Advanced Engineering Mathematics Probability and Statistics-1 Random Variables: Discrete: Countable outcomes. Continuous: Measurable outcomes. Probability Basics: Probability Distribution Function: Describes likelihood. Mathematical Expectations: Mean and variance. Probability and Statistics-2 Distributions: Binomial: Success/failure scenarios. Poisson: Events in fixed intervals. Normal: Bell-shaped curve. Uniform: Equal likelihood for all. Exponential: Time between events. Correlation and Regression: Correlation Coefficients: Measure relationships. Regression: Predicting one variable based on another. Optimization Techniques-1 Basics: Historical Development: Evolution of optimization. Engineering Applications: Real-world uses. Single and Multi-variable Optimization: Constraints: Conditions on variables. Equality and Inequality Constraints. Optimization Techniques-2 Linear Programming: Introduction: Basics of linear programming. Methods: Simplex, Big-M, Two Phase. Duality: Dual solu...
