# Textbook: MA202 Probability Distributions, Transforms and Numerical Methods

Syllabus :-

Module 1
Discrete Probability Distributions. (Relevant topics insection 4.1,4,2,4.4,4.6 Text1 )
Discrete Random Variables, Probability distribution function,
Cumulative distribution function.Mean and Variance of Discrete Probability Distribution. Binomial Distribution-Mean and variance. Poisson Approximation to the Binomial Distribution. Poisson distribution-Mean and variance.

Module 2
Continuous Probability Distributions. (Relevant topics in section 5.1,5.2,5.5,5.7 Text1)
Continuous Random Variable, Probability density function,Cumulative density function, Mean and variance. Normal Distribution, Mean and variance (without proof). Uniform Distribution.Mean and variance. Exponential Distribution, Mean and variance.

Module 3
Fourier Integrals and transforms. (Relevant topics in section 11.7, 11.8, 11.9 Text2)
Fourier Integrals. Fourier integral theorem (without proof). Fourier Transform and inverse transform. Fourier Sine & Cosine Transform, inverse transform.

Module 4
Laplace transforms. (Relevant topics in section6.1,6.2,6.3,6.5,6.6 Text2)
Laplace Transforms, linearity, first shifting Theorem.Transform of derivative and Integral, Inverse Laplace transform, Solution of ordinary differential equation using Laplace transform. Unit step function, second shifting theorem. Convolution Theorem (without proof). Differentiation and Integration of transforms.

Module 5
Numerical Techniques.( Relevant topics in section.19.1,19.2,19.3 Text2)
Solution Of equations by Iteration, Newton- Raphson Method. Interpolation of Unequal intervals-Lagrange’s Interpolation formula. Interpolation of Equal intervals-Newton’s forward difference formula, Newton’s Backward difference formula.

Module 6
Numerical Techniques. ( Relevant topics in section 19.5,20.1,20.3, 21.1 Text2)Solution to linear System- Gauss Elimination, Gauss Seidal Iteration Method. Numeric Integration-Trapezoidal Rule, Simpson’s 1/3 Rule. Numerical solution of firstorder ODE-Euler method,Runge-Kutta Method (fourth order).

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