Probability_and_Distributions_Updated.pptx

This presentation basically tells us how the probability and probability distributions is applied on mathematics and computer science

1. Probability and Probability Distributions Presented by: [Your Name] BSc Computer Science

2. Introduction to Probability - Probability quantifies uncertainty. - It is the foundation of statistics, AI, and real-world decision-making. - Probability is the likelihood of an event occurring, measured between 0 and 1.

3. Basic Probability Concepts - Sample Space (S): Set of all possible outcomes. - Event (E): A subset of the sample space. - Probability of Event: P(E) = Favorable outcomes / Total outcomes. - Probability Rules: Complement, Addition, Multiplication Rules.

4. Types of Probability - Classical Probability: Based on equally likely outcomes. - Empirical Probability: Based on experimental data. - Subjective Probability: Based on personal judgment.

5. Probability Distributions - A function that gives probabilities for different outcomes. - Types: • Discrete Probability Distributions • Continuous Probability Distributions

6. Discrete Probability Distributions - Deals with countable outcomes. - Examples: • Binomial Distribution: Models number of successes in repeated trials. • Poisson Distribution: Models rare event occurrences in a fixed interval.

7. Continuous Probability Distributions - Deals with continuous outcomes. - Examples: • Normal Distribution: Bell-shaped, used in natural and social sciences. • Exponential Distribution: Models time between events in a Poisson process.

8. Applications of Probability - Science & Engineering: Weather forecasting, AI, and quantum mechanics. - Finance: Risk assessment, stock market predictions. - Medicine: Disease prediction, drug testing.

9. Summary - Probability measures uncertainty. - Types: Classical, empirical, subjective. - Distributions: Discrete (Binomial, Poisson), Continuous (Normal, Exponential). - Applications in various fields.

10. Questions? Feel free to ask!

11. Bayes' Theorem - A fundamental rule for conditional probability. - Formula: P(A|B) = [P(B|A) * P(A)] / P(B). - Used in spam filtering, medical diagnosis, and AI.

12. Law of Large Numbers - As the number of trials increases, the observed probability converges to the theoretical probability. - Ensures stability in long-term predictions. - Important in gambling, insurance, and data science.

13. Central Limit Theorem (CLT) - The distribution of the sample mean approaches a normal distribution as sample size increases. - Key concept in inferential statistics. - Basis for hypothesis testing and confidence intervals.

14. Hypothesis Testing & p-Value - Hypothesis testing helps in decision-making. - Null Hypothesis (H₀): No effect or difference. - Alternative Hypothesis (H₁): Significant effect or difference. - p-Value: Probability of obtaining observed results under H₀.