5 Questions
What is the Axiomatic definition of Probability?
It is a mathematical concept that defines the likelihood of an event occurring.
Which Probability distribution deals with the number of successful trials?
Binomial Distribution
Interpolation involves the use of ____ to estimate values between known data points.
operators
LU Decomposition is a method to solve linear simultaneous equations using matrices.
True
Match the following numerical integration rules with their description:
Trapezoidal Rule = Approximates the area under the curve by dividing it into trapezoids Simpsons 1/3 Rule = Provides an estimate of the definite integral using quadratic interpolating polynomials
Study Notes
UNIT I: Probability and Probability Distributions
- Introduction to probability
- Axiomatic definition of probability
- Addition Theorem and Multiplication Theorem
- Conditional Probability and Bayes' Theorem with applications
- Random Variable, Probability Mass Function, and Probability Density Function
- Mathematical Expectations of a Random Variable
- Binomial Distribution, Poisson distribution, and Normal Distribution
UNIT II: Interpolation and Non-Linear Equations
- Operators: Shift, Forward Difference, Backward Difference and their interrelation
- Interpolation Formulae: Newton's Forward, Backward, and Divided difference Formulae
- Lagrange's Formula
- Solutions of Non-Linear Equations: Bisection Method, False Position Method, and Newton-Raphson Method
UNIT III: Linear Simultaneous Equations and Numerical Calculus
- Solution of Linear Simultaneous Equations: Gaussian Elimination Method with and without Row Interchange
- LU Decomposition: Gauss-Jacobi and Gauss-Seidel Method
- Gauss-Jordan Method and finding Inverse of a Matrix using this Method
- Numerical Differentiation: First and Second Order Derivatives at Tabular and Non-Tabular Points
- Numerical Integration: Trapezoidal Rule, Simpson's 1/3 Rule
UNIT IV: Linear Programming and Transportation Problem
- Linear Programming: formulation of linear Programming model
- Graphical Method of solving linear Programming problem
- Simplex Method (Maximization and Minimization)
- Transportation Problem: general structure, solution procedure, and methods for finding initial solution
- Test for optimality, Maximization of transportation problem, unbalanced transportation problem
- Assignment Problem: approach of the assignment model, solution methods, maximization, unbalanced assignment problem, and restriction on assignment
Quiz on probability and probability distributions, covering introduction, theorems, and applications of probability, as well as random variables and distributions.
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