Model Question paper GNEST305 AI and Data Science

 

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GNEST305 Introduction to Artificial Intelligence and Data Science KTU BTech S3 2024 Scheme - Dr Binu V P

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Bayes’ Theorem

  Bayes’ Theorem – Statement and Formula Bayes’ Theorem is a way to update our beliefs based on new evidence. Given events A A  and B B , where P ( B ) > 0 P(B) > 0 : P ( A ∣ B ) = P ( B ∣ A ) ⋅ P ( A ) P ( B ) \boxed{P(A \mid B) = \frac{P(B \mid A) \cdot P(A)}{P(B)}} ​ ​ More generally , Let E 1 , E 2 , … , E n E_1, E_2, \ldots, E_n  be mutually exclusive and exhaustive events (i.e., they partition the sample space), and let A A  be any event such that P ( A ) > 0 P(A) > 0 . Then the posterior probability of event E i E_i  given A A  is: P ( E i ∣ A ) = P ( E i ) ⋅ P ( A ∣ E i ) ∑ j = 1 n P ( E j ) ⋅ P ( A ∣ E j ) \boxed{ P(E_i \mid A) = \frac{P(E_i) \cdot P(A \mid E_i)}{\sum_{j=1}^n P(E_j) \cdot P(A \mid E_j)} } ​ ​ 📌 Terminology Term Meaning P ( E i ) P(E_i)                          Prior probability – belief before observing A P ( A ∣ E i ) P(A \mid E_i) ...
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Introduction to Probability

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When an experiment is repeated under similar and controlled conditions , we typically come across two types of situations: The outcome is unique or certain. The outcome is not unique and may vary. Deterministic Events These are events where the outcome is predictable with certainty if the initial conditions are known. The same conditions always produce the same result. Examples: Calculating the area of a rectangle when length and breadth are known. Water boiling at 100°C under normal atmospheric pressure. A ball dropped from a height in a vacuum will fall due to gravity. Probabilistic Events These are events where the outcome is uncertain and may vary even under the same conditions. We can only estimate the chances of each possible result. Examples: Tossing a fair coin (Outcome: Heads or Tails, each with 0.5 probability). Rolling a die (Possible outcomes: 1 to 6). Predicting tomorrow's weather (e.g., 70% chance of rain). Definitions of Various ...
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