engle in 1982, is used to model and forecast time-varying volatility in time series data, especially in financial markets where periods of high and low volatility alternate. Key Features: Conditional heteroskedasticity: The variance of the error term depends on past squared errors. Captures
Write short notes on the following: a) ARCH model b) Granger-causality Read More »
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