Probability Theory

  1. Applications of Probability Theory
    1. Risk Assessment
      1. Identifying potential hazards and estimating their probabilities
        1. Quantitative risk analysis techniques
          1. Fault Tree Analysis
            1. Event Tree Analysis
            2. Use of probability in insurance
              1. Actuarial models
                1. Premium calculations
                2. Risk management strategies
                  1. Risk matrices
                    1. Risk-averse vs risk-neutral decisions
                  2. Reliability Engineering
                    1. Predicting system failures
                      1. Failure rate modeling
                        1. Mean time between failures (MTBF)
                        2. Reliability testing and assessment
                          1. Accelerated life testing
                            1. Environmental stress screening
                            2. Reliability block diagrams and fault tree analysis
                              1. Use in product lifecycle management
                              2. Queueing Theory
                                1. Understanding and modeling queuing systems
                                  1. Characteristics of queue structures (FIFO, LIFO, etc.)
                                    1. Single vs multi-server queues
                                    2. Performance metrics
                                      1. Average wait times
                                        1. Queue lengths
                                        2. Applications in telecommunications and network traffic
                                          1. Optimization of service facilities
                                          2. Decision Theory
                                            1. Role of probability in making decisions under uncertainty
                                              1. Decision trees and payoff matrices
                                                1. Principles of expected utility
                                                  1. Multi-criteria decision analysis (MCDA)
                                                  2. Financial Mathematics
                                                    1. Option Pricing Models
                                                      1. Black-Scholes model
                                                        1. Binomial model
                                                        2. Portfolio Theory
                                                          1. Diversification and risk
                                                            1. Capital Asset Pricing Model (CAPM)
                                                            2. Financial derivatives and risk management
                                                              1. Hedging strategies
                                                                1. Use of probabilistic models in market analysis
                                                              2. Statistical Physics
                                                                1. Statistical mechanics and thermodynamics
                                                                  1. Boltzmann distribution
                                                                    1. Partition function
                                                                    2. Probability in predicting physical phenomena
                                                                      1. Random walks and diffusion models
                                                                        1. Applications in materials science and complex systems analysis
                                                                      12. Bayesian Probability
                                                                      First Page
                                                                      14. Advanced Topics in Probability