Probability distributions and Numerical Analysis

Paper – II : Probability distributions and Numerical Analysis
UNIT – I

Univariate distributions: Binomial, Poisson, Hypergeometric, Geometric and Negative

Binomial. Uniform (discrete & continuous), Normal, Exponential, Gamma, Beta
distributions. Cauchy, Laplace, Pareto, Weibull, Log normal Distributions. Normal and
Poisson distributions as limiting case of binomial distribution.

UNIT – II

Distributions of function of random variables: Distribution of sum, product and quotient of
two Variable. Reproductive property of standard distributions. χ2(chi-square), t and F
distributions ( Central cases only) and their limiting forms. Bivariate normal distribution and
its properties.

UNIT – III

Calculus of finite differences, operators, separation of symbols, examples and problems.
Interpolation formulas with remainder term. Newton’s forward and backward formulae.
Central difference formulae, Newton’s divided difference formulae for interpolation.
Lagrange’s interpolation formulae.

UNIT – IV

Numerical Integration: Derivation of general quadrature formula for equidistant ordinates.
Derivation of trapezoidal, Simpson’s 1\3rd and 3\8th rules. Weddle’s rule. Real roots of a
numerical equation by method of iteration.